RU2523876C1 - METHOD OF GENERATING LOGIC-DYNAMIC PROCESS OF CONVERTING CONDITIONALLY MINIMISED STRUCTURES OF ARGUMENTS OF ANALOGUE SIGNALS OF TERMS ±[ni]f(+/-)min AND ±[mi]f(+/-)min IN FUNCTIONAL ADDER STRUCTURE ±f1(ΣRU)min WITHOUT RIPPLE CARRY f1(±←←) AND PROCESS CYCLE ∆tΣ → 5∙f(&)-AND FIVE CONDITIONAL LOGIC FUNCTIONS f(&)-AND, REALISED USING PROCEDURE FOR SIMULTANEOUS CONVERSION OF ARGUMENTS OF TERMS THROUGH ARITHMETIC AXIOMS OF TERNARY NUMBER SYSTEM fRU(+1,0,-1) AND FUNCTIONAL STRUCTURES FOR REALISATION THEREOF (VERSION OF RUSSIAN LOGIC) - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: in one version, the functional structure is realised on logic elements AND, OR, NOR, NAND.

EFFECT: faster operation.

5 cl

Description

The invention relates to computer technology and can be used to build arithmetic devices for performing arithmetic procedures for summing and multiplying conditionally minimized arguments of analog signals of the terms ^± [n _i ] f (+/-) _min and ^± [m _i ] f (+/-) _min .

A known method implemented by means of functional input structures of an adder with selective logical differentiation d * / dn of the first intermediate sum ^± [S ¹ _i ] minimized structures of the arguments of the terms ^± [n _i ] f (+/-) _min and ^± [m _i ] f ( +/-) _min (see Patent No. 2 424 548 of November 10, 2009), according to which the procedure of selective logical differentiation d * / dn is introduced, which, in essence, is the procedure for the preliminary introduction of end-to-end transfer f ₁ ( ^± ← template). In this case, conditionally “i” discharge in the functional structure according to the first embodiment is made in the form of positive and conditionally negative channels for summing terms that are equivalent in structure of logical functions, and the positive channel is implemented in accordance with a mathematical model of the form

- логическая функция f₁(})-ИЛИ;

- логическая функция f₁(&)-И; Where

- logical function f ₁ (}) - OR;

- logical function f ₁ (&) - And;

- логическая функция f₁(}&)-ИЛИ-НЕ;

- логическая функция f₁(&)-И-НЕ;Where

- logical function f ₁ (} &) - OR NOT;

- logical function f ₁ (&) - AND NOT;

“= & ₁ =” - a logical function f ₁ (&) - NOT changes in the activity of an analog signal argument, but a conditionally negative channel is implemented in accordance with a mathematical model of the form

Moreover, according to the second embodiment, the functional structure of the parallel adder is also made in the form of positive and conditionally negative channels for summing terms that are equivalent in structure of logical functions, and the positive channel is implemented in accordance with a mathematical model of the form

and in the conditionally negative channel of the adder is made in accordance with the mathematical model of the form

Moreover, according to the third option, the functional structure of the parallel adder is also made in the form of positive and conditionally negative channels for summing terms that are equivalent in structure of logical functions, and the positive channel is implemented in accordance with a mathematical model of the form

and a conditionally negative channel is implemented in accordance with a mathematical model of the form

In this case, according to the fourth embodiment, the functional structure of the parallel adder is also made in the form of positive and conditionally negative channels for summing terms that are equivalent in structure of logical functions, and the positive channel is implemented in accordance with a mathematical model of the form

and a conditionally negative channel is implemented in accordance with a mathematical model of the form

in which the logical function f ₃ (}) - OR in the positive and conditionally negative channel of the functional structure of the adder is the logical output (prototype).

The well-known prototype has technological capabilities, which consist in the fact that to solve the problem of increasing the speed of arithmetic transformations of the arguments of the analogue signals of the terms, they use position-sign structures of the terms ^± [n _i ] f (+/-) _min and ^± [m _i ] f (+/-) _min .

The disadvantage of the prototype is that the resulting argument structure of the sum ^± [S ³ _i ], which is formed with alternating positive and conditionally negative active arguments, does not always allow the first level of summation of partial products in a parallel-serial multiplier ^± f _Σ (Σ _RU ) _min through a combination of logical functions ^± [f _1-4 (}) - OR], for example, in a graphical analytical expression of the form

which does not lead to a significant reduction in its technological cycle t_Σ conversion of partial product arguments. Since the functional structure of the adder does not provide the formation of the resulting structure of the sum of the arguments^±[S_j] f (+/-)_minin which only one argument is active in the conditionally “k” “Minimization Zone” of the factor^±[n_i]_min, and when implementing such a conditionally minimized structure of the arguments of the factor^±[n_i]_min procedure for summing partial products in the multiplier^±f_Σ(Σ_RU)_min  can be written as a graphoanalytic expression of the form

It should be noted that when using conditionally minimized structures of analog signals of the factors ^± [n _i ] f (+/-) _min and ^± [m _i ] f (+/-) _min in functional arithmetic structures, in which there are two consecutive active arguments of the factor ^± [n _i ] _min , positionally located between the "Zones of minimization", activate the arguments of partial products, and they are distributed between two consecutive functional structures of logical functions ^± [f _1-4 (}) - OR], which leads to a significant simplification of the functional structure amount Hur first level multiplier _{^{± f Σ (Σ RU) min}} , and subsequent adders functional structures can be formed without through carry.

The technical result of the proposed invention is to minimize the technological cycle t _Σ functional arithmetic structures.

     The specified technological result is achieved by the following method of forming the logical-dynamic process of converting conditionally minimized structures of the arguments of the analogue signal of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), which is implemented through various functional structures.

       The method of forming a logical-dynamic process of converting conditionally minimized structures of the arguments of the analogue signal of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1) (Russian logic), according to which in the “Positive channel of the adder“ i ”category” and “Conditionally negative channel of the adder“ i ”category” conditionally “k” “Minimization zones” perform simultaneous analysis the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minthrough functional structures

with output logical functions f ₅ (}) - OR and f ₆ (}) - OR, the system of which includes positive arguments of analog signals ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative arguments of analog signals ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” activating the positive “Complex argument” ( ⁺ nVm _i ) _k and conditionally negative “Complex argument” ( ^- nVm _i ) _k and by functional structures with output logical functions f ₁ (} &) - OR NOT, f ₃ (} &) - OR NOT and f ₁ (&) - AND NOT

in the "Positive channel of the adder" i "category", the system of which includes the positive arguments of the analog signals ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and the conditionally negative arguments of the analog signals ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” and activate the generalized “Complex argument” ( ^- Comp) S ^{i + 1} _i ) _k and ⁺ ( ^± Comp) S ^{i + 1} _i ) _k and the positive “Complex argument” ( ⁺ n & m _i ) _k with a changed level of the analog signal, and through functional structures with output logic functions f ₂ (} &) - OR-NOT, f ₄ (} &) - OR-NOT and f ₂ (&) - И- NOT kind

in the “Conditionally negative channel of the adder“ i ”category”, the system of which also includes the positive arguments of the analog signals ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and the conditionally negative arguments of the analog signals ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones”, activate the generalized “Complex argument” ( ⁺ Comp) S ^{i + 1} _i ) _k and ^- ( ^± Comp) S ^{i + 1} _i ) _k , which are fed to the corresponding functional input connections of the input logic functions f ₁ (&) - And - f ₆ (&) - And in the "Positive channel of the adder" i "discharge" and served on the corresponding functional input communication of input logical functions f ₁₁ (&) - And - f ₁₆ (&) - And in the "Conditionally negative channel of the adder" i "category" conditionally "k""Minimizationzones", which include in the system of output logical functions f ₁ (} ) -OR and f ₃ (}) - OR in accordance with an analytical expression of the form

and by means of which the positive argument of the resulting sum ( ⁺ S _i ) _k and the conditionally negative argument of the resulting sum ( ^- S _i ) _k are activated, characterized in that for the simultaneous analysis of the arguments of the analog signals of the terms ^± [n _i ] f (+/-) _min and ^± [m _i ] f (+/-) _min in accordance with the graphic-analytical expression of the form

и

- положительный аргумент и условно отрицательный аргумент соответственно;Where

and

- a positive argument and a conditionally negative argument, respectively;

и

- положительный двойной аргумент и условно отрицательный двойной аргумент в условно «i» и «i+1» разряда соответственно;

and

- positive double argument and conditionally negative double argument in conditionally “i” and “i + 1” categories, respectively;

in each conditionally “k” “Minimization Zone”, which includes two consecutive bits - conditionally “i” discharge and conditionally “i + 1” discharge and activate the following “Complex arguments”:

▶ “ ⁺ Complex argument” ( ⁺⁰¹ S ^{i + 1} _i ) _{k is} activated by the functional structure of a graphoanalytic expression of the form

with the input logical functions f ₅ (}) - OR, f ₁ (} &) - OR-NOT and f ₁ (&) - NAND and the output logic function f ₂₁ (&) - AND;

▶ “ ^- Complex argument” ( ^-01 S ^{i + 1} _i ) _{k is} activated by the functional structure of the form

with the input logical functions f ₆ (}) - OR, f ₂ (} &) - OR-NOT and f ₂ (&) - NAND and the output logical function f ₂₂ (&) - AND;

▶ “ ⁺ Complex argument” ( ⁺¹⁰ S ^{i + 1} _i ) _{k is} activated by the functional structure of a graph-analytical expression of the form

with the input logical functions f ₇ (}) - OR, f ₃ (} &) - OR-NOT and f ₃ (&) - NAND and the output logic function f ₂₃ (&) - AND;

и

- преобразованный положительный и условно отрицательный результирующие аргументы, которые активизированы посредством применения арифметических аксиом троичной системы счисления f_RU(+1,0,-1); Where

and

- converted positive and conditionally negative resulting arguments, which are activated through the use of arithmetic axioms of the ternary number system f _RU (+ 1,0, -1);

▶ “ ^- Complex argument” ( ^-10 S ^{i + 1} _i ) _{k is} activated by the functional structure of a graphoanalytic expression of the form

with the input logical functions f ₈ (}) - OR, f ₄ (} &) - OR-NOT and f ₄ (&) - NAND and the output logic function f ₂₄ (&) - AND;

▶ “ ⁺ Complex argument” ( ⁺¹¹ S ^{i + 1} _i ) _k is activated without changing the level of the analog signal by means of functional structures of a graphoanalytic expression of the form

with input logical functions f ₂₅ (&) - And and f ₂₆ (&) - And;

▶ “ ⁺ Complex argument” ( ⁺¹¹ S ^{i + 1} _i ) _k with a changed analog signal level is activated by functional structures of the form

with input logic functions f ₅ (&) - NAND and f ₆ (&) - NAND;

▶ “ ^- Complex argument” ( ^-11 S ^{i + 1} _i ) _k → { ^-11 S ^{i + 1} _i } _{k are} activated without changing the level of the analog signal by means of functional structures of a graphoanalytic expression of the form

with input logical functions f ₂₇ (&) - And and f ₂₈ (&) - And;

▶ “ ^- Complex argument” ( ^-11 S ^{i + 1} _i ) _k → { ^-11 S ^{i + 1} _i } _k with a changed level of the analog signal is activated by functional structures of the form

with input logic functions f ₇ (&) - NAND and f ₇ (&) - NAND;

▶ “ ⁺ Complex argument” ( ⁺ n & m _i ) _{k is} activated by means of the functional structure of a graphoanalytic expression of the form

with output logic function f ₂₉ (&) - And;

▶ “ ^- Complex argument” ( ^- n & m _i ) _{k is} activated by means of the functional structure of a graphoanalytic expression of the form

with output logic function f ₃₀ (&) - AND;

▶ “ ⁺ Complex argument” ( ⁺ n & m _{i + 1} ) _{k is} activated by the functional structure of a graph-analytical expression of the form

with output logic function f ₃₁ (&) - AND;

▶ “ ^- Complex argument” ( ^- n & m _{i + 1} ) _{k are} activated by the functional structure of a graphoanalytic expression of the form

with output logical function f ₃₂ (&) - And;

▶ “ ^± Complex argument” ( ^{+ 1x-1} S ^{i + 1} _i ) _k → { ^{+ 1х-1} S ^{i + 1} _i } _{k are} activated by the functional structures of a graphoanalytic expression of the form

with input logical functions f ₃₃ (&) - And and f ₃₄ (&) - And;

▶ “ ^± Complex argument” ( ^{-1x + 1} S ^{i + 1} _i ) _k → { ^{-1x + 1} S ^{i + 1} _i } _{k are} activated by functional structures of a graphoanalytic expression of the form

with input logic functions f ₃₅ (&) - AND f ₃₆ (&) - AND;

at the same time, “ ^{± 0} Complex argument” ( ^{± 0х0} S ^{i + 1} _i ) _k inactivity of the arguments in the conditionally “k” “Minimization Zone” is activated through the functional structure of a graphoanalytic expression

with input logic function f ₅ (} &) - OR NOT;

and “ ^± Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k simultaneous activity of positive and conditionally negative arguments in the conditionally “k” “Minimization Zone”, which correspond to the arithmetic axiom “+1” “- 1 ”→“ ^± 0 ¹ ”and inactivity of the arguments in the conditionally“ k ”“ Minimization zone ”are activated by means of the functional structure of a graphoanalytic expression of the form

with input logic functions f ₃₇ (&) - AND, f ₃₈ (&) - AND, f ₃₉ (&) - AND, f ₄₀ (&) - AND, and output logic function f ₉ (}) - OR;

then they perform a simultaneous analysis of the active “Complex arguments” of the analog signals of the terms in the corresponding conditionally “k” “Minimization Zones” in accordance with the graphic-analytical expression of the form

and activate possible additional "Complex arguments":

▶ “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k activate by means of the functional structures of the graphoanalytic expression of the form

with output logic function f ₁₀ (}) - OR;

▶ “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k are} activated by the functional structures of a graphoanalytic expression of the form

with output logic function f ₁₁ (}) - OR;

▶ “ ⁺ Complex transfer argument” ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _{k is} activated by means of the set of transformed positive arguments { ⁺¹¹ S ^{i + 1} _i } _{k of a} graphoanalytic expression of the form

with output logic function f ₁₂ (}) - OR;

▶ “ ^- Complex transfer argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k is} activated by means of a set of transformed conditionally negative arguments { ^-11 S ^{i + 1} _i } _{k of a} graphoanalytic expression of the form

an output logic function f ₁₃ (}) - OR;

▶ “ ⁺ Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _{k is} activated by the functional structures of a graphoanalytic expression of the form

with input logic functions f ₆ (} &) - OR-NOT, f ₁₄ (}) - OR and f ₉ (&) - NAND and with output logic function f ₄₁ (&) - AND;

▶ “ ^- Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k activate through the functional structures of a graphoanalytic expression of the form

with input logic functions f ₇ (} &) - OR-NOT, f ₁₅ (}) - OR and f ₁₀ (&) - NAND and with output logic function f ₄₂ (&) - AND;

▶ “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is activated without changing the level of the analog signal by means of functional structures of a graphoanalytic expression of the form

an output logic function f ₁₆ (}) - OR;

▶ “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k is activated without changing the level of the analog signal by means of functional structures of a graphoanalytic expression of the form

with output logic function f ₁₇ (}) - OR;

▶ “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal is activated by means of functional structures of a graphoanalytic expression of the form

with output logical function f ₄₃ (&) - And;

▶ “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is activated by means of functional structures of a graphoanalytic expression of the form

with output logical function f ₄₄ (&) - And;

▶ “Complex argument” ( ^{+ 01, -11, + 1x-1} S ^{i + 1} _i ) _k through the functional structures of a graphoanalytic expression of the form

with the output logical function f ₁₈ (}) - OR and the input logical functions f ₅ (}) - OR, f ₁ (} &) - OR-NOT, f ₂₁ (&) - AND, f ₁ (&) - AND- NOT, f ₂₇ (&) - And, f ₂₈ (&) - And, f ₃₃ (&) - And and f ₃₄ (&) - And;

▶ “Complex argument” ( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k through the functional structures of a graphoanalytic expression of the form

with the output logical function f ₁₉ (}) - OR and the input logical functions f ₆ (}) - OR, f ₄ (} &) - OR-NOT, f ₂₄ (&) - AND, f ₂ (&) - AND- NOT, f ₂₇ (&) - And, f ₂₈ (&) - And, f ₃₅ (&) - And and f ₃₆ (&) - And;

then through the output functional structure of the "Positive channel of the adder" i "discharge" type

with a common output logical function f ₁ (}) - OR and in accordance with a graphical analytical expression of the form

perform simultaneous analysis of the active "Complex arguments" of the analogue terms in the corresponding conditionally "k""MinimizationZones" and activate the positive resulting argument of the sum ( ⁺ S _i ) _k ,

where ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 - “Complex arguments” conditionally “k-1” “Minimization zones” and conditionally "k-1""Minimizationzones",respectively;

and also through the output functional structure "Conditionally negative channel of the adder" i "discharge" type

with a common output logical function f ₃ (}) - OR and in accordance with a graphoanalytic expression of the form

perform simultaneous analysis of the active "Complex arguments" of the analogue terms in the corresponding conditionally "k""MinimizationZones" and activate the resulting conditionally negative argument of the sum ( ^- S _i ) _k , while using an additional output functional structure with the output logical function f ₂ (} ) -OR "Positive channel of the adder" i + 1 "discharge" in accordance with the graphoanalytic expression of the form

and an additional output functional structure with the output logical function f ₂ (}) - OR "Conditionally negative channel of the adder" i + 1 "discharge" in accordance with a graphical analytical expression of the form

perform simultaneous analysis of the active “Complex arguments” of the analogue terms in the corresponding conditionally “k” “Minimization Zones” and activate the positive resulting argument of the resulting sum ( ⁺ S _{i + 1} ) _k and the conditionally negative argument of the resulting sum ( ^- S _{i + 1} ) _k conditionally "i + 1" discharge.

    Option 1. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, which include the output structure of logical functions implemented in accordance with with a mathematical model of the form

and with the input logic functions f ₁ (&) - And - f ₆ (&) - And with the input logic functions f ₁₁ (&) - And - f ₁₆ (&) - And, the functional output connections (=) of which are functional input connections of the output logical function f ₁ (}) - OR and f ₃ (}) - OR to activate a positive argument of the sum of ( ⁺ S _i ) _k conditionally “i” bits and to activate a conditionally negative argument ( ^- S _i ) _k conditionally “ i "discharge, while the" Positive channel of the adder "i" discharge "and" Conditionally negative channel of the adder "i" discharge "conditionally" k "" Minimization zones "also includes the function an input structure formed in accordance with a mathematical model of the form

and with output logical functions f ₅ (}) - OR and f ₆ (}) - OR, the functional input links of which are functional input links for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” to activate the positive “Complex argument” ( ⁺ nVm _i ) _k and conditionally negative “Complex argument” ( ^- nVm _i ) _k , while the "Positive channel of the adder" i "category" also includes the functional input the structures formed in accordance with the mathematical model of the form

and with output logic functions f ₁ (} &) - OR-NOT, f ₃ (} &) - OR-NOT and f ₁ (&) - NAND, the functional input connections of which are the functional input connections of the adder for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” for activating “Complex arguments ”( ^- Comp) S ^{i + 1} _i ) _k , ⁺ ( ^± Comp) S ^{i + 1} _i ) _k and“ Complex argument ”( ⁺ n & m _i ) _k with a changed level of the analog signal, while“ Positive adder channel “ i "discharge yes "also includes the logical function f ₂₁ (&) - And, and" Conditionally negative channel of the adder "i" category "also includes functional input structures formed in accordance with the mathematical model of the form

and with output logic functions f ₂ (} &) - OR-NOT, f ₄ (} &) - OR-NOT and f ₂ (&) - NAND, the functional input connections of which are the functional input connections of the adder for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” for activating “Complex arguments "( ⁺ Comp) S ^{i + 1} _i ) _k , ^- ( ^± Comp) S ^{i + 1} _i ) _k and" Complex argument "( ^- n & m _i ) _k with a changed analog signal level, while" Conditionally negative adder channel i »discharge" also includes logical function f ₂₂ (k) - and, at the same in a conventionally «k» «minimize Zone" administered in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f ₇ (&) - AND - f ₁₀ (&) - AND, the functional output links of which are functional input links of the logical function f ₂ (}) - OR, which activates a positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” discharge in the “Positive channel of the adder“ i + 1 ”discharge”, and an additional structure of logic functions with input logic functions f ₁₇ (&) - And - f ₂₀ (&) - And, whose functional output links are the functional input links of the logical function f ₄ ( }) - OR, which activates the conditionally negative resulting argument ( ^- S _{i + 1} ) _k conditionally “i + 1” bits in the “Conditionally negative channel of the adder“ i + 1 ”bits”, while in the system of input logic functions f ₁ ( &) - And - f ₁₀ (&) - And the "Positive channel of the adder" i "discharge" and the "Positive channel of the adder" i + 1 "discharge", which are formed in accordance with the mathematical model of the form

with the input “Complex arguments”, which are also included in the “Conditionally negative channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k functional input structure, which is formed in accordance with the mathematical model of the form

and with the output logical function f ₁₈ (}) - OR and the input logical functions f ₄₅ (&) - And, f ₄₆ (&) - And, f ₄₇ (&) - And and f ₄₈ (&) - And, in which “ ⁺ Complex argument” ( ⁺⁰¹ S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₅ (}) - OR, f ₁ (} &) - OR-NOT and f ₁ (&) - NAND and the output logic function f ₂₆ (&) - AND;

and in the system of input logical functions f ₁ (&) - And - f ₁₀ (&) - And "Conditionally negative channel of the adder" i "discharge" and "Conditionally negative channel of the adder" i + 1 "discharge", which are formed in accordance with mathematical model of the form

“Complex arguments” are included, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k functional input structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₈ (}) - OR and the input logical functions f ₂₂ (&) - And, f ₂₇ (&) - And, f ₂₈ (&) - And and f ₂₉ (&) - And, in which " ^- Complex argument ”( ^-01 S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₆ (}) - OR, f ₂ (} &) - OR-NOT and f ₂ (&) - NAND and the output logical function f ₃₀ (&) - AND;

at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:

▶ “ ^± Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₃₁ (&) - AND, f ₃₂ (&) - AND, f ₃₃ (&) - AND, f ₃₄ (&) - AND, and output logic function f ₉ (}) - OR, in which " ^{± 0} Complex argument ”( ^{± 0х0} S ^{i + 1} _i ) _k inactivity of the arguments in the conditionally“ k ”“ Minimization zone ”is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical function f ₅ (} &) - OR NOT, “ ⁺ Complex argument” ( ⁺ n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₃₅ (&) - And, and " ^- Complex argument" ( ^- n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₃₆ (&) - AND;

▶ “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₀ (}) - OR, in which “ ⁺ Complex argument” ( ⁺¹⁰ S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logic functions f ₁₁ (}) - OR, f ₃ (} &) - OR-NOT and f ₃ (&) - AND-NOT and the output logic function f ₃₇ (&) - AND, and “ ⁺ Complex argument” ( ⁺ n & m _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logical function f ₃₈ (&) - And;

▶ “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₂ (}) - OR, in which " ^- Complex argument" ( ^-10 S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₁₃ (}) - OR, f ₄ (} &) - OR-NOT and f ₄ (&) - AND-NOT and the output logic function f ₃₉ (&) - AND, and “ ^- Complex argument” ( ^- n & m _i ) _k is the transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₄₀ (&) - AND;

▶ “ ⁺ Complex transfer argument” ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₄ (}) - OR;

▶ “ ^- Complex transfer argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logical function f ₁₅ (}) - OR;

▶ “ ⁺ Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₆ (} &) - OR-NOT, f ₁₆ (}) - OR and f ₁ (&) - NAND and with the output logical function f ₄₁ (&) - AND, in which “ ⁺ Complex argument "{ ⁺¹¹ S ^{i + 1} _i } _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₅ (&) - NAND and f ₆ (&) - NAND;

▶ “ ^- Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₇ (} &) - OR-NOT, f ₁₇ (}) - OR and f ₂ (&) - NAND and with output logic f ₄₂ (&) - AND, in which “ ^- Complex argument "( ^-11 S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f ₇ (&) - NAND and f ₈ (&) - NAND;

▶ “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₁₈ (}) - OR;

▶ “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₁₁₉ (}) - OR;

▶ “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logical function f ₄₃ (&) - And;

▶ “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₄₄ (&) - And.

    Option 2. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, which include the output structure of logical functions implemented in accordance with with a mathematical model of the form

and with input logic functions f ₁ (&) - AND-NOT - f ₆ (&) - AND-NOT and with input logic functions f ₁₃ (&) - AND-NOT - f ₁₈ (&) - AND-NOT, functional output links (=) which are functional input links of the output logical function f ₁₁ (&) - AND-NOT and f ₂₃ (&) - AND-NOT to form a positive argument of the sum ( ⁺ S _i ) _k conditionally “i” of the discharge and for conditionally activating negative argument ^(- S _{i) k} conditionally «i» discharge, the "Positive channel« i adder "discharge" and "Related negative channel adder« i "discharge" conditionally «k» «minimize Zones" in Luciano functional input structure formed in accordance with the mathematical model of the form

and with output logical functions f ₁ (}) - OR and f ₂ (}) - OR, the functional input links of which are functional input links for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” to activate the positive “Complex argument” ( ⁺ nVm _i ) _k and conditionally negative “Complex argument” ( ^- nVm _i ) _k , while the "Positive channel of the adder" i "category" also includes the functional input the structures formed in accordance with the mathematical model of the form

and with output logical functions f ₁ (} &) - OR-NOT, f ₃ (} &) - OR-NOT and f ₂₅ (&) - NAND, the functional input connections of which are the functional input connections of the adder for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” to form a generalized “ complex argument ^»(- Comp) S ^{i + 1,} _{i) k} and ^{+ (±} Comp) S ^{i + 1,} _{i) k,} and positive" complex argument _{^{»(+ n & m i)}} k with altered levels of the analog signal, the" Put ny channel «i» adder discharge "also includes logical function f ₂₆ (k) - AND-NO and f ₅ (&}) - NOR;

and the "Conditionally negative channel of the adder" i "discharge" also includes functional input structures formed in accordance with the mathematical model of the form

and with output logical functions f ₂ (} &) - OR-NOT, f ₄ (} &) - OR-NOT and f ₂₇ (&) - NAND, the functional input connections of which are the functional input connections of the adder for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” to form a generalized “ Complex argument ”( ⁺ Comp) S ^{i + 1} _i ) _k and ^- ( ^± Comp) S ^{i + 1} _i ) _k and conditionally negative“ Complex argument ”( ^- n & m _i ) _k with a changed level of the analog signal, while as if the negative channel of the adder "i" category "also includes the logical function f ₂₈ (&) - AND-NOT and f ₆ (} &) - OR-NOT; at the same time, in the conditionally “k” “Minimization Zone” are introduced in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f ₇ (&) - AND-NOT - f ₁₀ (&) - AND-NOT, the functional output connections of which are functional input links of the logical function f ₁₂ (&) - AND-NOT, which activates the positive resulting argument ( ⁺ S _{i + 1} ) _{k is} conditionally “i + 1” of the discharge in the “Positive channel of the adder“ i + 1 ”of the discharge”, and the additional structure of logic functions with input logic functions f ₁₉ (&) - AND NOT - ₂₂ f (k) - NAND, functional output connection which are functional input for logical connections function f ₂₄ (k) - AND-NO, which activates conditional negative result argument ^(- S _{i + 1) k} conditionally «i + 1" digit in the "Related negative channel adder« i + 1 "discharge", wherein the system input logical functions f ₁ (&) - AND-NOT - f ₁₀ (&) - AND-NOT “Positive channel of the adder“ i ”discharge” and “Positive channel of the adder“ i + 1 ”discharge”, implemented in accordance with the mathematical model kind of

with the input “Complex arguments”, which are also included in the “Conditionally negative channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k functional input structure, which is formed in accordance with the mathematical model of the form

and with the output logical function f ₃ (}) - OR and the input logical functions f ₁ (&) - And, f ₂ (&) - And, f ₃ (&) - And and f ₄ (&) - And, in which “ ⁺ Complex argument” ( ⁺⁰¹ S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₁ (}) - OR, f ₁ (} &) - OR-NOT and f ₂₅ (&) - NAND and the output logic function f ₅ (&) - AND;

and in the system of input logic functions f ₁₁ (&) - AND-NOT - f ₂₀ (&) - AND-NOT “Conditionally negative channel of the adder“ i ”category” and “Conditionally negative channel of the adder“ i + 1 ”category”, formed in accordance with the mathematical model of the form

with the input “Complex arguments”, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _{k of the} functional input structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₄ (}) - OR and the input logical functions f ₆ (&) - And, f ₇ (&) - And, f ₈ (&) - And and f ₉ (&) - And, in which " ^- Complex argument ”( ^-01 S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₂ (}) - OR, f ₂ (} &) - OR-NOT and f ₂₇ (&) - NAND and the output logic function f ₁₀ (&) - AND;

at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:

▶ “ ^± Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₁₁ (&) - AND, f ₁₂ (&) - AND, f ₁₃ (&) - AND, f ₁₄ (&) - AND and output logic function f ₅ (}) - OR, in which " ^{± 0} Complex argument ”( ^{± 0х0} S ^{i + 1} _i ) _k inactivity of the arguments in the conditionally“ k ”“ Minimization zone ”is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical function f ₅ (} &) - OR NOT, “ ⁺ Complex argument” ( ⁺ n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₅ (&) - And, and “ ^- Complex argument” ( ^- n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₆ (&) - AND;

▶ “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₆ (}) - OR, in which " ⁺ Complex argument" ( ⁺¹⁰ S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₇ (}) - OR, f ₃ (} &) - OR-NOT and f ₂₆ (&) - NAND and the output logical function f ₁₇ (&) - AND, and “ ⁺ Complex argument” ( ⁺ n & m _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₈ (&) - AND;

▶ “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₈ (}) - OR, in which " ^- Complex argument" ( ^-10 S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₉ (}) - OR, f ₄ (} &) - OR-NOT and f ₂₈ (&) - NAND and the output logical function f ₁₉ (&) - AND, and “ ^- Complex argument” ( ^- n & m _i ) _k is the transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logical function f ₂₀ (&) - And;

▶ “ ⁺ Complex transfer argument” ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₀ (}) - OR;

▶ “ ^- Complex transfer argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₁ (}) - OR;

▶ “ ⁺ Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logical functions f ₆ (} &) - OR-NOT, f ₁₂ (}) - OR and f ₂₉ (&) - NAND and with output logic function f ₂₁ (&) - AND, in which “ ⁺ Complex argument "{ ⁺¹¹ S ^{i + 1} _i } _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₃₀ (&) - NAND and f ₃₁ (&) - NAND;

▶ “ ^- Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₇ (} &) - OR-NOT, f ₁₃ (}) - OR and f ₃₂ (&) - NAND and with the output logical function f ₂₂ (&) - AND, in which “ ^- Complex argument "( ^-11 S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logical functions f ₃₃ (&) - NAND and f ₃₄ (&) - NAND;

▶ “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₁₄ (}) - OR;

▶ “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logical function f ₁₅ (}) - OR;

▶ “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₂₃ (&) - And;

▶ “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₂₄ (&) - And.

    Option 3. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) with the procedure for simultaneously converting the arguments of the terms by means of arithmetic axioms of the ternary number system f_RU(+ 1.0, -1).

    Option 4. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, which include the output structure of logical functions implemented in accordance with with a mathematical model of the form

and with input logic functions f ₁ (}) - OR - f ₆ (}) - OR and with input logic functions f ₁₁ (}) - OR - f ₁₆ (}) - OR, whose functional output connections (=) are functional input connections of the output logical function f ₁ (&) - AND-NOT and f ₃ (&) - AND-NOT to form a positive argument of the sum ( ⁺ S _i ) _{k of} conditionally “i” discharge and to activate a conditionally negative argument ( ^- S _i ) _k conditionally «i» discharge, the "Positive channel adder« i »discharge" and "Related negative channel« i »discharge adder" conditionally «k» «minimize Zones" also including The flushes the functional structure of the input, which is formed in accordance with the mathematical model of the form

with the output logical function f ₂₁ (}) - OR and f ₂₂ (}) - OR, in which the functional input links are functional input links for receiving positive analog signals of the arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones”, to form a positive “Complex argument” ( ⁺ nVm _i ) _k and conditionally negative “Complex argument” ( ^- nVm _i ) _k , while the "Positive channel of the adder" i "category" also includes the functional input page uctury formed in accordance with the mathematical model of the form

with the output logical function f ₁ (} &) - OR NOT and f ₁ (&) - AND, the functional input connections of which are the functional input connections of the adder for receiving positive analog signals of the arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k conditionally “i” of category “k” “Minimization zones” to activate the generalized “Complex argument” ( ⁺ Comp) S ^{i + 1} _i ) _k and positive “Complex argument” ( ⁺ n & m _i ) _k without changing the level of the analog signal, at this "Positive channel of the adder" i "discharge" also includes the logical function f ₂₃ (}) - OR, and "Conditionally negative channel Al adder "i" category "also includes functional input structures formed in accordance with the mathematical model of the form

with output logical functions f₂(} &) - OR NOT and f₂(&) - And, the functional input connections of which are the functional input connections of the adder for receiving conditionally negative arguments of analog signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization” for the formation of a generalized “Complex argument” (^-Comp) s^{i + 1} _i)_k  and conditionally negative "Complex argument" (^-n & m_i)_k without changing the level of the analog signal, while the "Conditionally negative channel of the adder" i "discharge" also includes the logical function f₂₄(}) - OR, while in the conditionally “k” “Minimization Zone” are entered in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f ₇ (}) - OR - f ₁₀ (}) - OR, the functional output links of which are functional input links of the logical function f ₂ (&) - NAND, which activates a positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” discharge in the “Positive channel of the adder“ i + 1 ”discharge” and an additional structure of logic functions with input logic functions f ₁₇ (}) - OR - f ₂₀ (}) - OR whose functional output links are the functional input links of the logical fu f ₄ (&) - AND-NOT function, which generates a conditionally negative resulting argument ( ^- S _{i + 1} ) _k conditionally “i + 1” bits in the “conditionally negative channel of the adder“ i + 1 ”bits”, while in the system input logical functions f ₁ (}) - OR - f ₁₀ (}) - OR "Positive channel of the adder" i "discharge" and "Positive channel of the adder" i + 1 "discharge, implemented in accordance with a mathematical model of the form

with the input “Complex arguments”, which are also included in the “Conditionally negative channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with a mathematical model of the form

and with the output logic function f ₃ (} &) - OR NOT and the input logic functions f ₃ (&) - AND, f ₄ (&) - AND, f ₅ (&) - AND and f ₆ (&) - AND in which “ ⁺ Complex argument” ( ⁺⁰¹ S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logic functions f ₂₁ (}) - OR, f ₄ (} &) - OR-NOT and f ₁ (&) - NAND and the output logic function f ₇ (&) - AND;

and in the system of input logic functions f ₁₁ (}) - OR - f ₂₀ (}) - OR “Conditionally negative channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i + 1 ”discharge”, formed in accordance with the mathematical view model

“Complex arguments” are included, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logic function f ₅ (} &) - OR NOT and the input logic functions f ₈ (&) - AND, f ₉ (&) - AND, f ₁₀ (&) - AND and f ₁₁ (&) - AND, in which “ ^- Complex argument” ( ^-01 S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₂₂ (}) - OR, f ₆ (} &) - OR-NOT and f ₂ (&) - NAND and the output logic function f ₁₂ (&) - AND;

at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:

▶ “ ^± Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₁₃ (&) - AND, f ₁₄ (&) - AND, f ₁₅ (&) - AND, f ₁₆ (&) - AND and output logic function f ₇ (} &) - OR NOT, in which “ ^{± 0} Complex argument” ( ^{± 0х0} S ^{i + 1} _i ) _k inactivity of the arguments in the conditionally “k” “Minimization Zone” is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical function f ₈ (} &) - OR NOT, “ ⁺ Complex argument” ( ⁺ n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₇ (&) - And, and “ ^- Complex argument” ( ^- n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₈ (&) - AND;

▶ “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed analog signal level is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₉ (} &) - OR NOT, in which the “ ⁺ Complex argument” ( ⁺¹⁰ S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model kind of

with the input logical functions f ₂₃ (}) - OR, f ₁ (} &) - OR-NOT and f ₃ (&) - NAND and the output logic function f ₁₉ (&) - AND, and “ ⁺ Complex argument” ( ⁺ n & m _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁ (&) - And;

▶ “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₀ (} &) - OR, in which “ ^- Complex argument” ( ^-10 S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₂₄ (}) - OR, f ₂ (} &) - OR-NOT and f ₄ (&) - NAND and the output logic function f ₂₀ (&) - AND, and “ ^- Complex argument” ( ^- n & m _i ) _k is the transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₂ (&) - And;

▶ “ ⁺ Complex transfer argument” ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₁ (} &) - OR NOT;

▶ “ ^- Complex transfer argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed analog signal level is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logic function f ₁₂ (} &) - OR NOT;

▶ “ ⁺ Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the input logical functions f ₁₃ (} &) - OR-NOT, f ₂₅ (}) - OR and f ₆ (&) - NAND and with the output logical function f ₅ (&) - NAND, in which " ⁺ Complex argument "{ ⁺¹¹ S ^{i + 1} _i } _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f ₇ (&) - NAND and f ₈ (&) - NAND;

▶ “ ^- Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the input logical functions f ₁₄ (} &) - OR-NOT, f ₂₆ (}) - OR and f ₁₀ (&) - NAND and with the output logical function f ₉ (&) - NAND, in which " ^- Complex argument "( ^-11 S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f ₁₁ (&) - NAND and f ₁₂ (&) - NAND;

▶ “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₁₅ (} &) - OR NOT;

▶ “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₁₆ (} &) - OR NOT;

▶ “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₁₃ (&) - AND NOT;

▶ “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logic function f ₁₄ (&) - AND NOT.

    Option 5. Functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, including the output structure of logical functions, which is implemented in accordance with with a mathematical model of the form

and with input logic functions f ₁ (} &) - OR-NOT - f ₆ (} &) - OR-NOT and with input logic functions f ₁₁ (} &) - OR-NOT - f ₁₆ (} &) - OR -NOT, the functional output connections (=) of which are the functional input connections of the output logical function f ₁ (}) - OR and f ₃ (}) - OR to activate a positive argument of the sum ( ⁺ S _i ) _{k of} conditionally “i” discharge and for activating a conditionally negative argument ( ^- S _i ) _k conditionally “i” discharge, while “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones” also includes a functional input structure formed in accordance with the mathematical model of the form

and with output logical functions f ₅ (}) - OR and f ₆ (}) - OR, the functional input links of which are functional input links for receiving positive analog signals of arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k and conditionally negative analog signals of arguments ( ^- n _i ) _k and ( ^- m _i ) _k conditionally “i” of category “k” “Minimization zones” to activate the positive “Complex argument” ( ⁺ nVm _i ) _k and conditionally negative “Complex argument” ( ^- nVm _i ) _k , while the "Positive channel of the adder" i "category" also includes the functional input the structures formed in accordance with the mathematical model of the form

with output logical functions f ₂₁ (} &) - OR-NOT and f ₁ (&) - AND, the functional input connections of which are the functional input connections of the adder for receiving positive analog signals of the arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _k conditionally “i” of category “k” “Minimization zones” to activate the generalized “Complex argument” ( ⁺ Comp) S ^{i + 1} _i ) _k “Complex argument” ( ⁺ n & m _i ) _k , while the “Positive adder channel“ i The "discharge" also includes the logical function f ₂₂ (} &) - OR NOT, and the "Conditionally negative channel of the adder" i "of the discharge" also includes the functional n input structures formed in accordance with the mathematical model of the form

with output logical functions f_four(} &) - OR NOT and f₂(&) - And, the functional input connections of which are the functional input connections of the adder for receiving conditionally negative analogue argument signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization” to activate the generalized “Complex argument” (^-Comp) s^{i + 1} _i)_k and the “Comprehensive Argument” (^-n & m_i)_k, while the "Conditionally negative channel of the adder" i "discharge" also includes the logical function f₂₆(} &) - OR NOT, while in the conditionally “k” “Minimization Zone” are entered in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f ₇ (} &) - OR-NOT - f ₁₀ (} &) - OR-NOT, the functional output links of which are functional input links of the logical function f ₂ (}) - OR and which activates positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” discharge in the “Positive channel of the adder“ i + 1 ”discharge” and an additional structure of logic functions with input logic functions f ₁₇ (} &) - OR NOT - f ₂₀ (} &) - OR NOT, whose functional output links are functional input links logical function f ₄ (}) - OR and which activates the conditionally negative resulting argument ( ^- S _{i + 1} ) _k conditionally “i + 1” bits in the “conditionally negative channel of the adder“ i + 1 "bits", while in the input system logical functions f ₁ (} &) - OR-NOT - f ₁₀ (} &) - OR-NOT “Positive channel of the adder" i "discharge" and "Positive channel of the adder" i + 1 "discharge", which are implemented in accordance with mathematical model of the form

“Complex arguments” are included, which are also included in the “Conditionally negative channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”is included ( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k with a changed level of the analog signal and it is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logic function f ₂₂ (} &) - OR NOT and the input logic functions f ₃ (&) - And, f ₄ (&) - And, f ₅ (&) - And and f ₆ (&) - And, in which “ ⁺ Complex argument” ( ⁺⁰¹ S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₅ (}) - OR, f ₂₅ (} &) - OR-NOT and f ₁ (&) - NAND and the output logic function f ₇ (&) - AND;

and in the system of input logical functions f ₁ (}) - OR - f ₁₀ (}) - OR “Conditionally negative channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i + 1 ”discharge”, formed in accordance with the mathematical view model

“Complex arguments” are included, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as the“ Complex argument ”( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logic function f ₂₄ (} &) - OR NOT and the input logic functions f ₈ (&) - AND, f ₉ (&) - AND, f ₁₀ (&) - AND and f ₁₁ (&) - AND, in which “ ^- Complex argument” ( ^-01 S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₆ (}) - OR, f ₂₁ (} &) - OR-NOT and f ₂ (&) - NAND and the output logic function f ₁₂ (&) - AND;

at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:

▶ “ ^± Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic functions f ₁₃ (&) - AND, f ₁₄ (&) - AND, f ₁₅ (&) - AND, f ₁₆ (&) - AND and output logic function f ₂₇ (} &) - OR NOT, in which “ ⁺ Complex argument” ( ⁺ n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₇ (&) - And, " ^- Complex argument" ( ^- n & m _{i + 1} ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁₈ (&) - And, and “ ^{± 0} Complex argument” ( ^{± 0х0} S ^{i + 1} _i ) _k inactivity of the arguments in conditionally “k” “Minimization zone” is a transformed argument of the functional structure, which is formed in accordance with with a mathematical model of the form

with input logical function f ₂₈ (} &) - OR NOT;

▶ “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed analog signal level is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₂₉ (} &) - OR NOT, in which the “ ⁺ Complex argument” ( ⁺¹⁰ S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model kind of

with the input logical functions f ₇ (}) - OR, f ₂₁ (} &) - OR-NOT and f ₃ (&) - NAND and the output logical function f ₁₉ (&) - AND, and “ ⁺ Complex argument” ( ⁺ n & m _i ) _k is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₁ (&) - And;

▶ “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the output logical function f ₃₀ (} &) - OR, in which " ^- Complex argument" ( ^-10 S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with the input logical functions f ₈ (}) - OR, f ₂₃ (} &) - OR-NOT and f ₄ (&) - NAND and the output logical function f ₂₀ (&) - AND, and “ ^- Complex argument” ( ^- n & m _i ) _k is the transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₂ (&) - And;

▶ “ ⁺ Complex transfer argument” ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logical function f ₃₁ (} &) - OR NOT;

▶ “ ^- Complex transfer argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed analog signal level is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with output logical function f ₃₂ (} &) - OR NOT;

▶ “ ⁺ Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logical functions f ₃₃ (} &) - OR-NOT, f ₁₄ (}) - OR and f ₆ (&) - NAND and with output logic function f ₅ (&) - NAND, in which " ⁺ Complex argument "{ ⁺¹¹ S ^{i + 1} _i } _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f ₇ (&) - NAND and f ₈ (&) - NAND;

▶ “ ^- Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the input logical functions f ₃₄ (} &) - OR-NOT, f ₁₅ (}) - OR and f ₁₀ (&) - NAND and with the output logical function f ₉ (&) - NAND, in which " ^- Complex argument "( ^-11 S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f ₁₁ (&) - NAND and f ₁₂ (&) - NAND;

▶ “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logical function f ₃₄ (} &) - OR NOT;

▶ “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic function f ₃₅ (} &) - OR NOT;

▶ “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logical function f ₁₃ (&) - AND NOT;

▶ “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with the output logic function f ₁₄ (&) - AND NOT.

     The essence of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) with the procedure of simultaneous conversion of the arguments of the analog signals of the terms by means of arithmetic axioms of the ternary number system f_RU(+ 1,0, -1) and its various variants of functional structures will be explained during the synthesis of mathematical models of the proposed technological solution.

    Preliminary analysis of the possibility of forming a logical-dynamic process of transforming conditionally minimized structures of the arguments of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(⁺← ↓_-) with the procedure of simultaneous conversion of arguments by means of arithmetic axioms of the ternary number system f_RU(+ 1.0, -1). If we analyze at a formalized level the positional structure of the positive active arguments of the terms “+” [n_i] f (2ⁿ) in the form of a formalized expression (1)

and the positional structure of conditionally negative arguments of the terms “-” [m _i ] f (2 ⁿ ) in the form of a formalized expression (2),

then by the level of the analog signal “+” [U _i ], with the exception of the argument of the sign “+” and “-” they are equivalent. Therefore, the performance of any arithmetic operations on the arguments of the terms “+” [n _i ] f (2 ⁿ ) and “-” [m _i ] f (2 ⁿ ) at a formalized level causes a certain problem, which is associated with the need to take into account the sign digit “+ ”And“ - ”, and in this situation it represents some kind of symbol or“ label ”about the belonging of the structure of one or another category of information content. And only a positional position can eliminate ambiguity, therefore, the positive structure of the arguments of the term (1) can be written in the form of the expression (3),

and the conditionally negative structure of the arguments of the term (2) can be written in the form of the expression (4)

and only in such an interpretation not only the need for introducing additional characters “+” and “-” in expressions (1) and (2) is excluded, but it is also possible to perform arithmetic operations on the arguments without translating the structure of the arguments “-” [m _i ] f (+/-) in the so-called “Additional Code”. It should be especially noted that if the structure of arguments (4) is translated into the “Additional Code”, and this arithmetically correctly can only be implemented using arithmetic axioms of the ternary number system f (+ 1,0, -1) (5),

which includes the logical differentiation procedure ± d / dn of both a conditionally negative sequence of active arguments and a positive sequence of arguments, which we write in the form of a graphoanalytic expression (6).

And it, in essence, is a procedure for the preliminary introduction of end-to-end transfer, but it is performed at the local level in which the logical function f ₁ (&) - And forms a positive argument + n _{i of} local transfer + f (←) _{d / dn of the} active argument from the previous high order of the continuous sequence to the next inactive high order. And the logical function f ₂ (&) - And forms a conditionally negative argument -n _{i of the} local transfer -f (↓) _{d / dn} , and this transfer is performed in the conditionally “i” bit, which corresponds to the least argument of the continuous sequence, and when it is transferred a positive argument is converted to a conditionally negative argument. It should be noted that the use of arithmetic axioms of the ternary numeral system f (+ 1,0, -1) (5) allows us to carry out any procedure for converting arguments at a scientifically sound level, for example, the procedure for generating the “Additional Code” can be written in the form of a graphic-analytical expression ( 7)

in which inactive arguments after the first active conditionally negative argument in the original structure “-” [m _i ] f (+/-) are transformed in accordance with the arithmetic axiom “ ^± 0” → “+ 1 / -1” and perform the logical differentiation procedure d / dn conditionally negative arguments. As a result, the position-sign structure “- / +” [m _i ] f (+/-) is formed with the same information content “-“ “186”, but with the maximum number of positive arguments in the lower digits, the number of which can be minimized, and in this situation, using the procedure of logical differentiation of d / dn positive arguments in the structure, which is performed in accordance with the graphic-analytical expression (8).

And it, in essence, is a procedure for preliminary introduction of end-to-end transfer, but it is performed at the local level, in which the logical function f ₁ (&) - And forms a positive argument ⁺ n _{i of} local transfer + f (←) _{d / dn of the} active argument from the previous high order of the continuous sequence to the next inactive high order. And the logical function f ₂ (&) - And forms a conditionally negative argument ^- n _{i of the} local transfer -f (↓) _{d / dn} , and this transfer is performed in the conditionally “i” bit, which corresponds to the least argument of the continuous sequence, and when it is transferred a positive argument is converted to a conditionally negative argument. And if we apply the logical differentiation procedure d / dn, but only to a sequence of at least two active arguments in the resulting structure “- / +” [m _i ] f (+/-) of expression (7), then a graphoanalytic expression can be written (9 ),

in which active both positive arguments and conditionally negative arguments alternate through at least one inactive argument. As a result of applying the arithmetic axiom “± 0” → “+ 1 / -1” and performing the logical differentiation procedure d / dn, the positional number system “+” f (2 ⁿ ) positive arguments (10)

can be converted to a minimized number system "+" f (+/-) _min (11)

and such argument structures can significantly increase the performance of the multiplication procedure. Since the first stage of summing up partial products, if we write the procedure of parallel-sequential multiplication f _Σ (Σ) in the form of graphoanalytic expression (12),

it becomes a completely correct possibility of replacing the first level of the functional structures of adders f ₁ (Σ) - f ₄ (Σ) with the corresponding sequence of logical functions f _1-4 (}) - OR. And in order to form a minimized structure of the resulting sum “+” [S _Σ ] f (+/-) _{min, it} suffices to carry out the transfer of two active conditionally negative arguments in the conditionally “i” category in accordance with the graphic-analytical expression (13).

Since in the graphoanalytic expression (12) the first stage of summation reduces to combining the groups of partial products by means of the logical function f ₁ (}) - OR, then, for example, a 16-bit parallel-serial multiplier f _Σ (Σ) is converted to 8-bit, which, at least, leads to a decrease in the technological cycle of multiplication by half. And since the argument conversion processor in the parallel-serial multiplier f _Σ (Σ) includes the functional structure of the adder f (Σ), it makes sense to analyze the conversion technological cycle in it, but not in which all the actions on the arguments of the terms “+” [n _i ] f (+/-) and “+” [m _i ] f (+/-) are performed according to the “Rules”, according to which a procedure, for example, summing the arguments of terms with the same signs “+” [n _i ] f (2 ⁿ ) → “10111010” and “+” [m _i ] f (2 ⁿ ) → “10101101” can be written using the graphic-analytical expression (12),

and by arithmetic axioms (5). And if we analyze the conversion procedure, for example, of the arguments of the terms with different signs “+” [n _i ] f (2 ⁿ ) → “101000111” and “-” [m _i ] f (2 ⁿ ) → “010001101” in the graph-analytical expression ( 13),

in which only the procedure of removing active logical zero “+ 1 / -1” → “± 0” is performed, the resulting position-sign sum “+” [S _i ] f (+/-) is formed as a result of argument conversion or minimization. It should be noted that if in expression (12) the next procedure for summing the resulting sum [S _i ] f (2 ⁿ ) is impossible without performing end-to-end transfer + f (←), then in expression (13), end-to-end transfer is -f (← ←) a conditionally negative argument can be delayed, which is performed in accordance with the arithmetic axiom “-1” → “-2” “+ 1”. Since during the next summation procedure, conditionally negative arguments of not implemented hyphenations can form active logical zeros “+ 1 / -1” → “± 0” with active positive arguments of the next term. It should also be noted that a feature of the resulting sum “+” [S _i ] f (+/-) in expression (13) is that it can be minimized by the number of active arguments in its structure using the inverse arithmetic axiom “- 2 "" + 1 "→" -1 ", and this procedure can be written in the form of a graphic-analytical expression (14).

And if we combine the positional structure of the arguments “+” [S _i ] f (2 ⁿ ) → “10111010” with the minimized position-sign structure of the arguments “+” [S _i ] f (+/-) _min in the expression (15),

it can be stated that it was formed using the arithmetic axiom “0” → “+ 1 / -1” of the ternary number system f (+ 1,0, -1) (5) and the logical differentiation procedure d / dn. As a result, the logical-dynamic process of forming a positively minimized structure of the arguments “+” [S _i ] f (+/-) _min can be written in the form of a graphoanalytic expression (16),

and the logical-dynamic process of forming a conditionally negative structure of the arguments “-” [n _i ] f (+/-) _min can be written in the form of a graphic-analytical expression (17).

And the functional structure of this logical differentiation procedure d / dn for positive and conditionally negative position-sign arguments ± [n _i ] f (+/-) after combining the functional structures (6) and (8) by means of the logical function f ₁ (}) - OR and f ₂ (}) - OR can be written in the form of analytical expressions (18) and (19).

As a result, analytical expressions (17) and (18) are mathematical models of the conditionally “i” category of the logical differentiation procedure d / dn of both a structure with one active argument “010” and a structure with a continuous sequence of active arguments “0111 ... 10”. But if we return to the analysis of the logical-dynamic process of transforming arguments in expression (16), writing it in the form of graphoanalytic expression (20),

then the logical differentiation procedure d / dn (18) and (19) should include additional conditions for the activity of the previous argument ⁺ n _i-2 and ^- n _i-2 in the system of logical functions f ₁ (&) - And and f ₃ (&) - And, as well as additional conditions for the activity of the next argument ^- n _{i + 1} and ⁺ n _{i + 1} and the system of logical functions f ₂ (&) - And and f ₄ (&) - And, which allows d / dn to be excluded from the logical differentiation procedure structure "010" as positive arguments, and conditionally negative arguments. But in this situation, on the one hand, the active arguments of the “010” structure, both positive arguments and conditionally negative arguments, should be the resulting arguments. Therefore, we introduce functional additional structures into analytical expression (20) and write the graphoanalytic expression (21),

in which the logical functions f_one(&) - And and f_four(&) - And into the system of the logical function f_one(}) - OR and f₂(}) - OR and their resulting arguments + S_i and -S_i are activated even if the logical functions f_one(&) - And and f_four(&)-AND. Moreover, from the analysis of the logical-dynamic process of transformation of arguments (19) it follows that the logical functions f_one(}) - OR and f₂(}) - OR must be activated not only when in the structure “+” [n_i] f (+/-)  a sequence of active and inactive arguments is formed, but also in the case of activating inactive arguments by using the arithmetic axiom “0” → “+ 1 / -1”, and a conditionally negative argument in this particular situation is also the resulting argument. It should also be noted that, on the one hand, as a procedure of logical differentiation d₂/ dn with activation of the argument of structure “010”, and activation of inactive arguments in structure “01011” must be performed in expression (21) at the same time, since their converted arguments are arguments of the resulting minimized structure “+” [S_i] f (+/-)_min. On the other hand, at the first stage, before applying the logical differentiation procedure d₂/ dn in the initial structure "+" [n_i] f (2ⁿ) inactive arguments must be activated, which alternate with active arguments, but provided that the first inactive argument “0” is positioned after at least two consecutively active arguments “11” as, for example, in expression (22).

And such an activation of inactive arguments “0” → “+ 1 / -1” essentially represents the end-to-end activation f (←) ^{± 1} , which to some extent corresponds to the end-to-end transfer f (←) during the summation procedure arguments of the terms “+” [n _i ] f (2 ⁿ ) and “+” [m _i ] f (2 ⁿ ), but it has a peculiarity. And this feature is that the end-to-end activation f (←) ^{± 1} has two implementations, provided that the arguments “+” [n _i ] f (2 ⁿ ) are functionally divided into groups that would include only two consecutive arguments . As a result of this division of the structure of the arguments “+” [n _i ] f (2 ⁿ ), two functional structures of end-to-end activation f ₁ (←) ^{± 1} and f ₂ (←) ^{± 1} can be formed, for example, for expression (22 ) the logical-dynamic process of end-to-end activation f ₁ (← program) ^{± 1} can be written in the form of a graphic-analytical expression (23),

in which the argument (q _i ) ^{k-2 of the} end ^-to- end activation f ₁ (← begin) ^{± 1 of} inactive arguments “0” → “+ 1 / -1” is formed in the conditionally “i” category “k-2” of the group “Activation zones 11 ". And for the structure, for example, of the arguments “+” [n _i ] f (2 ⁿ ) → “01010110”, the logical-dynamic process of through activation of f ₂ (←) ^{± 1} inactive arguments 0 ”→“ + 1 / -1 ”can be in graphoanalytic expression (24),

in which the argument (q _{i + 1} ) ^{k-2 of the} end ^-to- end activation f ₂ (←) ^{± 1} is formed between the activation zones 11 in the conditionally “i + 1” category “k-2” of the group. And if we write a mathematical model of the formation of the argument ^{± 1} (←) ^k q _{i of the} end-to-end activation f ₁ (←to) ^{± 1} and the argument of ^{± 1} (←) ^k q _{i + 1 of the} end-to-end activation of f ₂ (←) ^{± 1} for the positive structure arguments "+" [n _i ] f (2 ⁿ ) → "10110111" in the form of a graphical analytical expression (25),

then it follows that the technological cycle Δt _Σ for the 8-bit structure of positional arguments [n _i ] f (2 ⁿ ) will correspond

two conditional logical functions f (&) - And. Moreover, if we analyze the logic of the formation of functional, for example, end-to-end activation f ₂ (← program) ^{± 1} , writing it in the form of graphoanalytic expression (26) and (27),

then it follows that with each subsequent additional “k” group of arguments, an additional logical function f_four(}) - OR, in which in addition to the input arguments (n_{i + 1})^k - (n_{i + 1})^k-3 conditionally "i" discharge of the logical function f_four(}) - OR an optional argument (n_{i + 1})^k-4 conditionally "i + 1" discharge "k-4" group. Moreover, from the system of the logical function f₃(}) - OR expressions (26) activation argument ↓ (←)^k-4q_{i + 1} decrease by one and introduce into the system an additional logical function f_four(}) - OR expressions (27), and instead of it in the system of the logical function f₃(}) - OR enter the input argument (n_i)^k-4 conditionally "i" discharge "k-4" group. As a result, for a 16-bit structure of positional arguments [n_i] f (2ⁿ) in the system of the logical function f_one(&) - And four additional logical functions f_5-8(}) - OR, in the last of which the system will include eight input arguments. Therefore, the technological cycle Δt_Σ functional structure of activation f_one(← program)^{± 1} and f₂(← program)^{± 1} procedures for converting the positional structure of the arguments “+” [n_i] f (2ⁿ) to the minimized position-sign structure of the arguments “+” [S_i] f (+/-)_min  for a 32-bit structure [n_i] f (2ⁿ) will match

four conditional logical functions f (&) - And. As a result, a functional 32-bit parallel adder structure ± f (Σ) _min can be formed. It should be noted in particular that the minimized structures of the position-sign arguments of the factors ± [n _i ] f (+/-) _min and ± [m _i ] f (+/-) _min in the parallel-serial multiplier ± f _Σ (Σ) _min also allows you to significantly reduce its technological cycle of forming the resulting amount. Since if for a concrete implementation of the arguments of the factors ± [n _i ] f (+/-) _min → “11101011” f (2 ⁿ ) and ± [m _i ] f (+/-) _min → “11010111” f (2 ⁿ ) write the procedure for the formation of partial works in a parallel-serial multiplier ± f _Σ (Σ) _min in the form of a graphic-analytical expression (28),

then the first level of summation of the arguments of partial products can be realized by linear logical functions f _1-4 (}) - OR, which will lead to a significant reduction in the technological cycle Δt _Σ in a parallel-serial multiplier ± f _Σ (Σ) _min . At the same time, in the second level of adders f ₁ (Σ) and f ₂ (Σ), all transformations of active arguments are performed both in the “Minimization Zones”, as was realized in the graph-analytical expression (29), and between the “Minimization Zones”, like this the procedure is implemented in graphoanalytic expression (30).

And all transformations of the arguments are performed in accordance with direct axioms, for example, “+1” → “+2” “- 1”, “-1” → “-2” “+ 1” and “+ 1 / -1” → “ ± 0 "and inverse arithmetic axioms, for example," +2 "" - 1 "→" +1 "," -2 "" + 1 "→" -1 "and" 0 "→" + 1 / -1 ", as well as using the logical differentiation procedure ^- d / dn and ⁺ d / dn sequences of active conditionally negative arguments and positive arguments. At the same time, the feature of logical-dynamic processes of transformation of arguments in the adder f ₃ (Σ) in both expression (29) and expression (30) is the procedure for through activation of f ₂ (←) ^{± 1} inactive arguments “± 0” → “ + 1 / -1 ”while minimizing the structure of the arguments“ + ”[S _j ] f (+/-) ₂ , which is essentially equivalent to the end-to-end carry f (←) in the positional adder. Since if we formulate a graphoanalytic expression for a 32-bit adder,

then the sequence of conditional logical functions f (&) - And in the logical-dynamic process of accelerated end-to-end transfer f (← direct) ₃₂ will correspond to 1 _lf & 14 _lf → 15 _lf , when, as in the through activation procedure f ₂ (←) ^{± 1} inactive arguments "± 0" → "+ 1 / -1" of expression (26) and (27) a sequence of conditional logical functions f (&) - And will correspond to 1 _lf & 4 _lf → 5 _lf . And if we take into account that the technological cycle t _Σ in the 8-bit combination multiplier f _Σ (Σ) includes 14 · f _p (Σ) total adders, and each of them is equivalent to 6 _lf , then it will correspond to 94 _lf . As a result, if we replace the positional argument structures of the factors [n _i ] f (2 ⁿ ) and [m _i ] f (2 ⁿ ) in the multiplier f _Σ (Σ) with the minimized argument structures of the factors ± [n _i ] f (+ / -) _min and ± [m _i ] f (+/-) _min , then its speed can be increased by at least an order of magnitude. And this fact creates the need for the synthesis of the mathematical model of the adder ± f (Σ) _min , which implements the procedure for converting minimized structures of position-sign arguments of the terms ± [n _i ] f (+/-) _min and ± [m _i ] f (+/- ) _min . It should be noted that in the parallel-serial multiplier ± f _Σ (Σ) _{min of the} graph-analytical expression (28), the minimized structures of the position-sign arguments of the terms ± [n _i ] f (+/-) _min and ± [m _i ] f ( +/-) _min were formed by the informal method, since in the structure of the multiplicand ± [m _i ] f (+/-) the active arguments were transformed between the “Minimization Zones”, and in the structure of the multiplier arguments ± [n _i ] the active arguments were transformed into "Zone of minimization." And if you perform this procedure using the informal method and write down the procedure for the formation of partial products in a parallel-serial multiplier ± f _Σ (Σ) _min or of the form,

where the transformation of the structures of the arguments of the factors is performed in the "Minimization Zone", or by a formalized method in which the transformations of the arguments of the factors ± [n _i ] _min and ± [m _i ] f (+/-) are performed only between the "Minimization Zones", and this procedure we write in the form of graphoanalytic expression (32).

It should be noted that a feature of the argument structure of the multiplied ± [n _i ] f (+/-) _min is the simultaneous activity of two arguments in the “Minimization Zone”, and in this situation, the input structure of the adder f ₃ (Σ) cannot be performed in as a system of logical functions f ₂ (}) - OR, since a functional input structure of the adder f ₀ (Σ) is necessary. But if we write the graphoanalytic expression (33),

in which successively active arguments are positionally positioned between the "Zones of minimization", the corresponding partial products functionally belong to two different groups of logical functions f ₂ (}) - OR. Therefore, the argument structures of the factor ± [n _i ] f (+/-) _min must be logically transformed before the formation of partial products, and this transformation must be performed only in the "Minimization Zones". And if we return to the logical-dynamic process (30) and write it in the form of a graphic-analytical expression (34),

then, if, on the one hand, when forming the subtotal, you do not perform conversions between the “Minimization Zones”, but only in the “Minimization Zones”, since the structure of active arguments belongs to the conditionally minimized category, and you only perform argument conversions in the “Minimization Zones” in accordance with arithmetic axioms “+2” “- 1” → “+1” and “-2” “+ 1” → “-1”, then the correct logical-dynamic process of converting partial products in the adder f ₃ (Σ) can be formed. On the other hand, in the intermediate structure of the sum “+” [S _j ] f (+/-) _1, it is necessary to activate inactive logical zeros “± 0” → “+ 1 / -1” only in the conditionally “i” category, because if you write logical-dynamic process of transformation of arguments (35),

then as a result of inactivation of inactive logical zeros “± 0” → “+ 1 / -1” in the conditionally “i” category, the resulting argument structure will be formed with “Defect”, since two successively active arguments are generated in the “Minimization Zone”. But if we write the graphoanalytic expression (36)

and activate inactive logical zeros “± 0” → “+ 1 / -1” in the conditionally “i” category, then after performing the logical differentiation procedure ⁺ d / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} , the correct conditionally will be formed minimized argument structure “+” [S _j ] f (+/-) _min . And all transformations of the arguments are performed in accordance with direct axioms, for example, “+1” → “+2” “- 1”, “-1” → “-2” “+ 1” and “+ 1 / -1” → “ ± 0 "and inverse arithmetic axioms, for example," +2 "" - 1 "→" +1 "," -2 "" + 1 "→" -1 "and" 0 "→" + 1 / -1 ", as well as using the logical differentiation procedure ^- d / dn and ⁺ d / dn sequences of active conditionally negative arguments and positive arguments. At the same time, the feature of logical-dynamic processes of transformation of arguments in the adder f ₃ (Σ) in both expression (29) and expression (30) is the procedure for through activation of f ₂ (←) ^{± 1} inactive arguments “± 0” → “ + 1 / -1 ”while minimizing the structure of the arguments“ + ”[S _j ] f (+/-) ₂ , which is essentially equivalent to the end-to-end carry f (←) in the positional adder. Since if we formulate a graphoanalytic expression for a 32-bit adder,

then the sequence of conditional logical functions f (&) - And in the logical-dynamic process of accelerated end-to-end transfer f (← direct) ₃₂ will correspond to 1 _lf & 14 _lf → 15 _lf , when, as in the through activation procedure f ₂ (←) ^{± 1} inactive arguments "± 0" → "+ 1 / -1" of expression (26) and (27) a sequence of conditional logical functions f (&) - And will correspond to 1 _lf & 4 _lf → 5 _lf . And if we take into account that the technological cycle t _Σ in the 8-bit combination multiplier f _Σ (Σ) includes 14 · f _p (Σ) total adders, and each of them is equivalent to 6 _lf , then it will correspond to 94 _lf . As a result, if we replace the positional argument structures of the factors [n _i ] f (2 ⁿ ) and [m _i ] f (2 ⁿ ) in the multiplier f _Σ (Σ) with the minimized argument structures of the factors ± [n _i ] f (+ / -) _min and ± [m _i ] f (+/-) _min , then its speed can be increased by at least an order of magnitude. And this fact creates the need for the synthesis of the mathematical model of the adder ± f (Σ) _min , which implements the procedure for converting minimized structures of position-sign arguments of the terms ± [n _i ] f (+/-) _min and ± [m _i ] f (+/- ) _min .

Synthesis of a mathematical model of the input logical-dynamic process of transforming conditionally minimized argument structures of the terms “+” [n _i ] f _RU (+/-) _min and “+” [m _i ] f _RU (+/-) _{min of the} ternary number system f ( + 1.0, -1) _{RU of the} adder ± f ₁ (Σ _RU ). Since from a preliminary analysis of the logical-dynamic process of converting the minimized structures of the arguments of the terms “+” [n _i ] f _RU (+/-) _min and “+” [m _i ] f _RU (+/-) _min in the adder ± f ₁ ( Σ _RU ) _min it follows that the procedure for generating the resulting sum “+” [S _i ] f _RU (+/-) _min in the same format can be implemented without the functional structure of end-to-end transfer ± f (←). Therefore, we carry out a generalized analysis of the procedures for converting active arguments and determine the functional structure of the adder ± f ₁ (Σ _RU ) _min , in which the peculiarity is the presence in it of two analytical expressions of the conditionally “i + 1” discharge and conditionally “i” of the discharge conditionally “k” "Zone of minimization." And for this we write the graphoanalytic expression (37).

From the analysis of the argument conversion procedure at the “First Stage” of expression (37), it follows that in the conditionally “k” “Minimization Zone” at the preliminary stage, the arguments of the second preliminary sum are formed (± [S ² _i ] f (&) - And and the arguments the first preliminary sum ± [S ¹ _i ] f (}) - OR) and they are activated through the functional structures of the “Positive summation channel”, which we write in the form of analytical expressions (38),

and for the “Conditionally negative summation channel” we write in the form of analytical expressions (39),

 as a result, we form the structure of the arguments (40).

It should be noted that the feature of the "First stage" of the transformation of the arguments of the preliminary sum (± [S ² _i ] f (&) - AND and the arguments of the first preliminary sum ± [S ¹ _i ] f (}) - OR) is the conversion only to "Zones of minimization." Since if we form a logical-dynamic process of converting the minimized arguments of the terms “+” [n _i ] f _RU (+/-) _min → “+” “0100110010110011” and “+” [m _i ] f _RU (+/-) _min → "+""0110101101110100" in the form of a graphic-analytical expression (41)

or minimized arguments of the terms “+” [n _i ] f (+/-) _min → “+” “0010101001010110” f (2 ⁿ ) and “+” [m _i ] f (+/-) _min → “+” “ 0011100100011010 »f (2 ⁿ ) in the form of a graphic-analytical expression (42),

then this procedure allows you to minimize the number of active arguments in the "Minimization Zones". Since if the transformation of the arguments in the structure of the second intermediate sum ± [S² _i] f_one(&) - And is performed in accordance with direct arithmetic axioms “+1” → “+2” “- 1” and “-1” → “-2” “+ 1” while deleting the active logical zero “+ 1 / -1” → “± 0”, then converting the arguments to the structure of the first intermediate sum ± [S^one _i] f (}) - OR is performed in accordance with the inverse arithmetic axioms   “+2” “- 1” → “+1” and “-2” “+ 1” → “-1”, which also leads to minimizing the number of active arguments in the structure of arguments “+” [S_i] f (+/-)_one. Moreover, if we form a logical-dynamic process of transforming the minimized arguments of the terms “+” [n_i] f_RU(+/-)_min → "+" "0100110010110011" and "+" [m_i] f_RU(+/-)_min→ "+" "01110001101 0100" in the form of a graphic-analytical expression (43),

then from the analysis the resulting sum “+” [S _i ] f _RU (+/-) _min implies that in its structure formed by “Defect 1” and “Defect 2” are directly related to the unrealized procedure for converting active arguments between “Minimization Zones”. And this conversion procedure must be performed for a conditionally negative argument in accordance with the graph-analytical expression (44)

provided that the positive argument of the same name S ¹ _i is active in the conditionally “k-1” “Minimization Zone”, it should be noted that as a result of applying the arithmetic axiom “-2” “+ 1” → “-1”, “Sequence break” was performed positive arguments, which excludes the formation of “Defect 2” in expression (43), and the functional structure of such a transformation is written in the form of an analytical expression (45),

and for the conditionally “k” “Minimization Zones” we write it in the form of a functional structure (46).

We will write down a similar procedure for converting arguments using the arithmetic axiom “-2” “+ 1” → “-1” for another sequence of arguments (47),

and for the conditionally “k” “Minimization Zones” we write the functional structure in the form of an analytical expression (48).

It should be noted that in the logical function system f ₁ (&) - And and f ₂ (&) - And of functional structures (46) and (48), an additional conditionally negative argument ( ^- S ¹ _i ) _k and an additional positive argument are introduced ( ⁺ S ¹ _i ) _k , which in the corresponding functional structure is the “Activation Condition” to eliminate the ambiguity of the transformation of active arguments as in the argument structure (49),

and in the structure of arguments (50),

where the transformation of the arguments by means of arithmetic axioms is performed in the conditionally “k” “minimization zones”. And if, taking into account the logical-dynamic process of functional structures (48) and (50), we adjust the procedure for converting the intermediate structure of the sum arguments in expression (43), writing this procedure in the form of a graphoanalytic expression (51),

then at the “Second stage” of the transformation of the structure of the arguments of the intermediate sum “+” [S _i ] f (+/-) ₁ the local transfer argument f ₁ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} in “k-5” “Minimization zone” can be adjusted. Moreover, the conversion to “k-4” “Minimization Zone” should be performed in accordance with the arithmetic axiom “+2” “- 1” → “+1” provided that the local transfer argument f ₁ ( ⁺ ← ⁺ ) _{d / dn of the} procedure is inactive logical differentiation d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} in “k-4” “Zone of minimization”. It should be noted that the adjustment of the structure of the arguments of the first intermediate sum ± [S ¹ _i ] f ₁ (}) - OR in the graph-analytical expression (51) can be performed at the stage of its formation, since if we write the graph-analytical expression (52),

then a preliminary analysis of the activity of the arguments of the terms ± [n _i ] ⁺ and ± [m _i ] ⁺ , which are positionally located between the “Minimization Zones”, allows, using the functional structures (53), (54) to significantly minimize the intermediate sum ± [S ¹ _i ] f ₁ (}) - OR.

    From the analysis of graphoanalytic expression (52) it follows that the removal of active logical zeros “+ 1 / -1” → “± 0” in the conditionally “k” “Minimization Zone” of expression (55)

should be performed in the "Minimization Zones" indirectly when activating the arguments of the intermediate sum ± [S ¹ _i ] f ₁ (}) - OR and such a procedure can be implemented when transforming the arguments of the terms ± [n _i ] ⁺ and ± [m _i ] ⁺ . A similar procedure should be implemented when the active argument of the second intermediate sum is activated ± [S ² _i ] f ₁ (&) - And in accordance with graph-analytical expressions (56)

or graphoanalytic expressions (57).

Moreover, the feature of the local transfer argument f ( ⁺ ← ⁺ ) _{d / dn} and f ( ^- ← ^- ) _{d / dn} in this situation is its implementation through the arithmetic axiom “+1” → “+2” “–1” and “- 1 "→" -2 "" + 1 "and through functional structures (58),

in which functional structures activate the positive resulting argument ( ⁺ S _{i + 1} ) _k and the conditionally negative resulting argument ( ^- S _{i + 1} ) _k in the conditionally “i + 1” category. In this case, it should be noted the logic of the formation of the conditionally minimized structure of the term ± [n _i ] f ₁ (+/-) _min and ± [n _i ] f ₁ (+/-) _min , according to which, if in conditionally “k” In the “Minimization Zone”, the arguments of the terms ( ⁺ n _i ) _k and ( ⁺ m _i ) _k or ( ^- n _i ) _k and ( ⁺ m _i ) _k are simultaneously active, then in this “Minimization Zone” in the conditionally “i + 1” the discharge must be inactive logical zero " ^± 0 _{i + 1} ". But if between “Minimization Zones” the arguments of the terms ( ⁺ n _{i + 1} ) _k and ( ⁺ m _{i + 1} ) _k or ( ^- n _{i + 1} ) _k and ( ⁺ m _{i + 1} ) _k are simultaneously active, then the transformation of these The arguments are ambiguous and depend on the specific activity of the arguments in the conditionally “k + 1” “minimization zone”. Therefore, similar functional structures that activate the resulting argument ( ⁺ S _i ) _k and ( ^- S _i ) _k conditionally “i + 1” bits in the conditionally “k” “Minimization Zone” are written in the form of analytical expressions (59),

but in this situation, the transformed argument ( ^± n _i Vm _i ) k and ( ^± n _i Vm _i ) _{k of a} functional additional structure with an output logical function are introduced into the system of the logical function f ₁ (&) - And and f ₂ (&) - And f ₁ (} &) - OR NOT and f ₁ (} &) - OR NOT, which are the “Conditions of activation”, since other situations are possible. It should be noted that at the output of the system of logical functions f ₁ (&) - And and f ₂ (&) - And, which are written in the form of an expression of the form

clarifying information has been introduced about the actions that a specific functional structure essentially performs, and if the lower set of information symbols ( ⁺ ← ⁺² ) _{i + 1} and ( ^- ← ^-2 ) _{i + 1} corresponds to the fact that “Preliminary action in i +1 category ”corresponds to the local transfer of two positive and conditionally negative arguments from the conditionally“ i + 1 ”category to the conditionally“ i ”category, where only one positive argument is activated, then the upper set of information symbols (| ^± 0 | ← ⁺ ) _i and (| ^± 0 | ← ^- ) _i corresponds to "Final action in i category. " And it consists in the fact that the activity of the arguments in the conditionally “i” category corresponds to absolute zero (| ^± 0 |), since in this category the arguments of the two terms are not active, therefore a positive (+) or conditionally negative (-) argument is activated in it local transfer, which was formed as a result of the “Preliminary action in i + 1 category”. It should be noted that the introduction of clarifying the information sequence of characters at the output of the logical function system allows you to clearly understand the logical-dynamic process of transforming such a functional structure.

Situation 1. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min between “Minimization Zones” in which active arguments form an active logical zero “+ 1 "" - 1 "→" ^± 0 "and it is possible in two versions.

Option 1. Active logical zero “+1” “- 1” → “ ^± 0” in the joint structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min → “0 ^- 1, ⁺ 10” and ± [m _i ] f ₁ (+/-) _min → “00, ⁺ 10” or ± [n _i ] f ₁ (+/-) _min → “0 ⁺ 1, ^- 10” and ± [m _i ] f ₁ (+ / -) _min → "00, ^- 10" and the transformation of the arguments in this situation can be written either in the form of a graph-analytical expression (60),

either in the form of a graphoanalytic expression (61),

and the functional structure for the positive argument ( ⁺ S _i ) _k and the functional structure for the conditionally negative argument ( ^- S _i ) _{k can be} written in the form of analytical expressions (62).

But the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min is possible, which can be written as a graph-analytical expression (63),

and in the form of a graphoanalytic expression (64),

in which the argument of the resulting sum is activated in the conditionally “i” category, because as a result of the transformation of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min by means of inverse arithmetic axioms “+2” “-1” → “+1” and “-2” “+1” → “-1” between “Minimization zones” in the conditionally “k-1” “Minimization zone” the active logical zero “+1 "" -1 "→" ^± 0 ". It should be noted that a feature of the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min is that between the “minimization zones” in the conditionally “k -1 ”“ Zone of minimization ”at the same time, the argument of one character of the conditionally“ i-1 ”discharge is activated, as a result, the activity of the argument of the same sign in the conditionally“ i ”of the discharge“ k ”of the“ Zone of minimization ”is the resulting argument, with the active argument of the opposite this category, therefore, we write the functional structure for this situation in the form of an analytical expression (65).

As for the information content of the “Final action in the i-th category”, which is written in the form of the expressions ( ^± 0 ← ⁺ ) _i and ( ^± 0 ← ^- ) _i , in this situation in the conditionally “i” category the activity of the arguments does not correspond to absolute zero ( | ^± 0 |), and in accordance with the inverse arithmetic axiom “+1” “- 1” → “ ^± 0”, the activity of the arguments is equivalent to the logical zero ( ^± 0) and only therefore the resulting argument ¹ ( ⁺ ) is activated in the functional structures (65) S _i ) _k and ¹ ( ^- S _i ) _k .

     We write a similar functional structure for the argument structure (63) in the form of an analytical expression (66).

And if analytic expressions (59), (65) and (66) are introduced into the logical function system f ₃ (}) - OR and f ₄ (}) - OR, then the combined functional structures are written in the form of analytical expressions (67),

which activate the resulting positive argument (+ S _i ) _k and conditionally negative argument (-S _i ) _k conditionally “i” discharge.

Situation 2. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min between the "Minimization Zones" is possible, as a result of the conversion of which arguments of different signs are simultaneously active, and if we convert the active arguments in accordance with the inverse arithmetic axioms “+2” “-1” → “+1” and “-2” “+1” → “-1”, then we will write down the procedure for converting them in the form of a graphic-analytical expression (68 ),

in which, after converting the arguments of the two terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min in accordance with the inverse arithmetic axiom “+2” “-1” → “ +1 ”in the conditionally“ i + 1 ”category“ k-1 ”of the“ Minimization Zone ”two positive arguments corresponding to one positive argument in the conditionally“ i ”category“ k ” _{1 of the} “ Minimization Zone ”are activated. A similar situation occurs after converting the arguments in accordance with the inverse arithmetic axiom “-2” “+1” → “-1” in the conditionally “i” category “k” ₂ “Minimization zones”. Moreover, the functional structure for the positive argument ( ⁺ S _i ) _k and the functional structure for the conditionally negative argument ( ^- S _i ) _{k can be} written in the form of an analytical expression (69),

with the output logical function f ₂ (&) - AND and f ₄ (&) - AND, which are introduced into the system of the output logical function f ₃ (}) - OR and f ₄ (}) - OR, respectively. It should be noted that the output logical functions f ₃ (}) - OR and f ₄ (}) - OR, which activate the positive resulting and conditionally negative argument ( ⁺ S _i ) _k and ( ^- S _i ) _k , are the output functional the structure of the mathematical model of the input structure of the adder ± f (Σ _RU ) _min conditionally "i" discharge. And if the functional structures with the output logical function f ₂ (&) - AND and f ₄ (&) - AND enter into the system of the logical function f ₃ (}) - OR and f ₄ (}) - OR analytical expression (70),

which is a mathematical model of the input structure of the adder ± f (Σ _RU ) _min conditionally "i" discharge at this stage of its synthesis.

Situation 3. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min is possible} , in which the positive and conditionally negative arguments of one local transfer are activated as a result of the transformation of the arguments using the logical differentiation procedure d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and d ₁ / dn → f ₁ ( ^- ← ↑ ⁺ ) _{d / dn} and write the functional structure of such a transformation either in the form of an analytical expression (71 ),

either in the form of an analytical expression (72),

which activate the positive resulting and conditionally negative argument ( ⁺ S _{i + 1} ) _k and ( ^- S _{i + 1} ) _k , are the functional input structure of the mathematical model of the adder ± f (Σ _RU ) _min conditionally “i + 1” discharge. And if functional structures with an output logical function f ₁ (&) - And and f ₂ (&) - And expressions (58), (71) and (72) are introduced into the system of a logical function f ₁ (}) - OR and f ₂ (}) - OR, then we write the analytical expressions (73)

mathematical model of the functional input structure of the adder ± f (Σ _RU ) _min at this stage of its synthesis.

Situation 4. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min is possible} , in which a positive and conditionally negative argument are activated as a result of the transformation of the arguments by the logical procedure of differentiation d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and d ₁ / dn → f ₁ ( ^- ← ↑ ⁺ ) _{d / dn} with the formation of two local translations, and write the functional structure of such a transformation either in the form of an analytical expressions (74),

and in the form of an analytical expression (75),

either in the form of an analytical expression (76),

and in the form of an analytical expression (77),

which activate the positive resulting and conditionally negative argument ( ⁺ S _{i + 1} ) _k and ( ^- S _{i + 1} ) _k , are the functional input structure of the mathematical model of the adder ± f (Σ _RU ) _min conditionally “i + 1” discharge. Therefore, we introduce the functional structures (74) - (77) into the corresponding logical function systems f ₁ (}) - OR and f ₂ (}) - OR expressions (73) and the structure of the logical functions of the positive resulting argument (+ S _{i + 1} ) _k we conditionally write the “i + 1” discharge in the form of an analytical expression (78),

and the structure of the logical functions of the conditionally negative resulting argument (+ S _{i + 1} ) _{k of the} conditionally “i + 1” discharge will be written in the form of an analytical expression (79).

And the structure of logical functions (70) of the positive resulting argument (+ S _i ) _k conditionally “i” of the discharge can be written in the form of an analytical expression (80)

and the structure of the logical functions (70) of the conditionally negative resulting argument (+ S _i ) _{k of the} conditionally “i” bit will be written in the form of an analytical expression (81).

Situation 5. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min is possible} , in which the positive and conditionally negative arguments of two local hyphenations are activated as a result of the transformation of the arguments using the logical differentiation procedure d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and d ₁ / dn → f ₁ ( ^- ← ↑ ⁺ ) _{d / dn} and write the functional structures of such a transformation in the form of analytical expressions (82) .

It should be noted that by means of functional structures (82), only the resulting argument ¹ ( ⁺ S _i ) _k and ¹ ( ^- S _i ) _{k are} conditionally “i” of the discharge, since in the analytical expressions (80) and (81) the activation of the resulting arguments ¹ ( ⁺ S _{i + 1} ) _k and ¹ ( ^- S _{i + 1} ) _k conditionally “i + 1” of the discharge are activated by means of functional structures that include the output logical function f ₇ (&) - And and which we write in the form of analytical expressions (83)

with the converted arguments ( ⁺ n & m _i ) _k and ( ^- n & m _i ) _k , and they can be introduced into the system of logical functions f ₁ (&) - And and f ₂ (&) - And expressions (82). Moreover, if we return to the analysis of functional structures (78) and (79), activating the positive and conditionally negative argument (+ S _{i + 1} ) _k and (-S _{i + 1} ) _k conditionally “i + 1” of the discharge, writing them in expression form (84)

and expressions (85),

in which the systems of logical functions f ₁ (&) - And, f ₂ (&) - And and f ₈ (&) - And, f ₉ (&) - And are included as positive arguments ( ⁺ n _{i + 1} ) _{k- 1} and ( ⁺ m _{i + 1} ) _k-1 , and conditionally negative arguments ( ^- n _{i + 1} ) _k-1 and ( ^- m _{i + 1} ) _k-1 , then in this situation functional structures are advisable (82) to adjust. And if we return to the analysis of functional structures (80) and (81), activating the positive and conditionally negative argument (+ S) _k and (-S _i ) _k conditionally “i” the discharge, writing them in the form of expression (86)

and expressions (87),

in which the logical function systems f ₁ (&) - And - f ₈ (&) - And include both positive arguments ( ⁺ n _{i + 1} ) _k-1 and ( ⁺ m _{i + 1} ) _k-1 , and conditionally If the arguments ( ^- n _{i + 1} ) _k-1 and ( ^- m _{i + 1} ) _{k-1 are} negative, then in this situation functional structures (86) and (87) with output logical functions f ₁ (&) - And and f ₅ (&) - And adjust in accordance with expression (88)

and write in the form of a structure of logical functions (89).

And if we introduce the adjusted corresponding functional structure (89) into the logical function system f ₃ (}) - OR expressions (86), then taking into account the adjusted functional structure (82)

we write the analytical expression (90),

which activates the positive argument (+ S) _k conditionally "i" discharge. And if we introduce the adjusted corresponding functional structure (89) into the logical function system f ₃ (}) - OR expressions (87), then taking into account the adjusted functional structure (82)

we write the analytical expression (91),

which activates the conditionally negative argument (-S _i ) _k conditionally “i” discharge. In this case, the functional structures of the conditionally “i + 1” discharge (84) and (85), taking into account the converted arguments ( ⁺ n & m _{i + 1} ) _k and ( ^- n & m _{i + 1} ) _{k of the} positive channel, can be written in the form of an analytical expression (92),

and for a conditionally negative channel, we write in the form of an analytical expression (93),

Situation 5. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (94),

in which the activation of the resulting arguments of the subtotal is realized with the active converted arguments ( ^± n _i Vn _i ) _k and ( ^± m _i Vm _i ) _k “Activation conditions” and the structure of the arguments of the terms is possible (95),

in which in conditionally “k” ₂ “Zone of minimization” the structure of the arguments of the terms by means of a functional structure with the output logical function f ₁ (&) - And activates the positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge. Since in the argument structure of the term ± [n _i ] f ₁ (+/-) _min in the conditionally “i + 1” category, both the positive argument ( ⁺ n _{i + 1} ) _k and the conditionally negative argument ( ^- n _{i +1} ) _k and in this situation, the transformed argument ( ^± nVn _{i + 1} ) _{k is} active. And in the conditionally “k” ₁ “Minimization zone” the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min excludes the activation of the conditionally “i + 1” category of the resulting conditionally negative argument ( ^- S _{i + 1} ) _k , since the converted argument ( ^± mVm _{i + 1} ) _{k of} logical zero is not active in this category. But if we write down the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (97),

and perform the transformations in accordance with the procedure of logical differentiation d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and d ₁ / dn → f ₂ ( ^- ← ↑ ⁺ ) _{d / dn} and the arithmetic axiom “-1” → “-2” “+1”, as well as transformations in accordance with the logic of functional structures (96), then a “Defect” will be generated, which can be excluded only after applying the next transform. It should be noted that if we write the graphoanalytic expression (98),

in which the argument in the conditionally “i” category was activated in accordance with the logic of functional structures (99),

then in the conditional “i” category a similar “Defect” cannot be formed, since two consecutive arguments cannot be activated in the “Minimization Zone”.

      Returning to the analysis of the graphoanalytic expression (97), writing it in the form of a graphoanalytic expression (100)

it can be noted that if in the conditionally “k” ₁ “Minimization Zone” the argument conversion is local in nature, then in the conditionally “k” ₁ “Minimization Zone” the argument transformation can form an end-to-end transfer f ₁ ( ⁺ ←empl ⁺ ) _{d / dn} . It should be noted that the argument structure of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min of} expression (100) has a peculiarity of the positional sequence of active arguments, since if we write logical-dynamic process of transformation of arguments (101),

then after the formation of the combined argument structure ± [S_i] f_one(+/-)_min in it, the active arguments are arranged in a sequence, and it corresponds to a conditionally negative end-to-end carry f_one(^-←^-)_{d / dn}and positive pass-through f₂(⁺←⁺)_{d / dn}, which in this situation are realized through the procedure of logical differentiation d_one/ dn → f_one(^-← ↑⁺)_{d / dn} and d₂/ dn → f₂(⁺← ↓_-)_{d / dn}. And if we analyze the positional sequence of active arguments in the structure of the arguments of the terms ± [n_i] f_one(+/-)_min  and ± [m_i] f_one(+/-)_min, the peculiarity lies in the sequential activity of at least two arguments of the conditionally “i + 1” discharge in the structure of one of the terms and the activity of the argument of the conditionally “i” discharge in the structure of the other term, which is positionally located between the active arguments of the conditionally “i + 1” discharge. It should be noted that such a feature, if we write the graphoanalytic expression  (102)

or graphoanalytic expression (103),

then it can be in the "Zones of minimization" in their unlimited sequence. It should also be noted that the end-to-end transfer f ₁ ( ⁺ ← dire ⁺ ) _{d / dn} or f ₁ ( ^- ← dire ^- ) _{d / dn} is formed only in the structure of argument arguments of the same name ± [n _i ] f ₁ (+/- ) _min and ± [m _i ] f ₁ (+/-) _min and the active argument of such a transfer can be activated at the local level. Therefore, we analyze the structure of the arguments of the terms (104),

in which the active arguments do not form the end-to-end transfer f ₁ ( ⁺ ←empl ⁺ ) _{d / dn} , but if we logically differentiate d ₁ / dn → f ₁ ( ^- ← ↑ ⁺ ) _{d / dn the} resulting sum ± [S _i ] f ₁ ( +/-) _min , then the adjusted resulting sum ± [S _i ] f ₂ (+/-) _min (105) will be generated, where the conditionally negative argument ( ^- S _{i + 1} ) _{k is} activated in the conditionally “i + 1” category local transfers f ₁ ( ⁺ ↓ _- ) _{d / dn} and f ₂ ( ⁺ ↓ _- ) _{d / dn} . It should be noted that if functional structures are formed (106),

then the conditionally negative argument ( ^- S _{i + 1} ) _{k of} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn} activates the functional structure with the output logical function f ₁ (&) - And, in which three input arguments ( ⁺ n _{i + 1} ) _{k + 1} , ( ⁺ m _i ) _{k + 1} and ( ⁺ n _{i + 1} ) _k can be included in the system of a separate logical function f ₀ (&) - And to form the transformed argument ⁰ ( ⁺ S _i ) _k . And this converted argument ⁰ ( ⁺ S _i ) _k → ⁰ ( ⁺ S _i ) _k-2 for conditionally “k” ₂ “Minimization zones” will be the input argument ⁰ ( ⁺ S _i ) _k-2 conditionally “k-2” "Minimization zones" for the functional structure (106) with the output logical function f ₂ (&) - And. And if you write down the corrected functional structures (107),

then the functional structure with the output logical function f _3.1 (&) - And, activating the positive local transfer argument f ₁ ( ⁺ ← ⁺ ) _{d / dn is} significantly minimized by the number of input arguments, while it correctly activates the positive resulting argument ( ⁺ S _i ) _k conditionally “i” of the discharge in conditionally “k” ₂ “Zone of minimization”. And in the conditionally “k” ₃ “Minimization Zone” this functional structure with the output logical function f _3.2 (&) - And is not active, since the input argument ( ⁺ m _i ) _k with the changed level of the analog signal is not active in its system, therefore, in In this “minimization zone”, the argument ( ⁺ S _{i + 1} ) _{k of the} local transfer f ₂ ( ⁺ ← ⁺ ) _{d / dn} must be activated in the conditionally “i + 1” category. And if for conditionally “k” ₃ “Minimization zones” write functional structures (108),

then the functional structure with the output logical function f ₄ (&) - And correctly activates the resulting argument ( ⁺ S _{i + 1} ) _k in the conditionally “i + 1” bit “k” of the “Minimization Zone”, when as the resulting argument ( ⁺ S _i ) _k conditionally “i” of discharge in this “Zone of minimization” is correctly inactive. In this case, the resulting conditionally negative argument ( ^- S _{i + 1} ) _{k is} conditionally “i + 1” of the discharge in the “k” ₂ “Zone of minimization” of the logical function f ₂ (&) - And it is also correctly inactive, since it is not active in this “ Minimization zone ”argument of the second term ( ⁺ m _i ) _k conditionally“ i ”discharge with a changed level of the analog signal. Therefore, the functional structures (108) are the functional structures of the mathematical model of the input structure of the adder ± f ₁ (Σ _RU ) _min , since if we write down the logical-dynamic process of transforming the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , in the joint structure of which end-to-end transfer f ₁ ( ⁺ ←empl ⁺ ) is active in the form of expression (109),

then the functional structures (110) are also correct, since the conditionally negative argument ( ^- S _{i + 1} ) _{k of the} functional structure with the output logical function f ₂ (&) - And in “k” _{1 the} “minimization zone” is not active, but in “k ” ₂ “ Zone of minimization ”the positive argument of end-to-end transfer f ₁ ( ⁺ ←empl ⁺ ) is activated. In this regard, we return to an additional analysis of the procedure for converting the arguments of the terms (71), writing it in the form of the expression (111),

in which functional structures (112) have a “Defect”, since on the one hand they do not take into account the possible activity of a positive argument ( ⁺ n _{i + 1} ) _k conditionally “i + 1” discharge, since its activity leads to an end-to-end transfer of f ₁ ( ⁺ ← ← ⁺ ) and f ₂ ( ^- ← program ^- ). On the other hand, functional structures (112) do not take into account the possible activity of a conditionally negative argument ( ^- n _{i + 1} ) _{k of} conditionally “i + 1” discharge, which excludes activation of a positive argument ² ( ⁺ S _{i + 1} ) _k or conditionally negative argument ² ( ^- S _{i + 1} ) _k in the conditionally “k” “minimization zone”. Therefore, in the system of logical functions f ₁ (&) - And and f ₂ (&) - And it is necessary to introduce a transformed argument ↓ ( ^± nVn _{i + 1} ) _{k of} inactivity of the arguments in the conditionally “i + 1” category, and functional structures (112) we write in the form of analytical expressions (113),

and taking into account the input transformed argument ( ⁺ n & m _{i + 1} ) _k-1 , we write the functional structures (113) in the form of analytical expressions (114).

 A similar adjustment is performed in analytical expressions (72), which we write in the form of adjusted functional structures (115),

with an additional transformed argument ( ^± mVm _{i + 1} ) _k inactivity of the arguments in the conditionally “i + 1” category, and taking into account the input transformed argument ( ^- n & m _{i + 1} ) _k-1 , we write the functional structures (115) in the form of analytical expressions ( 116).

Since functional structures (114) and (116) include additional input transformed arguments ↓ ( ^± nVn _{i + 1} ) _k , we therefore write the positive channel of the functional structure of the conditionally “i + 1” bit (92) in the form of an analytical expression (117),

and for a conditionally negative channel (93) we write in the form of an analytical expression (118).

It should be noted that in the analytical expressions (117) and (118) the transformed arguments ( ⁺ n & m _i ) _k ↑ and ( ^- n & m _i ) _k ↑ are introduced, since if we return to the analysis of the structure of the logical functions of the positive channel, the conditionally “i” discharge (90), writing it in the form of an analytical expression (119)

and return to the analysis of the structure of the logical functions of the conditionally negative channel of the conditionally “i” discharge (91), writing it in the form of an analytical expression (120),

then the positive transformed arguments ( ⁺ n & m _i ) _k ↑ are included in the system of logical functions f ₂ (&) - And and f ₃ (&) - And expressions (119), and conditionally negative arguments ( ^- n & m _i ) _k ↑ are included in the system logical functions f ₈ (&) - And and f ₉ (&) - And expressions (120).

Further, taking into account the equal probability of active arguments in the argument structure of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , we write the functional structures for this situation (121),

which are also functional correct structures of the mathematical model of the input structure of the adder ± f ₁ (Σ _RU ) _min . And since equal probability also applies to the signs of the arguments, it will therefore form functional additional structures for the conditionally negative arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , and write logical function structures (122)

structures of logical functions (123),

which adequately reflect the logical-dynamic process of transforming the arguments of the terms, therefore they are also the functional structures of the mathematical model of the input structure of the adder ± f ₁ (Σ _RU ) _min . Since if we write down the procedure for converting the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (124),

or the procedure for converting the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (125),

then on the one hand argument _⁽⁺ S _i ⁺ _{1) k} and ^(- S _{i + 1) k} f ₁ through carry ⁽⁺ ←← ⁺⁾ and f ₂ ^(- ←← ^-) by the functional structures (114) and (117 ) is activated correctly, but on the other hand, a “Feature” is formed in the conditional “k” “Minimization Zone”, and it is directly related to the activation of the resulting arguments ( ⁺ S _i ) _k and ( ^- S _i ) _k in the conditionally “i” category. It should be noted that the activity of the resulting arguments ( ⁺ S _i ) _k and ( ^- S _i ) _k in the conditionally “i” category is possible only if the positive arguments ( ⁺ n _i ) _k and ( ⁺ m _i ) _{k are} simultaneously active, so and conditionally negative arguments ( ^- n _i ) _k , ( ^- m _i ) _k two terms of this category and the activity of the converted arguments ⁰¹ ( ⁺ S _i ) _k-2 , ⁰² ( ⁺ S _i ) _k-2 and ⁰² ( ⁺ S _i ) _k-2 , ⁰¹ ( ⁺ S _i ) _k-2 conditionally "i-2" category. And if we take into account that in the structure of logical functions (117) and (118), the transformed positive argument ( ⁺ n & m _i ) _k and conditionally negative argument ( ^- n & m _i ) _{k are formed} ,

then the resulting argument ( ⁺ S _i ) _k and ( ^- S _i ) _k in the conditionally “i” category of expression (124) can be activated by means of the functional structure (126),

and the resulting argument ( ⁺ S _i ) _k and ( ^- S _i ) _k in the conditionally “i” category of expression (125) can be activated by means of the functional structure (127)

and at this stage of synthesis of the input structure of the adder ± f ₁ (Σ _RU ) _min, analytical expressions (126) and (127) are mathematical models of the concrete structures of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min .

Based on the results obtained after combining the formed functional structures (110), (121), (122), (123), (126) and (127), which activate the arguments of the through transfers f ₁ ( ⁺ ← ← ⁺ ) and f ₂ ( ^- ← set ^- ) for a positive channel conditionally “i” discharge, write in the form of a structure of logical functions (128)

for a conditionally negative channel, conditionally “i” of the discharge can be written in the form of a structure of logical functions (129),

 and the functional structures of the conditionally “i + 1” discharge are written for the positive channel in the form of the structure of logical functions (130)

for a conditionally negative channel in the form of a structure of logical functions (131).

Since the functional structures (128) - (131) were formed as a result of the analysis of specific structures of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , we therefore analyze the correctness their logical-dynamic process of activating the resulting arguments for other possible structures of the terms.

Version 1. If we return to the analysis of the logical-dynamic process of transforming the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (121), which can be written as an expression (132),

then in conditionally "k"  The “minimization zone” in the structure of the arguments of the first term ± [n_i] f_one(+/-)_min  possible activity taking into account the logic of formation of a conditionally minimized argument structure ± [S_i] f₂(+/-)_min  conditionally negative argument either in the conditionally “i + 1” category, or in the conditionally “i” category, therefore, into the system of logical functions f₃(&) - And and f₂(&) - And it is necessary to introduce an “Additional Condition” for activating the resulting argument (⁺S_i)_k and (^-S_{i + 1})_k, and the functional structures (133) are written in the form of analytical expressions (134).

As a result, if we write for the adjusted structure of the arguments of the first term ± [n _i ] f ₁ (+/-) _min in the form of a graphoanalytic expression (135),

then in the conditionally “i” category the active logical zero “+1” “- 1” → “ ^± 0” will be formed, therefore, the functional structure with the output logical function f ₂ (&) - And excludes the activation of the positive pass-through argument f ₁ ( ⁺ ← ⁺ ) _{d / dn} .

    From a preliminary analysis of the possibility of forming a logical-dynamic process of transforming conditionally minimized structures of the arguments of the terms ± [n_i] f (+/-)_min and ± [m_i] f (+/-)_min it follows that functional adder structure ± f_one(Σ_RU)_min without end-to-end transfer f_one(⁺← ↓_-) with the procedure of simultaneous transformation of the arguments of the first intermediate sum ± [S^one _i] f (}) - OR through arithmetic axioms of the ternary number system f_RU(+ 1,0, -1) can be formed if we exclude the activation of sequentially active arguments in the “Minimization Zone”, which will significantly simplify the functional structure of the first level of summation of partial products in a parallel serial multiplier ± f_Σ(Σ_RU)_min.

Synthesis of the mathematical model of the adder ± f ₁ (Σ _RU ) _{min of} conditionally minimized argument structures of the terms ± [n _i ] f (+/-) _min and ± [m _i ] f (+/-) _min with the procedure for simultaneously converting the arguments of the first intermediate sum ± [S ¹ _i ] f (}) - OR in accordance with the arithmetic axioms of the ternary numeral system f _RU (+ 1,0, -1). If we return to the analysis of the logical-dynamic process of transforming the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (132), we write it in the form of the expression (136 ),

then through the functional structure (137), which essentially activates the resulting conditionally negative argument^{-2 + 1}(^-S_i)_k in accordance with the inverse arithmetic axiom “-2” “+ 1” → “-1” and this is the action of the logical function f_one(&) - And can be written as (-_→↓⁺)_k, and as a result of such a conversion to conditionally “k”  The “minimization zone” will be activated (_→↓_-i)_k conditionally negative argument in conditionally “i” category minimized structure of the resulting sum ± [S_i] f₂(+/-)_min. In this case, it is advisable to write the functional structure (137) in the form of an analytical expression (138)

with two functional input structures with an output logical function f ₁ (&) - And and f ₃ (&) - And. And if the functional structure with the output logical function f ₁ (&) - And, writing it in the form of an analytical expression (139)

performs analysis {( ⁺ ← ⁺² ↓ _- ) ⁱ | _{i + 1} } the activity of positive arguments in accordance with the index “ ⁱ | _{i + 1} ”between“ Minimization Zones ”and activates as a positive argument ( ⁺ ← ⁺ ( ⁿⁱ | _{mi + 1} &) ⁺ S _{i + 1} ) _{k + 1} ↑, functionally belonging to {( ^± 0 _{i + 1} ⁺ ← ⁺ ) _{k + 1} } conditionally “i + 1” category “k + 1” “Minimization zones”, and conditionally negative argument ( ⁺ ↓ _- ( ⁿⁱ | _{mi + 1} &) ^- S _{i + 1} ) _k ↑, functionally belonging to { ( ⁺ ↓ _-i ) _k } conditionally “i” category “k” “Minimization zones”, then the functional structure with the output logical function f ₂ (&) - And, writing it in the form of an analytical expression (140)

analyzes ( ⁺ ← ⁺² _{i + 1} ⁱ ) _k-1 activity of positive arguments in accordance with the index “ _{i + 1} ⁱ ” in “k-1” of the “Minimization Zone” and activates as a positive argument ( ⁺ ← ⁺ ( _{mi + 1} ⁿⁱ &) ⁺ S _i ) _k ↑, functionally belonging to conditionally “i” category “k” “Minimization zones”, and conditionally negative argument ( ⁺ ↓ _- ( _{mi + 1} ⁿⁱ &) ^- S _{i + 1} ⁱ ) _{k -1} ↑, functionally belonging to {( ⁺ ↓ _-i ) _k-1 } conditionally "i" category "k-1""Minimizationzones". It should be noted that functional additional structures (139) and (140) were introduced in the structure of logical functions (138), since the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f is possible ₁ (+/-) _min , in which the procedure for activating the resulting argument ^{-2 + 1} ( ^- S _i ) _{k is} written by means of either in the form of an un minimized functional structure (141),

or taking into account the transformed arguments ( ⁺ ↓ _- ( ⁿⁱ | _{mi + 1} &) ^- S _{i + 1} ) _k ↑ and ( ⁺ ← ⁺ ( _{mi + 1} ⁿⁱ &) ⁺ S _i ) _k ↑ functional structures (139) and ( 140) we write in the form of a minimized functional structure (142),

in which, in accordance with the inverse arithmetic axiom “-2”, “+ 1” → “-1” in the conditionally “k” “minimization zone”, a conditionally negative argument ^{-2 + 1} ( ^- S _i ) _k is activated in the resulting structure of the arguments of the sum ± [S _i ] f ₂ (+/-) _min . It should be noted that the converted argument ↓ ( ^- m _i ) _{k + 1} with a changed level of the analog signal of the conditionally “i + 1” discharge is introduced into the system of the logical function f ₃ (&) - And, since the argument structure of the second term ± [ m _i ] f ₁ (+/-) _min with active arguments between the "Minimization Zones".

      Option 1. A conditionally negative argument is active (^-m_i)_{k + 1} at “K + 1” “Zone of minimization”, which in the logical-dynamic process of transforming the arguments of the terms (143),

which in the structure of the intermediate sum ± [S_i] f_one(+/-)_min through the inverse arithmetic axiom “-2” “+ 1” → “-1” was previously transformed into a conditionally negative argument (^-m_{i + 1})_kconditionally “i + 1” discharge in “k” “Minimization Zone”, after which, by the same inverse arithmetic axiom, it was activated in conditionally “i” discharge in the same “Minimization Zone”. The result was a local double reverse transfer f_one(^-→ ™^-), wherein at “K + 1” “Minimization zone” activated a positive resulting argument (⁺n_i→⁺S_i)_{k + 1}. And for the formation of its functional structure, it is necessary to analyze the conditions for its activation, and for this we write down possible situations.

Situation 1. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , for which a sequence of active arguments is formed, and they in their sequence correspond to the formalized end-to-end procedure transfer f ₁ ( ⁺ ← first ⁺ ) and when it is performed in the structure of the intermediate sum ± [S _i ] f ₁ (+/-) _{min of} expression (144)

form the structure of the arguments of the intermediate sum ± [S _i ] f ₂ (+/-) _min . And if, in the conditional “k” “Minimization Zone”, we perform the conversion of active arguments in accordance with the inverse arithmetic axiom “+2” “- 1” → “+1”, then the positive resulting argument ( ⁺ n _i → ⁺ S _i ) will be activated _k , which formally corresponds to the active positive argument ( ⁺ n _i ) _{k of the} first term ± [n _i ] f ₁ (+/-) _min .

Situation 2. The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , for which a sequence of active positive arguments is formed with a conditionally negative argument between them, and they in their sequence correspond to the local transfer procedure f ₁ ( ⁺ ← ⁺ ), and when it is performed in the intermediate sum structure ± [S _i ] f ₁ (+/-) _min expressions (145)

form the structure of the arguments of the intermediate sum ± [S _i ] f ₂ (+/-) _min . And if in conditionally “k” “Minimization Zone” we perform transformations of active arguments in accordance with the inverse arithmetic axiom “-2” “+ 1” → “-1”, then conditionally “k-1” “Minimization Zone” will be conditionally activated negative argument ( ^- m _i → ^- S _{i + 1} ) _k-1 , which formally corresponds to the active conditionally negative argument ( ^- m _i ) _k conditionally “k” of the “Minimization zone” of the second term ± [m _i ] f ₁ (+ / -) _min . Moreover, in the conditionally “k” “Minimization Zone”, the positive argument ( ⁺ n _i → ⁺ S _i ) _k will also be active, which formally corresponds to the active positive argument ( ⁺ n _i ) _{k of the} first term ± [n _i ] f ₁ (+ / -) _min .

From the results it follows that the activation of the positive argument ( ⁺ n _i ) _k → ( ⁺ S _i ) _{k of the} first term ± [n _i ] f ₁ (+/-) _min in the resulting sum ± [S _i ] f ₃ (+ / -) _min does not depend on the activity of the arguments in the conditionally “i” category “k-1” of the “Minimization Zone”, and by the condition of its activation in the conditionally “Minimization Zone” of the form,

if we write the functional structure (146)

is the activity of the transformed conditionally negative argument ( ^- nVm _{i + 1} ) _k-1 conditionally “i + 1” of the discharge “k-1” of the “Minimization Zone”, which activates the logical function f ₁ (} &) - OR-NOT, and it an active functional structure is a “condition for activation”. It should be noted that the active arguments conditionally “k” and “k-1” “Minimization zones” are introduced into the system of logical functions f ₁ (}) - OR, f ₂ (}) - OR and f ₃ (}) - OR due to the fact that the resulting argument ( ⁺ S _i ) _k in the conditionally “i” category is activated in the following possible variants of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+ / -) _min , which we write in the form of graphoanalytic expressions (146) - (148).

     Option 1.

     Option 2

     Option 3

And if we take into account that in the structure of the resulting sum ± [S _i ] f ₂ (+/-) _min in the conditionally “i + 1” category “k-1” of the “Minimization Zone”, the conditionally negative argument ^is activated ( ^- S _{i + 1} ) _k-1 , then we write the functional structure for its activation in the conditionally “k” “Minimization Zone” in the form of an analytical expression (149),

in which the “Activation Condition” is a conditionally transformed negative argument ( ^- nVm _i ) _k conditionally “i” of the discharge “k” of the “Minimization Zone” and a transformed positive argument ( ⁺ nVm _{i + 1} ) _k-1 conditionally “i + 1” of the discharge “K-1” “Minimization zones”. And if in the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , for example, expression (150), the transformed argument “Activation conditions” is not active, then we will write down the logical-dynamic transformation process in the form of a graphic-analytical expression (151),

in which the transformed conditionally negative argument ( ^- nVm _i ) _{k is} conditionally “i” of the discharge in the “k” “Minimization Zone” and to form the resulting sum ± [S _i ] f ₃ (+/-) _min transformation in the argument structure ± [S _i ] f ₂ (+/-) _{min is} performed in accordance with the inverse arithmetic axiom “-2” “+ 1” → “-1”. As a result, the conditionally negative argument ( ^- S _i ) _{k of the} conditionally “i” discharge is activated in the conditionally “k” “Minimization Zone”, and we write the functional structure for its activation in the form of an analytical expression (152),

in which the “Activation Condition” is a conditionally transformed negative argument ( ^- nVm _i ) _{k of} conditionally “i” discharge with a changed level of the analog signal “k-1” “Minimization Zones”.

And if in the argument structure of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min of} expression (150), the transformed positive argument ( ⁺ nVm _{i + 1} ) _{k is} not active _-1 “Conditions of activation”, then the logical-dynamic process of transformation will be written in the form of a graphic-analytical expression (153),

in which the transformed positive argument ( ⁺ nVm _{i + 1} ) _{k-1 is} conditionally “i + 1” of the discharge in the “k-1” “Minimization Zone”, and for the formation of the resulting sum ± [S _i ] f ₂ (+ / -) _min transformation in the structure of arguments ± [S _i ] f ₁ (+/-) _{min is} performed in accordance with the inverse arithmetic axiom “+2” “- 1” → “+1”. As a result, in the conditionally “k” “Minimization Zone” the positive argument ( ⁺ S _i ) _{k of the} conditionally “i” discharge is activated, and the functional structure for its activation is written in the form of an analytical expression (154),

in which the “Activation Condition” is the transformed positive argument ( ^- nVm _{i + 1} ) _{k-1 of} conditionally “i + 1” discharge with the changed level of the analog signal “k-1” “Minimization Zones”. It should be noted that in this situation, in the conditionally “k + 1” “Zone of minimization” of the logical-dynamic process of argument conversion, the positive resulting argument ( ⁺ S _i ) _{k + 1 of the} conditionally “i” discharge is not activated. And if we return to the analysis of the functional structure (146), by means of which we activate in the conditionally “k + 1” “Minimization Zone” the positive resulting argument ( ⁺ S _i ) _k conditionally “i” of the discharge, writing it in the form of an analytical expression (155),

then there are no restrictions on the activation of this argument. Since if we write down the graph-analytic expression (156) for the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min expressions (153),

then the positive argument ( ⁺ S _i ) _k conditionally “i” of the discharge in the functional structure (157) is not activated correctly. Therefore, we determine the possible input converted arguments “Activation conditions” of the functional structure (157) with the output logical function f ₁ (&) - And, the system of which includes the converted arguments ( ^- nVm _i ) _k and ( ⁺ nVm _i ) _k corresponding to the active logical zero "+ 1 / -1" → "± 0", and this was due to the fact that to exclude the preliminary stage of summation, including the procedure for removing it from the structure of the intermediate sum ± [S _i ] f ₁ (+/-) _min , which will lead to a reduction in the technological cycle ∆t _Σ in the functional structure of the adder ± f (Σ _RU ) _min . And if we write the resulting sum ± [S _i ] f ₂ (+/-) _{min of} expression (156) in the form of a graphoanalytic expression (158),

then from his analysis it follows that in order to activate a positive argument ( ⁺ S _i ) _k conditionally “i” the discharge in conditionally “k” “Minimization Zone” it is necessary that in the conditionally “k-1” “Minimization Zone” an active logical zero be activated ("+ 1 / -1" _i → "± 0" _i ) _k-1 . And such a situation is excluded in the logical-dynamic process of converting the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min expressions (156), because if we write the graphoanalytic expression ( 159)

then non-activated logical zeros (“+ 1 / -1” _i → “± 0” _i ) _k-1 can be combined using the functional structure with the output logical function f ₁ (}) - OR in expression (160) with the input converted arguments ( ⁺ ↕ _- ( _-ni | ^{+ ni + 1} &) ^{± 0} S _i ) _k-1 , ( ⁺ ↕ _- ( _-ni | ^{+ ni + 1} &) ^{± 0} S _i ) _k-1 , ( ⁺ ↕ _- ( _-mi | ^{+ mi + 1} &) ^{± 0} S _i ) _k-1 and ( ⁺ ↕ _- ( _-mi | ^{+ mi + 1} &) ^{± 0} S _i ) _k-1 , which were formed between the “minimization zones” by means of the logical function f (&) - And and activate the resulting argument ( ^{± 0} S _i ) _k-1 , and it is introduced into the system of the logical function f ₁ (&) - And (161), excluding its activation in graphoanalytic expression (159). As a result, after combining the functional structures (160) and (161), we write the analytical expression (162),

by means of which the positive resulting argument ( ⁺ S _i ) _{k of} conditionally “i” discharge in the conditionally “k” “Minimization zone” is activated. It should be noted that the functional structure (162) can be minimized if we consider that the active input arguments ( ^- nVm _i ) _k and ( ⁺ nVm _i ) _k in the functional structure (157), which can be written in the form of an analytical expression (163 )

taken together, they correspond to an active logical zero “+ 1 / -1” → “± 0”, and in this situation, the resulting argument can be activated only by means of a positive local transfer argument f ₁ ( ⁺ | ← ⁺ ) from conditionally “k-1” “Zone of minimization”, and this is possible in this “Zone of minimization” in only three situations of activity of arguments | ^{+ ni + 1} _{+ mi + 1} |, | _{+ mi + 1} ^{+ ni} | and | ^{+ ni + 1} _{+ mi} |, which is activated by the logical function f ₁ (}) - OR. Indeed, if we write down the logical-dynamic process of transforming the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min in the form of a graphoanalytic expression (164)

or in the form of a graphic-analytical expression (165)

then the positive resulting argument ( ⁺ S _i ) _k conditionally “i” of the discharge is correctly activated. Moreover, in the conditionally “k-1” “Minimization Zone”, the conditionally negative resulting argument ( ^- S _i ) _k conditionally “i” of the local transport discharge f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn → f is activated ₁ ( ⁺ ← ↓ _- ) _{d / dn} for the same input arguments “Activation conditions” that were not transformed by the logical function f ₁ (} &) - OR NOT, and write the functional structure of this procedure in the form of an analytical expression (166).

in which activity is necessary in the conditionally “k” “minimization zone” of one of the input converted arguments ( ⁺ n _{i + 1} & m _i ) _k or ( ⁺ m _{i + 1} & n _i ) _k , which, through the logical function f ₁ (}) - OR and f ₁ (&) - AND activates the resulting conditionally negative argument ( ^- S _i ) _k . But there are two more possible structures of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , the active positive arguments of which are also excluded in the conditionally “k” “Minimization Zone” activation of the resultant conditionally negative argument ( ^- S _i ) _k , and we write them in the form of a graphic-analytical expression (167)

and in the form of a graphic-analytical expression (169),

in which functional structures (168) and (170) with output logical functions f ₁ (&) - NAND and f ₂ (&) - NAND after introducing logical functions (166) into the system, writing it in the form of an analytical expression (171),

when they are active, they will be the “Activation Condition 2” for a positive sequence of arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min . As a result, the functional structure (169) is a correct functional structure that activates the resulting conditionally negative argument ( ^- S _i ) _k in the conditionally “i” category in the structure of positive arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min . But the conditionally negative argument ( ^- S _i ) _k in the conditionally “i” category in the structure of the positive arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min can be formed not only as a result of local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} , but also when it is locally transferred f ₁ ( ⁺ | ← ⁺ ) _{d / dn} from conditionally “k-1” “Minimization zones”. Since if we return to the analysis of the logical-dynamic process of transforming the arguments of the terms (151), writing it taking into account the functional structure (152) in the form of a graphic-analytical expression (172),

in which the resulting conditionally negative argument ( ^- S _i ) _k in the conditionally “i” category in the positive structure of the argument arguments is activated as a result of the transformation of the arguments into the conditionally “k” “Minimization Zone” by applying the inverse arithmetic axiom “-2” “+ 1” → “-1”, and its application in the subtotal is possible only with an active positive local transfer argument f ₁ ( ⁺ | ← ⁺ ) _{d / dn} from the conditionally “k-1” “Minimization Zones”. A local transfer f ₁ ( ⁺ | ← ⁺ ) _{d / dn} in this situation is possible only if the sequence of positive arguments in the intermediate sum ± [S _i ] f ₁ (+/-) _min , which is not taken into account in the functional structure (173) therefore, it is formed with “Defect” and “Redundant Arguments”. Since, on the one hand, the transformed positive argument ( ⁺ nVm _{i + 1} ) _k-1 introduced into the system of the logical function f ₁ (&) - And does not meet the condition for activating the positive local transfer argument f ₁ ( ⁺ | ← ⁺ ) _{d / dn} , s on the other hand, to apply the inverse arithmetic axiom “-2” “+ 1” → “-1”, it is sufficient to analyze the activity of the arguments in the conditionally “k” “Minimization Zone”, therefore, we write the functional structure (173) as an analytical expression (174).

     From the analysis of the logical-dynamic process of transformation of arguments in the structure of the intermediate sum ± [S_i] f_one(+/-)_min  expression (175) it follows that for the formation in this case, the minimized structure of the arguments of the resulting sum ± [S_i] f₂(+/-)_minit is necessary to perform the procedure of selective logical differentiation d_one ^*/ dn⁺→ f_one(⁺← ↓_-)^* _{d / dn} with the following argument conversion logic, which we write in the form of a graph-analytical expression (176)

with the formation of the resulting minimized sum ± [S _i ] f ₂ (+/-) _min and in the form of a graphic-analytical expression (177)

with the formation of the resulting conditionally minimized sum ± [S _i ] f ₂ (+/-) _min and the active arguments between the "Zones of minimization". It should be noted that the conversion of inactive arguments in an alternating sequence of the same name arguments is performed in accordance with the arithmetic axiom “ ^± 0” → “+1” “- 1”, only if they are positionally located in the conditionally “i” category. Since if we write the graphoanalytic expression (178),

in which inactive arguments are activated in accordance with the arithmetic axiom “ ^± 0” → “+1” “–1”, positionally located in the conditionally “i + 1” category, then the structure of the resulting sum is ± [S _i ] f ₂ (+/- ) _min does not belong to the category of conditionally minimized amounts, since two successively active arguments are positionally located in the “Minimization Zone”. Similar transformations are performed through the selective logical differentiation procedure d ₁ ^* / dn ^- → f ₁ ( ^- ← ↑ ⁺ ) ^* _{d / dn} and in the structure of the intermediate sum ± [S _i ] f ₁ (+/-) _min with an alternating sequence of conditionally negative arguments

as a result, the structure of the resulting sum ± [S _i ] f ₂ (+/-) _{min is also} formed in a conditionally minimized form, since consecutive active arguments are positionally located between the “Minimization Zones”. It should be noted that the activation of conditionally negative arguments in expression (177) and positive arguments in expression (179) in accordance with the arithmetic axiom “ ^± 0” → “+1” “-1” is performed in an alternating sequence in which there is no positive local transfer argument f ₁ ( ⁺ | ← ⁺ ) _{d / dn} from the previous “Minimization Zone”. And the functional structure of such a transformation for the positive structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min can be} written in the form of an analytical expression (180),

and for the conditionally negative structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min, we write in the form of an analytical expression (181),

in which, through a functional structure with an output logical function f ₁ (&) - And the positive resulting argument ( ⁺ S _i ) _k conditionally “i” of the discharge is activated. And if we return to the reanalysis of functional structures (174), writing it in the form of an analytical expression (182),

then, taking into account the functional structure (181) in the analytical expression (182), the “Un minimized structure” with the output logical function f ₁ (}) - OR is included in the system of the output logical function f ₁ (&) - and it can be excluded, and we write the corrected analytical expression in the form of a functional structure (183),

which includes two conditions for activation. But a functional structure with an output logical function f ₁ (}) is OR in expression (182), if it is written in the form of an analytical expression (184),

activates the local transfer argument f ₁ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and also activates the positive argument ( ⁺ S _i ) _k conditionally “i” of the discharge , but under the relevant “Activation Conditions”. Therefore, we will determine these conditions, and for this we write for the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _{min the} logical-dynamic process of forming a conditionally minimized resulting sum in the form of graphoanalytic expression (185),

in which, to activate the positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _k-1, conditionally “k-1” “Minimization zones” of local transfer f ₁ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} the “Activation condition” is introduced, and it consists in the fact that in the conditionally “k” “Minimization Zone” all arguments of the terms ± [n _i ] f ₁ ( +/-) _min and ± [m _i ] f ₁ (+/-) _min , and only in this situation activate the resulting positive argument ( ⁺ S _i ) _{k of the} functional structure (186). But since the positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _k-1 is the conditionally “k-1” argument of the “Minimization Zones”, and the conditionally negative argument ^{(+ ↓ -) d is} activated in this “Minimization Zone” ^{/ dn} ( ^- S _i ) _{k-1 of} local transport f ₁ ( ⁺ ↓ _- ) _{d / dn} . Therefore, we write the functional structure (186) in the form of an analytical expression (187)

with the converted input argument ↓ ^{(+ ← +) d / dn} ( ⁺ S _i ) _k-1 conditionally “k-1” “Minimization zones”, and activation of the conditionally negative argument ^{(+ ↓ -) d / dn} ( ^- S _i ) _{k-1 of the} local transport f ₁ ( ⁺ ↓ _- ) _{d / dn} in this zone, taking into account the synthesis of the mathematical model, conditionally “k” “Minimization zones” can be written as a functional structure (188),

in which the transformed additional argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _k ↑ is introduced for the next “Minimization Zone”. It should be noted that only one transformed positive argument ( ⁺ nVm _{i + 1} ) _{k-1 is} introduced into the system of the output logical function f ₁ (&) - And as the “Activation Condition”, since only its inactivity excludes the activation of the conditionally negative resulting argument ( ^- S _i ) _k , and its inactivity is directly related to the activity of the positive argument of one of the terms ± [n _i ] f ₁ (+/-) _min or ± [m _i ] f ₁ (+/-) _min

or with simultaneously the activity of the positive argument of the two terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min.

And if in the logical-dynamic process of converting arguments (189) as a result of the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} in the conditionally “k-1” “Minimization Zone”, the resulting conditionally negative argument is activated , then in the argument conversion procedure (190) this conditionally negative argument with a positive argument forms an active logical zero “+1” “- 1” → “ ^± 0”, therefore, in the functional structure (188), the converted positive argument ( ⁺ nVm _{i + 1} ) _k-1 introduced into the system logical function f ₁ (k) - and correctness . The structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min is also possible, which we write in the form of a graphoanalytic expression (191),

in which the resulting structure of the sum ± [S _i ] f ₂ (+/-) _min has a “Defect”, since the transformation of the arguments for exclusion must be performed in accordance with the logical-dynamic process (192).

And for this structure of the arguments of the terms in the functional structure (193), an additional logical function f ₂ (}) is introduced - OR, the system of which includes the transformed argument ( ⁺ n _{i + 1} & ^- m _i ) _k-1 conditionally “k-1” “Minimization zones”, which in this situation is the argument “Activation conditions” of the resulting conditionally negative argument ( ^- S _i ) _{k of the} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} in the “k” “minimization zone”. And the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min is also possible, which we write in the form of a graphoanalytic expression (193),

in which the resulting conditionally negative argument ( ^- S _i ) _{k of} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ is also active in the conditionally “k” “Minimization Zone” _- ) _{d / dn} . Therefore, in the system of the additional logical function f ₂ (}) - OR expressions (193), it is necessary to introduce two converted arguments ( ⁺ n _{i + 1} & ^- m _{i + 1} ) _k-1 and ( ^- n _{i + 1} & ⁺ m _{i + 1} ) _k-1 “k-1” “Minimization zones” of the additional “Activation conditions”, and write the functional structure for this situation in the form of an analytical expression (194),

which is the mathematical model of the functional structure for activating the resulting conditionally negative argument ( ^- S _i ) _{k of the} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} . It should be noted that in the functional structure (194) in the system of the input logical function f ₁ (}) - OR, the “Excessive argument” ( ⁺ n & m _{i + 1} ) _k is included, which in the logical-dynamic process of transforming the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (195)

active when the “Activation Condition ( ^- S _i ) _k ” is active, which will lead to the formation of a “Defect”. Therefore, we write the functional structure (194) in the form of an analytical expression (196),

in which the logical function f ₁ (}) - OR performs only the function of activating a conditionally negative argument ^{(+ ↓ -) d / dn} ( ^- S _i ) _{k of} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} , and write the functional structure that activates the positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _{k of the} local transfer f ₁ ( ⁺ ← ⁺ ) _{d / dn} in the form of an analytical expression (197).

Further, if we return to the analysis of the functional structure (166), which also performs only the function of activating the conditionally negative argument ^{(+ ↓ -) d / dn} ( ^- S _i ) _{k of the} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} , writing it in the form of an analytical expression (198),

and conduct a comparative analysis with the structure of logical functions (196), then they have different functional structures “Conditions of activation”. Therefore, we will carry out an additional analysis of the correctness of activation of the resulting conditionally negative argument ( ^- S _i ) _k , and for this we will form a graphoanalytic expression (199),

in which the functional structure (200) correctly activates the resulting conditionally negative argument ( ^- S _i ) _k . But the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (201),

in which the resulting conditionally negative argument ( ^- S _i ) _{k of the} functional structure (202) is activated with "Defect", since the transformed conditionally negative argument ( ^- n & m _{i + 1 is} not included in the logical function system f ₁ (} &) - OR ) _k-1 , which in this situation is the “Activation Condition”. Therefore, we write the functional structure (202) either in the form of an analytical expression (203),

either in the form of an analytical expression (204),

which correctly exclude the activation of the resulting conditionally negative argument ( ^- S _i ) _k , since the transformed conditionally negative argument ( ^- n & m _{i + 1} ) _{k-1 is} included in the logical function system f ₁ (} &) - OR NOT expressions (203), formed by the logical function f (&) - AND. And in expression (204), the correct result was obtained in connection with the inactivity of the transformed conditionally negative argument ( ^- n & m _{i + 1} ) _k-1 , formed by the logical function f (&) - AND NOT, which is included in the system of the output logical function f ₁ (&)-AND. But at the same time, in the conditionally “k” “Minimization Zone”, the positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge should be activated and it is activated through the functional structure (205),

and if we take into account that it will be included in the output system of the logical function of the general mathematical model of the adder ± f ₁ (Σ _RU ) _min , then we will minimize it, since in this implementation its technological cycle ∆t _Σ transforms the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min corresponds to

∆t _Σ → f (&) → f ₁ (}) → f ₂ (&) → f (}) _out → 4 ∙ f (&)

four conditional logical functions f (&) - And. And for this we write the vector structure (206)

transferring the output logical function through the system of the logical function and write the structure of the logical functions (207),

in which “Variant 1” and “Variant 2” are formed of a functional structure that activates the positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge with the technological cycle ∆t _Σ

∆t _Σ → f (&) → f ₂ (&) → f ₁ (}) _out → 3 ∙ f (&)

equal to three conditional logical functions f (&) - And.

     Further, if we return to the analysis of the functional structure (203), writing it in the form of an analytical expression (208)

and to the analysis of the functional structure (204), writing it in the form of an analytical expression (209)

then they can also be minimized. Because if you write down the functional structure (“Conditions”) with the output logical function f ₁ (} &) - OR NOT ↔ f ₂ (}) - OR = f ₁ (&) - NOT expressions (203) in the corrected form

and carry out the transfer of the logical function f ₁ (&) - NOT through the system of the logical function f ₂ (}) - OR, then its properties will change to the properties of the logical function f ₂ (&) - AND, and the further transfer of the logical function f ₁ (&) - NOT through the converted input arguments will change the logical function f (&) - AND → f (&) - AND NOT, by which they were formed, as a result, we write the adjusted functional structure (210).

And if we take into account that the adjusted functional structure (210) (“Conditions”) with the output logical function f ₂ (&) - And should be included in the system of the logical function f ₁ (&) - And expressions (208), then after combining the same logical functions, we write the analytical expression (211),

in which we carry out the transfer of the functional structure with the output logical function f ₁ (&) - AND through the system of the logical function f ₁ (}) - OR and write the analytical expression (212)

with the technological cycle ∆t _Σ

∆t _Σ → f (&) Vf (&) → f ₂ (&) → f ₁ (}) _out → 3 ∙ f (&)

equal to three conditional logical functions f (&) - And. It should be noted that the “Activation Conditions” of expression (212) must also be introduced into the functional structure (197), which activates the positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _{k + 1} local transfer f ₁ ( ⁺ ← ⁺ ) _{d / dn} logical differentiation procedures d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} in the conditionally “k-1” “minimization zone”,

but this “Activation Condition” (213) directly concerns only the converted input arguments ( ⁺ n _i & m _{i + 1} ) _k-1 and ( ⁺ n _{i + 1} & m _i ) _k-1 , because if we write down the logical-dynamic process of converting arguments terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (214),

then the activity of the positive transformed argument ( ⁺ n & m _{i + 1} ) _k-1 does not depend on the activity of the transformed conditionally negative argument ( ^- n & m _{i + 1} ) _k-2 conditionally "k-2""Minimizationzones". Therefore, we write the functional structure (213) for the next “k” of the “Minimization Zone” in the form of an analytical expression (215),

in which the general "Conditions 2" are introduced into the system of logical functions f ₁ (&) - And - f ₂ (&) - And to activate the positive resulting argument ( ⁺ S _i ) _k in this "Minimization zone" as a result of performing as a local transfer f ₁ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} activating the positive transformed argument ^{1 (+ ← +) d / dn} ( ⁺ S _i ) _k and ^{2 (+ ← +) d / dn} ( ⁺ S _i ) _k through the logical functions f ₁ (&) - And and f ₂ (&) - And, as well as the local transfer f ₁ ( ⁺¹ ← ⁺² ) of the double argument from the previous category, activating a positive transformation ized argument ^{(+ 1 ← + 2) (+} S _{ⁱ⁾ k} by f ₃ (&) logical functions - I. It should be noted that for all logical functions f ₁ (&) - And - f ₃ (&) - And “Conditions 2” is a general “Activation condition”, therefore, we form the logical-dynamic processes of transformation of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , in which the positive transformed argument ^{(+ 1 ← + 2)} ( ⁺ S _i ) _k is activated and we determine all possible conditions for it revitalization.

Version 1, 2 and 3. Activation of the positive transformed argument ^{(+ 1 ← + 2)} ( ⁺ S _i ) _k in the conditionally “k” “Minimization Zone” is possible in the graph-analytical expression (216)

in conditionally “k” ₁ “Zone of minimization” with simultaneous activity in the conditionally “i + 1” category of both positive arguments and conditionally negative arguments of the two terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , and in the conditionally “k” ₂ “Minimization zone” with the active zero argument “+1” “- 1” → “ ^± 0” in the conditionally “i” category and the “Activation conditions” in In this situation, we introduce into the system of the logical function f ₃ (&) - And expressions (215). As a result, we write the functional structure in the form of an analytical expression (217),

in which “Conditions 2” represent a functional structure with an output logical function f ₃ (&) - And with input converted arguments ( ⁺ n & m _{i + 1} ) _k , ( ^- n & m _{i + 1} ) _k , ( ⁺ n & ^- m _i ) _k and ( ^- n & ⁺ m _i ) _k , the activity of one of them activates, with the active converted argument ( ⁺ n & m _{i + 1} ) _k-1 activates the positive resulting argument ^{(+ 1 ← + 2)} ( ⁺ S _i ) _k . It should be noted that the technological cycle ∆t _Σ “Conditions 2” corresponds to

∆t _Σ → f (&) → f ₁ (}) → 2 ∙ f (&)

two conditional logical functions f (&) - And, and if we introduce “Conditions 2” into the system of logical functions f ₁ (&) - And and f ₂ (&) - And expressions (215), writing the analytical expression (218),

then the technological cycle Δt _{Σ of} activation of the intermediate arguments ^{1 (+ ← +) d / dn} ( ⁺ S _i ) _k and ^{2 (+ ← +) d / dn} ( ⁺ S _i ) _k will correspond

∆t _Σ → f (&) → f ₁ (}) → f ₁ (&) → f ₂ (}) → 4 ∙ f (&)

four conditional logical functions f (&) - And. But if the functional structure (218) is written in the form of a corrected analytical expression (219)

and carry out the transfer of functional structures with the output logical functions f ₁ (&) - AND and f ₂ (&) - AND with the same arguments through the logical function system f ₂ (}) - OR, then write the adjusted structure of the logical functions (220),

in which the technological cycle ∆t _{Σ of} activating the intermediate arguments ^{1 (+ ← +) d / dn} ( ⁺ S _i ) _k and ^{2 (+ ← +) d / dn} ( ⁺ S _i ) _k will also correspond

∆t _Σ → f (&) → f ₂ (}) → f ₁ (&) → f ₃ (}) → 4 ∙ f (&)

four conditional logical functions f (&) - And, but with a minimum number of logical functions, therefore it is an optimized structure of logical functions. And if you write graphoanalytic expression (221)

then “Condition 3” in the conditionally “k” ₂ “Minimization zone” is the transformed argument ( ^± n, ^± m _{i + 1} ) V ( ^± n, ^± m _i ) _{k of the} functional structure (222),

it should be noted that “Condition 2” of expression (220) and “Condition 3” of expression (222) are not functionally compatible, since the activity of one excludes the activity of the other. Indeed, to activate the transformed argument ( ^± n, ^± m _{i + 1} ) V ( ^± n, ^± m _i ) _k Condition 3 »↑ it is necessary that in the system of the logical function f ₁ (} &) - OR NOT expressions (222 ) all input arguments were inactive, and in this situation, if you activate the input arguments in accordance with the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min ( 223)

then the positive resulting argument ( ⁺ S _i ) _k in the functional structure (224) will not be activated. Therefore, it is necessary to introduce a functional additional structure “Conditions 3” of expression (222) into the system of the logical function f ₂ (}) - OR expressions (224) and write in the form of an analytical expression (225),

in which the positive resulting argument ( ⁺ S _i ) _{k is} correctly activated with the active positive argument ( ⁺ n & m _{i + 1} ) _k-1 local transfer f ₁ ( ⁺ ← ⁺² ), since it is active in the logical function system f ₁ (} &) -OR-NOT her transformed argument ( ^± n, ^± m _{i + 1} ) V ( ^± n, ^± m _i ) _k in conditionally “k” ₂ “Zone of minimization”. But if we analyze the procedure for activating the conditionally negative resulting argument ( ^- S _i ) _k in the conditionally “k” ₁ “Zone of minimization” of the graph-analytical expression (226), then it is activated with the active positive argument ( ⁺ n & m _{i + 1} ) _k-1 local transfer f ₁ ( ⁺ ← ⁺² ) and the active positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _{k of the} local transfer f ₁ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} . And this requires simultaneous activity in the “i” category of simultaneously two conditionally negative arguments ( ^- n & m _i ) _k terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , it should be noted that with an active positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _{k of} local transfer f ₁ ( ⁺ ← ⁺ ) _{d / dn} “Conditions 1” of the structure of logical functions (225) must be met . Therefore, it is advisable to write down these “Conditions 1” in the form of a separate functional structure with the output logical function f ₁ (&) - And in the analytical expression (227),

in which additional transformed positive arguments ^{(+ ← +) d / dn} ( ⁺ S _i ) _k ↑ and “ ⁺ Conditions ( ⁺ ← ⁺ ) _k-2 ” ↑ are introduced. As a result, the functional structure by which the conditionally negative resulting argument ( ^- S _i ) _k is activated is written as an analytical expression (228)

with the output logical function f ₁ (}) - OR and a non-optimized functional structure (211) can be introduced into its system, writing it in the form of the expression (230),

activating also a conditionally negative resulting argument ( ^- S _i ). It should be noted that a feature in the system of the output logical function f ₁ (&) - AND expressions (230) is the totality of the transformed arguments formed by the logical function f ₁ (&) - И-NOT, which in the system of this function activate the argument " Conditions 1 ” _k-1 conditionally“ k-1 ”“ Minimization zones ”, and this converted argument is included in the system of other logical functions. Therefore, it is advisable to write the functional structure (230) in the form of an analytical expression (231)

with the transformed positive argument “ ⁺ Conditions ( ⁺ ← ⁺ ) _k-1 ” conditionally “k-1” “Minimization zones”, while the logical function f ₁ (}) - OR, can be excluded from the functional structure (23) included in the structure of logical functions of expression (227).

As a result, after combining the functional structures (228) and (231), we write the analytical expression (232),

- система преобразованных аргументов, которые формирует одна функциональная структура, активизирующая положительный аргумент ^(+←+)d/dn(⁺S_i)_k↑ локального переноса f₁(⁺←⁺)_d/dn и условно отрицательный аргумент ^(+↓-)d/dn(^-S_i)_k↑ локального переноса f₁(⁺↓_-)_d/dn процедуры логического дифференцирования d₁/dn → f₁(⁺←↓_-)_d/dn. А, учитывая то, что в структуре логических функций выражения (232) включена функциональная структура преобразованного положительного аргумента «⁺Условия (⁺←⁺)_k-1»↑ условно «k-1» «Зоны минимизации», поэтому функциональную структуру (227) запишем в виде аналитического выражения (233)Where

                           - a system of transformed arguments that forms one functional structure that activates a positive argument^{(+ ← +) d / dn}(⁺S_i)_k↑ local transfer f_one(⁺←⁺)_{d / dn} and conditionally negative argument^{(+ ↓ -) d / dn}(^-S_i)_k↑ local transfer f_one(⁺↓_-)_{d / dn} logical differentiation procedures d_one/ dn → f_one(⁺← ↓_-)_{d / dn}. And, given the fact that in the structure of logical functions of expression (232) the functional structure of the transformed positive argument “⁺Conditions (⁺←⁺)_k-1"↑ conditionally" k-1 "" Zones of minimization ", therefore, we write the functional structure (227) in the form of an analytical expression (233)

with the converted positive argument “ ⁺ Conditions ( ⁺ ← ⁺ ) _k-2 ” conditionally “k-2” “Minimization zones”.

      Further, if we return to the analysis of the functional structure (205), writing it in the form of an analytical expression (234),

then, to activate the positive resulting argument ( ⁺ S _{i + 1} ) _{k of the} conditionally “i + 1” bit, the transformed argument ( ^- n & m _{i + 1} ) _k-1 is not a sufficient “Activation Condition”, since two more structures of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , the conversion of which also activates this argument. Therefore, we write the functional structure (234) in the form of an analytical expression (235),

into which it is necessary to introduce “Additional activation condition” conditionally “k-2” “Minimization zones”, and they directly relate only to conditionally transformed negative arguments ( ^- n _i & m _{i + 1} ) _k-1 and ( ^- n _{i + 1} & m _i ) _k-1 . Therefore, the functional structure (235), taking into account the functional structure (233), we write in the form of an analytical expression (236),

in which, as an “Additional activation condition”, a positive inactive transformed argument “ ⁺ Conditions ( ⁺ ← ⁺ ) _k-2 ” conditionally “k-2” of “Minimization zones” formed in the functional structure (231) is introduced into the system of a logical function. As a result, the functional structure (236) does not correctly activate the resulting conditionally negative argument ( ^- S _{i + 1} ) _{k of} conditionally “i + 1” of the discharge, but at the same time, in the conditionally “k-2” “Zone of minimization”, the conditionally negative argument ( ^- S _i ) _k conditionally “i” of the discharge, and for its activation a functional structure is formed (231). Therefore, we analyze its correctness of activating this argument, and for this we write the vector structure of the activation of arguments (237).

From the analysis of the vector structure of the activation of arguments in the functional structure (237) it follows that the resulting conditionally negative argument ( ^- S _i ) _k conditionally “i” of the discharge is activated correctly, but if we write down the structure of the arguments of the terms ± [n _i ] f ₁ (+/- ) _min and ± [m _i ] f ₁ (+/-) _min (238),

then the activation of this argument depends on the sequential activity of the transformed positive and conditionally negative arguments “ ⁺ Conditions ( ⁺ ← ⁺ ) _k ” → “ ^- Conditions ( ^- ← ^- ) _k-1 ” → “ ⁺ Conditions ( ⁺ ← ⁺ ) _k-2 ” → " ^- Conditions ( ^- ← ^- ) _k-3 ""Minimizationzones", which, in essence, belong to the category of through transfer f ₁ ( ⁺ ← ^- ← ⁺ ). And in this situation, ambiguity arises in activating both the resulting conditionally negative argument ( ^- S _i ) _k in the conditionally "k" ₁ "Minimization Zone" and the positive resulting argument ( ⁺ S _{i + 1} ) _k in the conditionally "k + 1" “Zone of minimization”, since the analysis of the previous “Zone of minimization” is necessary. A similar situation is possible in the conditionally “k” ₂ “minimization zone”, if we write the graphoanalytic expression (239),

where " ⁺ Conditions V ( ⁺ ← ⁺ ) _k " and " ^- Conditions V ( ^- ← ^- ) _k " is a positive and conditionally negative transformed argument of possible local transfers of the logical differentiation procedure d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} d ₂ / dn → f ₂ ( ^- ← ↑ ⁺ ) _{d / dn} , which is formed by the functional structure (240)

and through the functional structure (241),

which are formed by the logical function f ₁ (}) - OR and f ₂ (}) - OR in the conditionally "k""MinimizationZone", and the system includes two positive converted arguments ( ⁺ n _{i + 1} & m _i ) _k and ( ⁺ n _i & m _{i + 1} ) _k and conditionally negative arguments ( ^- n _{i + 1} & m _i ) _k and ( ^- n _i & m _{i + 1} ) _k, respectively. It should be noted that the converted argument ( ⁺ m _{i + 1} & n _i ) _k and ( ^- m _{i + 1} & n _i ) _{k are} not introduced into the system of logical functions f ₁ (}) - OR and f ₂ (}) - OR , since their activity does not lead to ambiguity when converting the arguments of the terms in the conditionally “k + 1” “minimization zone”. It should be noted that such an ambiguity in activating the resulting conditionally negative argument ( ^- S _i ) _k and the positive resulting argument ( ⁺ S _i ) _k in the conditionally “k” “minimization zone” is directly related to the alternating structure of positive doubles and conditionally negative arguments in the combined structure of the terms ± [S _i ] f ₁ (+/-) _min . And if we form a graphoanalytic expression (242),

then the transformation of the combined argument structure of the terms ± [S _i ] f ₁ (+/-) _min can be performed either through the procedure of logical differentiation of conditionally negative successively active arguments, as in expression (239),

or by applying the inverse arithmetic axioms “+2” “-1” → “+1” and “-2” “+ 1” → “-1”, as a result it will be formed in the “Minimization Zones” with an alternating structure of positive doubles and conditionally negative arguments conditionally minimized structure of the resulting sum ± [S _i ] f ₂ (+/-) _min . It should be noted that the transformation of such structures at the local level can be performed for the positive converted argument “ ⁺ Conditions V ( ⁺ ← ⁺ ) _k ” by means of the functional structure (243)

and the conversion can be performed for the conditionally negative transformed argument " ^- Conditions V ( ^- ← ^- ) _k " by means of the functional structure (244),

as a result, the transformed positive argument “ ⁺ Conditions V ( ⁺ ← ⁺ ) _k in the functional structure (243) activates the resulting conditionally negative argument ( ^- S _{i + 1} ) _k conditionally“ i + 1 ”bits, and the conditionally negative argument“ ⁺ Conditions V ( ⁺ ← ⁺ ) _k in the functional structure (244) activates the positive resulting argument ( ⁺ S _{i + 1} ) _k in the same category. It should be noted that all transformations of the arguments in the combined structure of the terms ± [S _i ] f ₁ (+/-) _min in expressions (244) and (245) are performed between the “minimization zones” using the inverse arithmetic axioms “+2” “-1” → “+1” and “-2” “+ 1” → “-1”. Similar transformations are performed when the argument structures of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min form either one positive transformed argument “ ⁺ Conditions V ( ⁺ ← ⁺ ) _k ”and activates the functional structure in this situation (245)

conditionally negative argument ( ^- S _{i + 1} ) _k , or one conditionally negative transformed argument " ^- Conditions V ( ^- ← ^- ) _k ", and in this situation the functional structure (246)

activates the positive argument ( ⁺ S _{i + 1} ) _k conditionally "i + 1" category. Moreover, the feature of functional structures (245) and (246) is the totality of the transformed arguments, and if we write them down for the conditionally “k” “Minimization Zones” in the form of an analytical expression (247)

and in the form of an analytical expression (248)

then the functional structures (247) and (248) are mathematical models of activating the conditionally negative argument ¹ ( ^- S _i ) _k and the positive argument ¹ ( ⁺ S _i ) _k in the combined structure of the terms ± [S _i ] f ₁ (+/-) _min , and to activate them, only two “Conditions” are needed. On the one hand, in the conditionally “k” “minimization zone” there should not be two arguments of the same name, therefore, the converted argument ( ⁺ nVm _i ) _k and ( ^- ) are introduced into the system of logical functions f ₂ (&) - AND f ₁ (}) ^- nVm _i ) _k, respectively, which are formed by the logical function f (&) - AND NOT. On the other hand, in conditionally “k” “Minimization Zone” there should not be an active logical zero “+1” “- 1” → “ ^± 0”, therefore, into the system of logical functions f ₂ (&) - And f ₁ (}) - OR the transformed argument ( ^- n & m _i ) _k and ( ⁺ n & m _i ) _k, respectively, which are formed by the logical function f (} &) - OR-NOT → (V), is entered. And if we write functional structures in the form of an analytical expression (249)

and in the form of an analytical expression (250)

then the functional structures (249) and (250) are mathematical models of activating the conditionally negative argument ¹ ( ^- S _{i + 1} ) _k and the positive argument ¹ ( ⁺ S _{i + 1} ) _k in the combined structure of the terms ± [S _i ] f ₁ ( +/-) _min conditionally "i + 1" category. As a result, the mathematical model of the adder ± f (Σ _RU ) _min conditionally "k""Minimizationzones" can be formed by analyzing the combined structure of the arguments of the terms ± [S _i ] f ₁ (+/-) _min , which will significantly accelerate its synthesis. Therefore, we return to the procedure for activating the resulting conditionally negative argument ( ^- S _{i + 1} ) _k conditionally “i + 1” of the discharge in the graph-analytical expression (243) and for the conditionally “k” “Minimization Zones” we write down the adjusted functional structure (251),

in which the feature is a conditionally transformed negative argument ( ^- S _i ) _{k + 1} conditionally “i” of the discharge conditionally “k + 1” “Minimization zones” and its activity is sufficient to activate the resulting argument. It should be noted that in the functional initial structure (243), the conditionally negative argument ↓ " ^- Conditions V ( ^- ← ^- ) _{k + 1} " in the system of the output logical function f ₁ (&) - And restricts the activation of the resulting argument, since the structure is possible the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min in the conditionally “k + 1” “Minimization Zone”, the transformation procedure of which is written in the form of a graphic-analytical expression ( 252)

in which the conditionally negative argument ↓ “ ^- Conditions V ( ^- ← ^- ) _{k + 1} ” conditionally “k + 1” “Minimization zones” is inactive, but the resulting argument ( ^- S _{i + 1} ) _k in this situation is conditionally “k »“ The minimization zone ”is activated correctly and the functional structure activates it (251). A similar result will be obtained in graphoanalytic expression (253),

when the conditionally negative argument ( ^- n & m _{i + 1} ) _{k-1 is} active in the conditionally “k-1” “Minimization Zone”, which is included in the functional structure (253) in the system of the additional logical function f ₂ (}) - OR and in which the conditionally negative argument is included ↓ " ^- Conditions V ( ^- ← ^- ) _k-1 " conditionally "k-1""Minimizationzones", because only with their activity can the resulting argument ( ^- S _{i + 1} ) _k be activated, and in all other situations it cannot be activated.

Situation 1. In the combined argument structure of the terms ± [S _i ] f ₁ (+/-) _min in the conditionally “k-1” “Minimization zone”, the conditionally negative argument ( ^- S _i ) _{k-1 is} active.

Situation 2. In the combined structure of the arguments of the terms ± [S _i ] f ₁ (+/-) _min in the conditionally “k-1” “Minimization Zone”, the positive argument ( ⁺ S _i ) _{k-1 is} active.

Situation 3. In the combined argument structure of the terms ± [S _i ] f ₁ (+/-) _min in the conditionally “k-1” “Minimization Zone” two conditionally negative arguments ( ^- S _i ) _k-1 are active.

Situation 4. In the combined argument structure of the terms ± [S _i ] f ₁ (+/-) _min in the conditionally “k-1” “Minimization Zone” two positive arguments ( ⁺ S _i ) _k-1 are active.

Since in graphoanalytic expressions (254) - (257) in the conditionally “k” “minimization zone”, a conditionally negative argument ^is activated ( ^- S _i ) _{k is} conditionally “i” of the discharge and the condition for its activation in the functional structure (237) is a conditionally negative argument ( ^- n & m _{i + 1} ) _k-1 and the positive transformed argument " ⁺ Conditions ( ⁺ ← ⁺ ) _k-1 ",

but if we analyze the conditions for the activity of a conditionally negative argument ( ^- S _i ) _k in the conditionally “i” category at the level of the combined structure of the arguments of the terms ± [S _i ] f ₁ (+/-) _min , then such one and only correct “Activation condition” is the inactivity of the combined argument ¹ ( ^± S _{i + 1} ) _k-1 → “ ^± 0” “i + 1” of the discharge in the conditionally “k-1” “Minimization Zone”, and we write it in the form of an analytical expression (259),

in which, in comparison with the functional structure (258), the number of input transformed arguments is minimized and included in the output logical function system f ₁ (&) - And only two transformed arguments ( ⁺ nVm _{i + 1} ) _k-1 and ( ^- nVm _{i + 1} ) _k-1 , formed by the logical function f (} &) - OR NOT. As a result, the combined argument ¹ ( ^{± 0} S _{i + 1} ) _k-1 “i + 1” of the discharge in the conditionally “k-1” “Minimization Zone” can be active only when in the functional structure (259) at the same time the positive transformed arguments ( ⁺ nVm _{i + 1} ) _k-1 and the conditionally negative transformed argument ( ^- nVm _{i + 1} ) _k-1 ^are active. And if we return to the analysis of the logical-dynamic processes of transforming the arguments of the terms (254) - (257) and activating the conditionally negative argument ( ^- S _i ) _{k of the} conditionally “i” discharge in the conditionally “k” “Zone”, then the functional structure for it activation we write in the form of an analytical expression (260).

And it includes a functional input structure with an output logical function f ₁ (}) - OR to activate a conditionally transformed conditionally negative transformed argument ^{(+ ↓ -) d / dn} ( ^- S _i ) _k local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn} and positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _k local transfer ^{(+ ← +) d / dn} ( ⁺ S _i ) _k logical differentiation procedures d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and includes functional input structure to the output of the logical function f ₁ (k) - and for activating the converted argument ^{1 (± 0} S _{i + 1) k-1} «i + 1" discharge conditionally «k-1""Zones mini ization ", which in the unified structure of summands ± [S _i] f ₁ (+/-) _min is inactive argument. It should be noted that the functional structure (260) is one of the functionally complete mathematical model, which in the conditionally “k” “Minimization Zone” activates the conditionally negative argument ( ^- S _i ) _k “i” of the discharge, which is essentially an argument ^{(+ ↓ -) d / dn} ( ^- S _i ) _{k of} local transfer f ₁ ( ⁺ ↓ _- ) _{d / dn} and is independent of the activity of the arguments conditionally “k-2” of “Minimization zones”. Since in the combined structure of the terms ± [S _i ] f ₁ (+/-) _min in the conditionally “k-1” “Minimization Zone” argument ¹ ( ^± S _{i + 1} ) _k-1 → “ ^± 0” “i + 1 »Of the discharge is inactive and possible active argument structures in the conditionally" k-2 "" Minimization Zone "can only activate the resulting argument of the sum in the conditionally" i + 1 "discharge conditionally" k-1 "" Minimization Zones "and such activation does not violate the logic the formation of the resulting conditionally minimized structure of the sum ± [S _i ] f ₂ (+/-) _min , which allows active arguments only between the "Minimization Zones". It should be noted that the uniqueness of activating the argument of the resulting sum ± [S _i ] f ₂ (+/-) _min in the conditionally “k” “Minimization Zone” is possible not only with the inactive argument ¹ ( ^± S _{i + 1} ) _k-1 → “ ^± 0” “i + 1” of the discharge “k-1” “Minimization zones”, but also with its active argument ¹ ( ^± S _{i + 1} ) _k-1 → “ ^± 1”, because if we return to the procedure for converting the terms (229), writing it down for positive arguments ¹ ( ⁺ S _{i + 1} ) _k-1 → “ ⁺ 1” in the form of expression (261),

and for conditionally negative arguments ¹ ( ^- S _{i + 1} ) _k-1 → " ^- 1" in the form of expression (263),

and return to the procedure for transforming the terms in expression (265),

then for the subsequent formalized synthesis of the resulting mathematical model conditionally “k” “Minimization zones” of the adder ± f (Σ _RU ) _min, it is necessary to analyze only all the structures of the positive arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min in the conditionally “k” “Minimization Zone” and write down the general analytical expression, and the general analytical expression for all structures of conditionally negative argument terms can be written down by changing the signs of the arguments in the analytical expression of the positive structure terms. Since arguments of different signs are equally probable, therefore, functional input structures with output logical functions f ₁ (&) - And and f ₂ (&) - And can be temporarily excluded from the functional structure (265), and we write it in the form of an analytical expression (266 )

in connection with their belonging to the activation of a conditionally negative argument ( ^- n & m _i ) _k and as a result of the transformation of this argument, a functional structure (262) was formed, which we write in the form of an analytical expression (266).

And the transformation of the positive transformed argument ( ⁺ n & m _i ) _k was performed in the functional structure (264), and if we write it in the form of an analytical expression (267),

then from a comparative analysis of functional structures (266) and (267) it follows that they are equivalent with the exception of signs of arguments. Therefore, the further synthesis of the mathematical model of the conditionally “k” “Minimization Zones” of the adder ± f (Σ _RU ) _min will analyze only all possible structures of the positive arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min in conditionally “k” “Minimization Zone”. And for this, taking into account the logic of forming a conditionally minimized structure of the arguments of the resulting sum ± [S _i ] f ₁ (+/-) _min , we write down all possible structures of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min , which can activate both the positive resulting argument of the sum ( ⁺ S _i ) _k and the conditionally negative argument ( ^- S _i ) _{k of the} conditionally “i” bit, and the positive resulting argument of the sum ( ⁺ S _{i +1} ) _k and conditionally negative argument ( ^- S _{i + 1} ) _k conditionally “i + 1” categories, and we will determine the conditions for their activation. Moreover, the “Activation Conditions” of all the resulting arguments ( ^± S _i ) _k and ( ^± S _{i + 1} ) _k should be limited, taking into account the active arguments only in the previous conditionally “k-1” and “k-2” “Minimization Zones”, because for some argument structures of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min, only the arguments are conditionally “k-1” and “k-2” “Minimization zones "Are the" Terms of activation. "

Situation 1. Activation of the positive resulting argument of the sum ( ⁺ S _i ) _k conditionally “i” of the discharge and “Condition of activation” in the conditionally “k” “Minimization zone” in the functional structure (268)

we write in the form of two converted arguments ↓ ¹ ( ^{± 0} S _{i + 1} ) _k conditionally “k” “Minimization zones” and a transformed argument ↓ ¹ ( ^{± 0} S _{i + 1} ) _{k + 1} conditionally “k-1” “Minimization zones ". It should be noted that if we return to the analysis of the functional structure (259), which we write in the form of an analytical expression (269),

then its converted argument ¹ ( ^{± 0} S _{i + 1} ) _k-1 can be used as an “Activation condition” only as a converted argument ¹ ( ^{± 0} S _{i + 1} ) _k-1 conditionally “k” “Minimization zones” with functional structure (270).

Since the active logical zero “+1” “- 1” _{i + 1} → “ ^± 0” in the conditionally “k” “Minimization Zone” with an active positive argument ( ⁺ n) _k or ( ⁺ m _i ) _k conditionally “i” the discharge of one of the terms and this is due to the conditions for the formation of a conditionally minimized structure of the arguments. Moreover, in the conditionally “k-1” “minimization zone”, if we write graphoanalytic expressions (271),

both an active logical zero “+1” “- 1” _{i + 1} → “ ^± 0” and an inactive logical zero are possible, and the functional structure of such activation can be written in the form of an analytical expression (273), in which, essentially, in the system logic function f ₁ (}) - OR three possible “Activation conditions” are included when logical zero “+1” “- 1” _{i + 1} → “ ^± 0” is not active (functional structure with output logic function f ₁ (} & ) -OR-NOT) and when it is active, in this situation either the converted argument ( ^- n & ⁺ m _{i + 1} ) _k-1 or the converted argument ( ⁺ n & ^- m _{i + 1} ) _{k-1 is} active. And if we take into account that the functional structure (272) will be included in the logical function system f ₂ (&) - AND expressions (268) with the output logical function f ₁ (}) - OR, writing the general structure of logical functions taking into account the functional structure (270 ) of the first “Conditions of activation” in the form of either an analytical expression (273),

or after combining the logical functions of the same name f ₃ (&) - And and f ₂ (&) - And we write down the structure of logical functions (274),

then the general technological cycle ∆t _{Σ of} activating the resulting argument of the sum will be increased to ∆t _Σ → 5 ∙ f (&) of five conditional logical functions f (&) - And. And to minimize the technological cycle ∆t _Σ → 4 ∙ f (&) to four conditional logical functions f (&) - And we write the functional structure (272) in the form of the expression (275),

in which we carry out the transfer of the functional structure with the output logical function f ₁ (}) - OR through the system of the logical function f ₁ (&) - And and write the structure of the logical functions (276).

Moreover, a feature of the functional structure (276) is the output logical function f ₁ (&) - And, which we introduce into the system of the output logical function f ₂ (&) - And expressions (274) and write the structure of the logical functions (277),

and after combining the logical functions of the same name f ₂ (&) - And and f ₃ (&) - And we write the corrected analytical expression (278).

From the analysis of the structure of logical functions (278) it follows that f ₂ (&) - And is included in the system of the output logical function as a transformed positive argument ( ⁺ nVm _{i + 1} ) _k and conditionally negative argument ( ^- nVm _{i + 1} ) _k conditionally “ k "" Minimization zones ", and by means of the logical function f ₁ (}) - OR and f ₂ (}) - OR the converted positive argument ( ⁺ nVm _{i + 1} ) _k-1 and conditionally negative argument ( ^- nVm _{i + 1} ) _k-1 conditionally "k-1""Minimizationzones". And since we are creating a mathematical model of the adder ± f (Σ _RU ) _min conditionally “k” “Minimization zones”, therefore, we write the adjusted structure of logical functions (279),

in which functional structures with output logical function f_one(}) - OR and f₂(}) - OR functionally belong to the conditionally “k” “minimization zone”, and the converted arguments (⁺nVm_{i + 1})_k and (^-nVm_{i + 1})_k  expressions (278) are written in the system of the output logical function f₂(&) - And through the converted arguments ↓^one(^{± 0V1}S_{i + 1})_k-1 and ↓^one(^{± 0V1}S_{i + 1})_k-1formed in conditionally "k-1" "Zone of minimization."  And if for the structure of the arguments of the terms ± [n_i] f_one(+/-)_min  and ± [m_i] f_one(+/-)_mintwo “Combination” to write graphoanalytic expression (280),

then the active converted arguments^one(^{± 0V1}S_{i + 1})_k↑ and²(^{± 0V1}S_{i + 1})_k↑ activated in conditionally “k” “Zone of minimization” in conditionally “k + 1” “Zone of minimization”, which, when analyzing the arguments of the terms in it will be conditionally “k” “Zone of minimization”, are active arguments conditionally “k-1” "Zone of minimization."   As a result, the functional structure (279) is one of the functional structures of the mathematical model of the adder ± f (Σ_RU)_min   conditionally “k” of the “Minimization Zone”, which activates a positive argument (⁺S_i)_kthe resulting amount.

Situation 2. Activation of the positive resulting argument of the sum of ( ⁺ S _i ) _k conditionally “i” bits in conditionally “k” “Minimization Zone” and its “Activation Conditions”, which include the analysis of active arguments in conditionally “k + 1”, “k "," K-1 "and" k-2 "" Minimization zones ",

with the active argument ¹ ( ⁺ S _{i + 1} ) _k-1 conditionally “i + 1” of the category, the functional structure of which will be included in the structure of logical functions, activating the positive resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” discharge. It should be noted that if we write the graphoanalytic expression (282),

then successively active positive arguments in the combined argument structure of the terms ± [S _i ] f ₁ (+/-) _min , positionally located between the “Minimization Zones” under certain “Activation Conditions”, are the resulting arguments. But the argument structures of the terms (283) - (285) are possible,

in which the unambiguous transformation of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min has only the combined argument structure ± [S _i ] f ₁ (+/-) _min , but in it the active arguments, taking into account the graph-analytical expression (285), are activated by functional double structures. On the one hand, for example, in graphoanalytic expressions (283) and (284), they are activated in the conditionally “i” category by means of the functional structure (248),

on the other hand, in the graph-analytical expression (285), the same positive resulting argument ¹ ( ⁺ S _i ) _{k is} activated in the conditionally “i” category by the transformed argument ( ⁺ n & m _{i + 1} ) _k-1 conditionally “k-1” “Minimization zones ". And if we combine them in the system of the logical function f ₁ (}) - OR, then we write the functional structure (286),

in which the resulting argument ¹ ( ⁺ S _i ) _k conditionally "i" discharge activated in two situations. And since the combined argument structure ± [S _i ] f ₁ (+/-) _min in the conditionally “i” discharge, the resulting argument ¹ ( ⁺ S _i ) _k conditionally “i” of the discharge may be inactive, therefore, we write the functional structure (287) ,

in which we combine the logical function f ₁ (&) - NOT with the logical function f ₁ (&) - AND and with the logical symbol (&) of the converted argument ( ⁺ n & m _{i + 1} ) _k-1 . As a result, we write the minimized functional structure (288)

with the output logical function f ₁ (&) - And. And if we write the graphoanalytic expression (289),

¹ ( ⁺ S _i ) _{k of the} functional structure (286) is correctly activated in the “Minimization zone” → “k” ₂ , and the combined argument ¹ ( ⁺ S _i ) _k with a changed signal level of the functional structure (288) is not correctly activated in the “Zone minimization ”→“ k ” ₁ . It should be noted that the combined argument ¹ ( ⁺ S _i ) _k was formed with a changed signal level to activate the output logical function f ₂ (&) - And, which activates the resulting argument of the sum ( ⁺ S _i ) _k in conditionally “i” discharge.

We write a functional similar structure for the combined argument ¹ ( ⁺ S _{i + 1} ) _{k of} conditionally “i + 1” discharge without a changed analog signal level in the form of a functional structure (290)

and for the combined argument ¹ ( ⁺ S _i ) _k conditionally “i + 1” discharge with a changed level of the analog signal in the form of a functional structure (291),

in which additional transformed arguments ( ⁺ n & m _i ) _k and ( ⁺ n & m _i ) _{k are} formed in the conditionally “k” “Minimization Zone”.

Further, if we return to the analysis of the procedure for activating the resulting argument of the sum ( ⁺ S _i ) _k in the graph-analytical expression (280), writing down its functional structure in the form of an analytical expression (292),

and for a comparative analysis of the correctness of the functional structure, we write the adjusted functional structure (293),

or after combining the logical functions of the same name f ₂ (&) - And - f ₄ (&) - And we write the optimized functional structure (294),

then the optimized functional structure (294) includes two “Variants” of activating the resulting argument ( ⁺ S _i ) _k , when as a functional structure (292) includes only “Variant 1”. Moreover, the structure of logical functions (294) includes only one functional structure “Activation conditions” with the output logical function f ₁ (&) - NAND, and the input converted arguments in its system correspond to the converted input arguments of “Option 1”, when the structure of logical functions (292) includes two functional structures “Activation conditions” with the output logical function f ₁ (}) - OR and f ₂ (}) - OR with other converted input arguments. But the technological cycle ∆t _{Σ of the} transformation of arguments in the functional structure (294) compared with the technological cycle ∆t _{Σ of the} conversion of arguments in the functional structure (292) is increased ∆t _Σ → 5 ∙ f (&) - And up to five conditional logical functions f ( &) - And, but it can be minimized if the functional structure is transferred with the “Activation Conditions” through the logical function system f ₁ (}) - OR.

As a result of such a transfer, we write the analytical expression (295)

with a technological cycle ∆t _Σ → 4 ∙ f (&) - And conversion of arguments, which corresponds to four conditional logical functions f (&) - And. But if in a functional structure with “Activation conditions” with the output logical function f ₁ (&) - AND-NOT expressions (294), and it corresponds to the sequence f ₁ (&) - And → f ₁ (&) - NOT, then we write optimized structure of logical functions (296)

with a technological cycle ∆t _Σ → 5 ∙ f (&) - And conversion of arguments, which corresponds to five conditional logical functions f (&) - And. Since the structure of logical functions (296) includes the transformed combined argument ↓ ¹ ( ⁺ S _{i + 1} ) _{k of} conditionally “i + 1” bits of the conditionally “k” of “Minimization Zones”, therefore it will form its functional structure, and for this we write an analytical expression, which activates the resulting argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge “k” of the “Minimization Zone” in the form of an unoptimized structure of logical functions (297).

And after combining the logical functions of the same name f ₂ (&) - And - f ₄ (&) - And we write the optimized structure of logical functions (298),

in which the functional structure with the output logical function f ₁ (&) - AND-NOT can be adjusted, since it corresponds to the sequence f ₁ (&) - And → f ₁ (&) - NOT with the input converted argument ¹ ( ⁺ S _i ) _k conditionally “i” of the discharge conditionally “k” of the “Zone of minimization”. And if the functional structure (296), activating the resulting argument ( ⁺ S _i ) _k conditionally “i” discharge write in the form of an analytical expression (299)

with the converted argument ( ^{0V ± 1} S _i ) _k ↑ with the changed level of the analog signal of the conditionally “i” discharge, then we write the structure of logical functions (298) as a functional structure (300)

with the transformed argument ( ^{0V ± 1} S _{i + 1} ) _k ↑ with the changed level of the analog signal conditionally “i + 1” of the discharge. It should be noted that in order to activate the transformed argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge, it is necessary to the system of logical function f ₂ (&) - And enter the “Additional activation condition”, which is the inactivity of two arguments conditionally “k-1” “Zone of minimization” of both positive arguments ¹ ( ⁺ S _{i + 1} ) _k-1 and ¹ ( ⁺ S _i ) _k-1 , and conditionally negative arguments ¹ ( ^- S _{i + 1} ) _{k- 1} and ¹ ( ^- S _i ) _k-1 . And the argument of the “Additional activation condition” at the level of the combined structure of the arguments of the terms ± [S _i ] f ₁ (+/-) _{min is} written as a structure of logical functions (301), and if it is introduced into the system of the logical function f ₂ (&) And expressions (300), then the technological cycle ∆t _{Σ of} transforming the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) will be significantly increased. Therefore, we return to the analysis of the functional structure (205), writing it in the form of a graphoanalytic expression (302),

with the structure of logical functions (303), which activates the positive argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1” discharge and in which, on the one hand, the technological cycle ∆t _Σ transforms the arguments of the terms ± [n _i ] f ₁ (+ / -) _min and ± [m _i ] f ₁ (+/-) _min corresponds to

∆t _Σ → f (&) → f ₁ (}) → f ₂ (&) → f (}) _out → 4 ∙ f (&)

four conditional logical functions f (&) - And. On the other hand, a functional structure with an output logical function f ₁ (}) - OR, which activates both the conditionally negative argument ^{(+ ↓ -) d / dn} ( ^- S _i ) _k and the positive argument ^{(+ ← +) d / dn} ( ⁺ S _i ) _k logical differentiation procedures d ₁ / dn → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} , in essence, is a functional structure for activating a positive transformed argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k . But in the system of this functional structure there are only two converted arguments ( ⁺ n _{i + 1} & m _i ) _k and ( ^- n _{i + 1} & m _i ) _k , and it does not take into account two other possible variants of the converted argument (( ⁺ n _{i + 1} ) _k & ( ⁺ n _{i + 1} & m _{i + 1} ) _k-1 ) _k and (( ⁺ m _{i + 1} ) _k & ( ⁺ n _{i + 1} & m _{i + 1} ) _k-1 ) _k ,

which forms a functional structure with the output logical function f (&) - And with three input arguments in its system. As a result, we write the structure of logical functions (303) in the form of an analytical expression (304),

in which the functional structure with the output logical function f ₁ (}) - OR activates the transformed argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k in the conditionally “k” “Minimization zone” without changing the level of the analog signal with the technological cycle ∆t _Σ → 2 ∙ f (&) - And with two conditional logical functions f (&) - And. And the functional structure is conditionally “k” of the “Minimization Zone”, by means of which the transformed argument “Additional activation condition” ( ^{± (11)} S ⁱ _{i + 1} ) _k-1 is activated after transferring the logical function f ₁ (&) - NOT in the expression ( 305)

through the system of the logical function f ₁ (}) - OR, which will lead to a change in its logical properties to the properties of the logical function f ₁ (&) - AND. And further combining the transferred logical function f ₁ (&) - NOT with the logical symbol (&) of the input converted arguments will lead to the change of the logical symbol (&) → (&) to the symbol of the logical function f ₁ (&) - AND NOT. As a result, we write the adjusted functional structure with the output logical function f ₁ (&) - And in the form of an analytical expression (306),

in which the technological cycle ∆t _Σ → 2 ∙ f (&) - And the transformation of the arguments corresponds to two conditional logical functions f (&) - And, but if we take into account that the functional structure with the output logical function f ₁ (&) - And is included in system of the logical function f ₂ (&) - And (307),

then the technological cycle ∆t _Σ → 1 ∙ f (&) - AND of the “Additional activation conditions” corresponds to one conditional logical function f (&) - And, and the technological cycle ∆t _Σ “Additional activation conditions” taking into account the logical functions f ₂ ( &) - AND f ₂ (}) - OR corresponds to ∆t _Σ → 3 ∙ f (&) - AND to three conditional logical functions f (&) - And. It should be noted that to minimize the analytical record of the structure of logical functions (307), the technological cycle ∆t _Σ → 4 ∙ f (&) - And of the “Additional activation conditions” can be increased to four conditional logical functions f (&) - And, and for this we will correct the functional structure (306) and write it in the form of parallel sequential logical functions of the same name f ₁ (&) - And ║ f ₂ (&) - And → f ₃ (&) - And (308),

and after transferring the logical functions f ₁ (&) - NOT through the system of the logical function f ₁ (&) - And and f ₂ (&) - And, which will lead to a change in their logical properties to the properties of the logical function f ₁ (}) - OR and f ₁ (}) - OR. And after combining them with the transferred logical function f ₁ (&) - DO NOT write the optimized analytical expression (309),

in which only the "Positive arguments" included in the logical function system f ₁ (} &) - OR NOT activate the converted positive argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k-1 ↑, which is the input argument of the functional structure of the conditionally negative adder channel ± f (Σ _RU ) _min conditionally “k” “Minimization zones”. And such a redistribution of the functional structures of “Positive arguments” and “Conditionally negative arguments” of the structure of logical functions (308) allows us to optimize the analytical expression (307) and write it in the form of a functional structure (310),

in which the positive “Additional activation condition” is included in the system of the logical function f ₂ (&) - AND in the form of a functional structure with the output logical function f ₁ (} &) - OR NOT and the transformed conditionally negative argument ↓ ( ^{- (11)} S ⁱ _{i + 1} ) _k-1 . Since the “Activation Condition” includes the transformed argument ↓ ( ^{0V ± 1} S _i ) _k with the changed level of the analog signal, which, to activate the positive resulting argument of the sum ( ⁺ S _{i + 1} ) _k, includes a sequence of logical functions f ₁ (&) - And → f ₁ (&) is NOT, and it leads to an increase in the technological cycle ∆t _Σ → 5 ∙ f (&) - And conversion of arguments, therefore, we will combine them f ₁ (&) - And + f ₁ (&) - NOT → f ₁ (&) - AND NOT and write the minimized functional structure in the form of an analytical expression (311).

Moreover, the sequence of logical functions f ₁ (&) - AND → f ₁ (}) - OR → ¹ ( ⁺ S _{i + 1} ) _k ↑ in expression (310), which, in essence, forms the combined argument of the term ¹ ( ⁺ S _{i + 1} ) _k , we also adjust in accordance with the vector structure of the transfer of functional structures (312)

and write the structure of logical functions (313)

with three input logical functions f ₁ (}) - OR - f ₃ (}) - OR, forming the "Complex argument", and the output logical function f ₁ (&) - AND. As a result, we write the structure of logical functions (310) in the form of an analytical expression (314),

in which the “Complex argument” “Variants ¹ ( ⁺ S _{i + 1} ) _k ” is introduced into the system of the logical function f ₁ (&) - And with the symbol (≡) - the totality of functional digital connections. To minimize the analytical form of writing the mathematical model of the adder ± f (Σ _RU ) _min conditionally “k” “Minimization zones” using the “Complex argument” in the functional structure (314) we write the set of converted arguments

and the totality of the converted arguments,

as a result, we write it in the form of an analytical expression (315).

Further, if we return to the analysis of the procedure for converting the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min in expression (304),

in which the positive resulting argument of the sum ( ⁺ S _{i + 1} ) _k is also activated, it is activated through the functional structure (316) only for one of the possible active conditionally negative arguments ( ^- n & m _{i + 1} ) _k-1 , and the remaining four variants that the functional structure activates (317)

conditionally negative adder channel f (Σ_RU)_min   in “k-1”, the “minimization zone” is not included in the functional structure (316). But if through the logical function f₃(}) - OR enter into the functional structure (317) the transformed conditionally negative argument (^-(eleven)Sⁱ _{i + 1})_k  and write down the structure of logical functions (318),

in which we perform the union of the logical functions of the same name f ₁ (}) - OR and f ₂ (}) - OR, as a result, we write the analytical expression (319).

with technological cycle ∆t_Σ→ 4 ∙ f (&) - And four conditional logical functions f (&) - And. Moreover, from the analysis of positive and functional structures with output logical functions f_one(}) - OR and f₂(}) - OR it follows that if the system of logical function f_one(}) - OR enter an additional converted positive argument (⁺n & m_{i + 1})_k-1then from the system  logical function f_one(&) - And the functional structure with the output logical function f can be excluded₂(}) - OR, and instead, into a minimized analytical expression (320)

transformed conditionally negative argument ↓ ( ^{- (11)} S ⁱ _{i + 1} ) _k .

     Since the functional structure of the transformed conditionally negative argument (^-(eleven)Sⁱ _{i + 1})_k↑    in expression (319) and the functional structure of the transformed positive argument (^{+ (11)}Sⁱ _{i + 1})_k↑ in the expression were adjusted, which are formed at the level of analysis of the arguments of the terms ± [n_i] f_one(+/-)_min  and ± [m_i] f_one(+/-)_min, therefore, let us return to the functional structure (310), writing it in the form of a graphic-analytical expression (321).

From the analysis of the structure of the arguments of the terms ± [n _i ] f ₁ (+/-) _min and ± [m _i ] f ₁ (+/-) _min (322) it follows that the logical function system f ₁ (} &) is OR -NOT it is necessary to introduce an additional transformed argument ( ⁺ n & m _{i + 1} ) _k-1 , and from the logical function system f ₂ (&) - And it is necessary to exclude the positive “Excessive argument” ( ⁺ n & m _{i + 1} ) _k , since it is included in logical function system f ₁ (&) - And to activate the combined argument ¹ ( ⁺ S _{i + 1} ) _k . It should be noted that if the converted argument ( ⁺ n & m _i ) _k is active in the logical function system f ₁ (}) - OR without changing the level of the analog signal, then the conditional “k” “Minimization zone” transforms the argument ( ⁺ n & m _{i + 1} ) _k with a changed analog signal level is always active. As a result, after combining the functional structures (220) and (221), we activate the resulting argument ( ⁺ S _{i + 1} ) _{k of the} “i-1” discharge in the form of an analytical expression (323),

where “Variants ¹ ( ⁺ S _{i + 1} ) _k ” is the “Complex argument” of the structure of logical functions (313), which we write in the form of an analytical expression (324).

It should be noted that since the structure of logical functions of expression (323) includes a functional structure with an output logical function f ₁ (}) - OR and a functional structure with an output logical function f ₁ (} &) - OR NOT with the same converted arguments . Therefore, their converted arguments are written as the argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k ↑ conditionally “k” “Minimization zones” without changing the level of the analog signal and as the argument ( ^{+ (11)} S ⁱ _{i + 1} ) _{k -1} ↑ conditionally “k-1” “Minimization zones” with a changed analog signal level, respectively. And, taking into account the fact that they form the mathematical model conditionally “k” of the “Minimization Zone”, therefore, from the structure of logical functions (323) a functional structure with an output logical function f ₁ (} &) - should NOT be excluded and presented in the form of a transformed argument ↓ ( ^{+ (11)} S ⁱ _{i + 1} ) _k-1 conditionally “k-1” “Minimization zones”. Moreover, the “Complex argument” “Variants ¹ ( ⁺ S _{i + 1} ) _k ” conditionally “i + 1” category, which includes three functional structures and is included in the system of the logical function f ₁ (&) - And expressions (323), is included of activity activates the positive resulting argument of the sum ( ⁺ S _{i + 1} ) _k , therefore, we analyze the possibility of activating it to introduce the transformed argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k ↑ conditionally “k” “Minimization zones” with a changed analog signal level . And for this we return to an additional analysis of the adjusted functional structure (321), writing it in the form of a structure of logical functions (325),

in which a positive functional structure is introduced that forms the transformed argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k ↑ and the conditionally negative transformed argument ↓ ( ^{- (11)} S ⁱ _{i + 1} ) _k conditionally “k” “Minimization zones” with altered analog signal level. As a result, on the one hand, in the logical function system f ₁ (&) - And with the corrected “Activation conditions” of the resulting argument of the sum ( ⁺ S _{i + 1} ) _{k, the} transformed argument ( ⁺ n & m _{i + 1} ) _k with the changed level of the analog signal is “ An extra argument ”, since its function is performed by the converted argument ( ⁺ n & m _{i + 1} ) _k without changing the level of the analog signal in the logical function system f ₁ (} &) - OR NOT. On the other hand, the “Excessive arguments” ↓ ( ^{0V ± 1} S _i ) _{k + 1} and ↓ ( ^{0V ± 1} S _i ) _k conditionally “i” bits “k + 1” are included in the system of the logical function f ₂ (&) - And “Minimization zones” and “k” “Minimization zones”, respectively, and the logical function system f ₁ (}) - OR includes an excess transformed argument ( ⁺ n & m _i ) _k “Option 2” for activating the resulting argument of the sum ( ⁺ S _{i + 1} ) _k . And if the input argument ↓ ( ^{0V ± 1} S _i ) _{k + 1} conditionally “i” of the discharge “k + 1” “Minimization zones” can be excluded due to the fact that this condition is redundant, since the argument ¹ ( ⁺ S _{i +1} ) _k “Option 1” satisfies the logic of forming a conditionally minimized amount, then the input argument ↓ ( ^{0V ± 1} S _i ) _k conditionally “i” of the discharge “k” of the “Minimization zone” can be excluded due to the fact that it has been changed functional structure, which we write in the form of an analytical expression (326)

with the output logical function f ₁ (&) - NAND, which we introduce in the adjusted functional structure (325). As a result, we write the adjusted structure of logical functions (325) in the form of an analytical expression (327).

In this case, the functional structure by which the transformed argument ( ⁺ n & m _i ) _k “Option 2” is activated is written in the form of an analytical expression (328),

in which only two converted arguments ↓ ( ^{+ (11)} S ⁱ _{i + 1} ) _k-1 and ↓ ( ^{- (11)} S are the condition for activating the resulting argument of the sum of ( ⁺ S _{i + 1} ) _k conditionally “i + 1” bits ⁱ _{i + 1} ) _k-1 . And this functional structure is correctly inactive if the structure of the arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min includes an active positive argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k-1 conditionally “k-1” “Minimization zones” (329),

then, to form a minimized structure of the arguments, the sums ^± [S _i ] f ₂ (+/-) _min carry out the procedure of logical differentiation d ₁ / dn ⁺ → f ₀ ( ⁺ ← ↓ _- ) _{d / dn of a} positive sequence of arguments taking into account the arithmetic axiom “ ^± 0 "→" +1 "" - 1 ". At the same time, in the conditionally “k” “Minimization Zone”, the resulting conditionally negative argument of the sum ( ^- S _i ) _{k is} conditionally “i + 1” of the discharge, taking into account the inverse arithmetic axiom “-2” “+ 1” → “-1”. But the procedure of activating conditionally negative arguments activated by using the arithmetic axiom “ ^± 0” → “+1” “–1” can be excluded. Since in the conditionally “k” “Minimization Zone” the second positive argument can be transformed using the arithmetic axiom “+1” → “+2” “- 1” and in this situation we write the graphoanalytic expression (329) as expression (330),

in which the activation of the arguments is also carried out in accordance with the procedure of logical differentiation d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} and activate it by means of the functional structure (331).

And if the activity is a conditionally negative argument (^-S_i)_k conditionally “i” of the discharge is unique, then the activity of the arguments of local transfers f_one(⁺←⁺)_{d / dn}and f_one(⁺↓_-)_{d / dn} logical differentiation procedures d_one/ dn⁺ → f_one(⁺← ↓_-)_{d / dn}  essentially depends on the active arguments in the conditionally “k + 1” and “k-2” “Minimization Zones”, so we will form all possible options for activating the resulting sum arguments in these “Minimization Zones”. And since the resulting argument of the sum of local carry f_one(⁺←⁺)_{d / dn}and f_one(⁺↓_-)_{d / dn} can be activated in conditionally “i” category, therefore the functional structure of a positive argument (⁺S_i)_k of this category in the conditionally “k” “minimization zone” when it is activated without conversion, and we write this structure of logical functions in the form of an analytical expression (332).

in addition, a positive argument ( ⁺ n & m _{i + 1} ) _{k was} introduced to form an intermediate argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k ↑, common to two conditional digits in the “k” “Minimization Zone”. Since if we return to the analysis of the functional structure (327), which activates the resulting argument of the sum of ( ⁺ S _{i + 1} ) _k conditionally “i + 1” bits, writing it in the form of an analytical expression (333),

then a positive input argument ( ⁺ n & m _{i + 1} ) _{k is} introduced into the system of the logical function f ₁ (} &) - OR NOT, and to minimize the mathematical model of the adder ± f (Σ _RU ) _{min, the} conditional “k” of the “Minimization zone” is functional the structure in expression (333) with the logical function f ₁ (} &) - OR can NOT be replaced by an intermediate argument ( ^{+ (11)} S ⁱ _{i + 1} ) _k , as a result, we write the adjusted structure of logical functions (333) in the form minimized analytic expression (334)

and the structure of logical functions (332) can also be written with the transformed positive argument ↓ ( ^{+ (11)} S ⁱ _{i + 1} ) _k in the system of the logical function f ₂ (&) - And in the form of an analytical expression (335).

Moreover, the functional structure with the output logical function f ₁ (} &) - OR NOT expressions (332) for generating positive arguments ( ^{+ (11)} S ⁱ _{i + 1} ) _k ↑ and ( ^{+ (11)} S ⁱ _{i + 1} ) _k ↑ without changing the level of the analog signal and with a changed level of the analog signal, we write accordingly in the form of a structure of logical functions (336).

And if we take into account that when analyzing the active arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min in the conditionally “k” “Minimization Zone”, converted arguments are also possible ( ⁺ n & m _{i + 1} ) _k and ( ⁺ n & m _i ) _k , as well as the transformed arguments of the functional structure (337),

which form in this zone the arguments ( ^{+ (1x1)} S ⁱ _{i + 1} ) _k ↑ and ( ^{+ (1x1)} S ⁱ _{i + 1} ) _k ↑ local transfers with a constant level of the analog signal and with a changed level of the analog signal, therefore, to minimize analytical records of the analyzed structures of logical functions that activate the resulting arguments, we will use only the converted arguments.

And if we write down the structure of the arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min (338),

then for the synthesis of the mathematical model of the adder ± f (Σ_RU)_min  conditionally “k” “Minimization zones” with the technological cycle ∆t_Σ→ 4 ∙ f (&) - And it is necessary to form additional transformed arguments in which the technological cycle ∆t_Σ→ 2 ∙ f (&) - And should not exceed two conditional logical functions f (&) - And. And such functional structures are analytical expressions (339), which activate as a transformed argument (("^{± 1}0 ") Sⁱ _{i + 1})_k↑ active logical zeros “+1” “- 1” → “^{± 1}0 "_iV "^{± 1}0 "_{i + 1}, and the converted argument of inactive logical zeros "^±0 "_i& "^±0 "_{i + 1}    in conditionally “i + 1” and “i” digits in the “k” “Minimization Zone” and which are a necessary and sufficient condition for activating a positive argument (⁺n & m_{i + 1})_k-1 and a positive argument (^{+ (1x1)}Sⁱ _{i + 1})_k-1 expressions (337) “k-1” “Minimization zones” in the conditionally “k” “Minimization zone”. It should be noted that since the converted arguments (("^{± 1}0 ") Sⁱ _{i + 1})_k and (("^±0 ") Sⁱ _{i + 1})_k at the level of the unified argument structure^±[S_i] f_one(+/-)_min, for example, in the structure of the arguments of the terms^±[n_i] f_one(+/-)_min  and^±[m_i] f_one(+/-)_min   (340)

are equally probable, and their combination will lead to an increase in the technological cycle ∆t _Σ → 4 ∙ f (&) - And the transformation of the arguments of the terms, but will greatly simplify the synthesis of the mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization zones”, therefore, at the preliminary stage of its synthesis, it will form a functional structure (341)

with a complex argument ((" ^± 0V ^{± 1} 0") S ⁱ _{i + 1} ) _k , combining the five possible input arguments that allow us to uniquely activate the resulting arguments of the sum. Moreover, if we analyze the technological cycle ∆t _Σ , for example, of a 32-bit adder f ₁ (Σ) with accelerated transfer, writing it in the form of expression (342),

then the sequence of conditional logical functions (lf) → f (&) - And taking into account the procedure of accelerated end-to-end transfer f (← begin) ₃₂ will correspond to 15 _lf & 3 _lf → 18 _lf or ∆t _Σ → 18 ∙ f (&) - And eighteen conditional logical functions f (&) - And. And the adder technological cycle ^± f ₁ (Σ _RU ) _min with ∆t _Σ → 4 ∙ f (&) - And and with ∆t _Σ → 5 ∙ f (&) - And is minimized by 4.5 and 3.5 times compared with the technological cycle of expression (342), while increasing the functional structure of the adder ^± f ₁ (Σ _RU ) _min by one conditional logical function f (&) - And leads to an increase of ↑ ∆t _Σ → by 25%, which leads to a a substantial increase in it. Therefore, after synthesizing the mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” of the “Minimization Zone”, we analyze the practical feasibility of forming a functional structure (341) with a technological cycle ∆t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And. And there is such a possibility, because if in the structure of logical functions (341) carry out the transfer in accordance with the vector structure (343),

functional structure with the output logical function f ₁ (}) - OR through the system of the logical function f ₁ (&) - AND, then we write the structure of the logical functions (344),

which includes four functional input structures with output logical functions f ₁ (}) - OR - f ₄ (}) - OR, which activate a set of complex arguments ^1-4 ((" ^± 0V ^{± 1} 0 ^& ") S ⁱ _{i + 1} ) _k ↑, are the “Conditions of activation” of the activated argument structure “Activated argument” of the terms in the analytical expression (345).

As a result, the technological cycle ∆t _Σ → 4 ∙ f (&) - and the formation of the resulting sum argument in the functional structure (345) with the complex “Activation condition” ↓ ^1-4 ((“ ^± 0V ^{± 1} 0 ^& ”) S ⁱ _{i +1} ) _k will correspond to four conditional logical functions f (&) - And.

    Further, if we return to the analysis of the structure of the arguments of the terms (104), writing down their logical-dynamic transformation process in the form of a graphic-analytical expression (343),

then to activate the local transfer argument f ₁ ( ⁺ ↓ _- ) _{d / dn} , f ₂ ( ⁺ ↓ _- ) _{d / dn} and f ₂ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d _1,2 / dn ⁺ → f _1,2 ( ⁺ ← ↓ _- ) _{d / dn} , functional structures (344) must be formed with the converted positive arguments ( ⁺ S ⁱ | _{i + 1} ) _k and ( ⁺ S _i | ^{i + 1} ) _k , which are activated between " Zones of minimization ”and in which the superscript ( ⁱ | _{i + 1} ) and ( _i | ^{i + 1} ) of the discharge of the combined argument corresponds to the conditionally“ k ”of“ Zones of minimization ”. It should be noted that the converted positive argument ( ⁺ S ⁱ _{i + 1} ) _k conditionally “k” of the “Minimization Zone” was previously generated and it is active when two consecutive arguments in the “Minimization Zone” are active. As a result of the introduction of intermediate or “Complex arguments” functionally belonging to the combined structure ^± [S _i ] f ₁ (+/-) _min , and it will significantly simplify the synthesis of the mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “ Minimization Zones. ” But for this it is necessary to analyze the logical-dynamic process of converting arguments to the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min and form additional “Complex arguments” at the level of the combined structure the arguments of the terms ^± [S _i ] f ₁ (+/-) _min , which took into account the characteristic structural “Features” of the terms and allowed to indirectly perform the end-to-end transfer procedure with the simultaneous formation of the arguments of the conditionally minimized sum ^± [S _i ] f ₂ (+/- ) _min . So, for example, in graphoanalytic expression (343), “Feature” is an alternating sequence of positive arguments in the combined term structure ^± [S _i ] f ₁ (+/-) _min , which has uniquely correct transformation only with the indirect logical differentiation procedure d ₀ / dn ⁺ → f ₀ ( ⁺ ← ↓ _- ) _{d / dn} , for example, in the graph-analytical expression (345),

in which, through the functional structure (346) with the output logical function f ₃ (&) - And the “Complex argument” ¹ ( ⁺¹⁰ S _{i + 1} ^& ) _k “i + 1” bits in the conditionally “k” “Minimization zone” is activated . It should be noted that a feature of the functional structure (346) is the output logical function f ₃ (&) - And, which, if we write it in the form of an analytical expression (347),

may include the complex argument “Activation conditions” to activate the resulting conditionally negative argument of the sum ( ^- S _i ) _k conditionally “i” of the category “k” “Minimization zones”. The resulting conditionally negative argument of the sum ( ^- S _i ) _{k of the} conditionally “i” discharge in the graph-analytical expression (345) is also activated in the situation when before the sequence of positive arguments in the combined structure of the terms ^± [S _i ] f ₁ (+/-) _min at least two conditionally negative arguments are activated in a continuous sequence. Indeed, if we write the structure of logical functions (348),

which activates the resulting conditionally negative argument of the sum ( ^- S _i ) _{k of} conditionally “i” discharge in various situations and which, for the sake of uniqueness, we write in the form of a graphoanalytic expression (349),

then the transition to the level of "Complex arguments" activated in the combined structure of the terms ^± [S _i ] f ₁ (+/-) _min , functionally related to the particular structure being analyzed, will correctly form the mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally " k "" Zone of minimization. "

Since a functional structure is formed that activates a conditionally negative argument of the sum ( ^- S _i ) _{k of} conditionally “i” bits in the “k” “Minimization Zone” when converting positive arguments, we therefore write for the other possible “Combinations” of positive arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min (350)

functional additional structures (351) that activate the same conditionally negative argument of the sum ( ^- S _i ) _k . At the same time, a functional structure with an output logical function f ₁ (&) - And was introduced into the system of logical functions f ₂ (&) - And and f ₃ (&) - And, which activates the transformed argument of inactive logical zero “ ^± 0” to conditionally “i +1 ”category and functional structure with the output logical function f ₁ (}) - OR, activating the transformed argument of active logical zero“ ^± 0 ¹ ”in the conditionally“ i + 1 ”category. And if these functional structures are written in the form of the corresponding converted arguments ((“ ^± 0”) S _{i + 1} ^& ) _k-1 and ((“ ^± 0 ¹ ”) S _i ^& ) _k-1 conditionally “i-1” bits with the corresponding combined argument structure of the terms ± [S _i ] f ₁ (+/-) _min , then we write the graph-analytical expression (352),

which we then combine with the graphoanalytic expression (348) and write the combined structure of logical functions (353).

As a result, the conditionally negative argument of the sum ( ^- S _i ) _{k of the} conditionally “i” discharge when converting the positive arguments of the combined terms ^± [m _i ] f ₁ (+/-) _min can be activated in six different situations. Moreover, from the analysis of the argument conversion procedure of the conditionally “k” “minimization zone” it follows that the functional structure with the output logical function f ₃ (&) - AND is included in the output system of the logical function f ₁ (}) - OR is not correct. Since the conditionally negative argument ¹ ( ^- S _{i + 1} ) _k is transformed into the “minimization zone” in connection with the active positive local transfer argument f ₁ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure d ₁ / dn ⁺ → f ₁ ( ⁺ ← ↓ _- ) _{d / dn} , therefore, it functionally relates to the structure of the conditionally negative adder channel ± f (Σ _RU ) _min and therefore the functional structure with the output logical function f ₃ (&) - И (354)

it is necessary to exclude from the system the output logical function f ₁ (}) - OR expressions (353) and write in the form of a structure of logical functions (355).

As a result, the conditionally negative argument of the sum ( ^- S _i ) _{k of the} conditionally “i” discharge when transforming the positive arguments of the combined terms ^± [m _i ] f ₁ (+/-) _min can be activated at the first stage of synthesis in five different situations. But there are argument structures of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min (356),

in which the conditionally negative argument of the sum ( ^- S _i ) _{k of} conditionally “i” discharge is also activated. Therefore, for a positive “ ⁺ Combination 3”, we write the functional structure (357),

for a positive “ ⁺ Combination 4” we write the functional structure (358),

for a positive “ ⁺ Combination 5”, we write the functional structure (359),

which can be written as a combined expression (360) (360)

And if functional combined structures (360) are introduced into the system of the output logical function f ₁ (}) - OR expressions (355), then the functionally complete structure of the logical function can be written as an analytical expression (361).

It should be noted that the structure of logical functions (361), which activates a conditionally negative argument of the sum ( ^- S _i ) _k conditionally “i” the discharge and is formed as a result of the transformation of the positive arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min , functionally refers to the structure of the conditionally negative adder channel ± f (Σ _RU ) _min . And when converting conditionally negative ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min in similar structural situations, the positive argument of the sum ( ⁺ S _i ) _k conditionally “i »Discharge, and such a functional structure can be written in a formalized way by changing the signs of the arguments in expression (362).

From the analysis of the procedure for activating the positive argument of the sum ( ⁺ S _i ) _{k of} conditionally “i” bits in the conditionally “k” “Minimization” zone of expression (362), it follows that all functional structures with output logical functions f ₁ (&) - And - f ₈ (&) - And they activate it correctly. It should be noted that since the formalized method of writing the functional structure that activates the argument of the resulting sum of the opposite sign is correct, therefore, we will continue to analyze and form additional structures for the “Positive channel of the adder“ i ”category” and for the “Conditionally negative channel of the adder“ i "Discharge". And for this, we return to the analysis of the expression (345, writing it in the form of a graphoanalytic expression (363)

and additional analysis of the functional structure with the output logical function f ₁ (&) - And, activating the resulting conditionally negative argument of the sum ( ^- S _i ) _k . Since if we write down the possible arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min in the form of a graph-analytical expression (364),

then it is necessary to introduce an additional transformed argument ¹ ((“ ^± 0”) S _i ) _{k of} inactive logical zero into the logical function system (363), and write the functional structure in this situation in the form of an analytical expression (365), and only it can correctly activate the resulting conditionally negative argument of the sum ( ^- S _i ) _k . Therefore, we introduce this functional structure into the structure of logical functions of the “Conditionally negative channel of the adder“ i ”category” (361), which we write in the form of expression (366).

And the functional structure that activates the positive argument of the sum ( ⁺ S _i ) _k in the "Positive channel of the adder" i "category", we write in the form of an analytical expression (367)

and introduce it into the structure of logical functions of the “Positive channel of the adder“ i ”category” (362), which we write in the form of an analytical expression (368).

     Further, to form the functionally complete “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” it is necessary to form functional additional structures of local transfers in the following situations.

      Situation 1. The arguments of the opposite sign are active in the conditionally “k” “Minimization Zone” and the “Activation Conditions” are active, which we write in the form of a graphic-analytical expression (369)

and which are converted in accordance with the arithmetic axioms “+2” “-1” → “+1” and “-2” “+1” → “-1”, but with specific “Conditions of activation”, and we write these conditions in the form different options. And for the formation of analytical additional structures for the “Positive and conditionally negative channel of the adder“ i ”category” of the first situation, we write the converted arguments, the technological cycle of which ∆t _Σ → 2 ∙ f (&) - And minimized to two conditional logical functions f (&) -I, and such a “ ⁺ Complex argument” ( ^{(± 1x1) +} S ^{i + 1} _i ) _k in the conditionally “k” “Minimization Zone” is activated through the functional structure (370).

And “ ^- Complex argument” ( ^{(± 1x1) -} S ^{i + 1} _i ) _k in the conditionally “k” “Minimization Zone” is activated by the functional structure (371),

in which the technological cycle ∆t _Σ → 2 ∙ f (&) - And is minimized to two conditional logical functions f (&) - And. It should be noted that in the conditionally “k” “Minimization Zone” both “ ⁺ Complex argument” ( ^{(± 1x1) +} S ^{i + 1} _i ) _k and “ ^- Complex argument” ( ^{(± 1x1) -} S are equally probable ^{i + 1} _i ) _k , and a situation is possible when the argument ( ^{(± 1x1) +} S ^{i + 1} _i ) _k or ( ^{(± 1x1) -} S ^{i + 1} _i ) _{k is} active in the conditionally “k” “Minimization Zone” , and in the conditionally “k-1” “Minimization Zone” the argument ( ^{(± 1x1) +} S ^{i + 1} _i ) _k-1 or ( ^{(± 1x1) -} S ^{i + 1} _i ) _{k-1 is} also active, which can be combined in a logical function system f ₁ (}) - OR expressions (372),

in which the technological cycle ∆t _Σ → 3 ∙ f (&) - And is increased to three logical functions f (&) - And. And if we take into account that ( ^{(± 1x1) +} S ^{i + 1} _i ) _k-1 or ( ^{(± 1x1) -} S ^{i + 1} _i ) _k-1 are also formed by the logical function f ₁ (}) - OR in the expressions (370) and (371), then the “Complex argument” ( ^1x1 | ⁺ _- | S ^{i + 1} _i ) _k-1 in the conditionally “k-1” “Minimization zone” must be formed through the functional structure (373),

in which the technological cycle ∆t _Σ → 2 ∙ f (&) - And is minimized to two conditional logical functions f (&) - And. As a result, we write the first version of the functional additional structure either in the form of an analytical expression (374),

either as an analytical expression (375),

in which the functional structure (372) is included in the logical function system f ₁ (&) - AND. It should be noted that the functional structure (375) with the input logical function f ₁ (}) - OR allows you to include in your system an additional “Activation condition ( ^{± 1} S ^{i + 1} _i ) _k-1 ”, which is active in conditionally “ k-1 ”“ Zone of minimization ”and such a condition is an active logical zero“ +1 ”“ - 1 ”→“ ^± 0 ¹ ”and it in graph-analytical expression (376)

in the system of a logical function, we write in the form of two converted arguments ((“ ^± 0 ¹ ”) S _{i + 1} ) _k-1 conditionally “i-1” bits and ((“ ^± 0 ¹ ”) S _i ) _k-1 conditionally “ i "discharge. At the same time, the “Complex argument” inactive logical zeros “ ^± 0” _k conditionally “k-1” “Minimization zones”, the functional structure of which can be written in the form, can be included in the system of the input logical function ₁ (}) - OR expression (376) analytical expression (377),

in which the logical function f_one(} &) - OR will NOT be active only if all input arguments of the terms are inactive at the same time^±[n_i] f_one(+/-)_min  and^±[m_i] f_one(+/-)_min. But if we take into account the logic of the formation of a conditionally minimized structure of arguments, then to activate the transformed argument in conditionally “k” “Zone of minimization”, the inactivity of the “Complex argument” is a necessary and sufficient condition (^{(± 0) ±}S_{i + 1})_k-1 functional structure (378),

since any transformations in the conditionally “k-1” “minimization zone” lead to the formation of a conditionally minimized argument structure. It should be noted that the technological cycle ∆t _Σ → 1 ∙ f (&) - And is minimized to one conditional logical function f (&) - And, as a result of “Complex argument” ( ^{(± 0х0) ±} S ^{i + 1} _i ) _{k-1 of} expression (378) can be written in one logical function system f ₁ (}) - OR, expression (376) together with arguments ((“ ^± 0 ¹ ”) S _{i + 1} ) _k-1 and (( “ ^± 0 ¹ ”) S _i ) _{k-1 of the} active logical zero “+1” “- 1” → “ ^± 0 ¹ ” and the combined expression in this situation can be written in the form of a graphoanalytic expression (379).

At the same time, the “Complex argument” ( ^1x1 | _- ⁺ | S ^{i + 1} _i ) _{k-1 of the} functional structure (380) can be included in the system of the input logical function f ₁ (}) - OR expression (379),

which is also the “Activation Condition” of the positive resulting argument of the sum ( ⁺ S _i ) _k in the conditionally “k” “Minimization Zone”, resulting in the structure of logical functions (379) after combining the logical function f ₂ (}) - OR expressions (380) and the logical function f ₁ (}) - OR expressions (379) we write in the form of an analytical expression (381).

Moreover, if in the system of a logical function f ₁ (}) - OR expressions (381) are a set of input converted arguments (382)

and a set of input transformed arguments (383)

written by means of “Complex arguments”, then we write the structure of logical functions (381) in the form of a minimized analytical expression (384).

     Option 1.

It should be noted that the functional structure (380) was formed in a situation where all the arguments of the combined structure of the terms ^± [S _i ] f ₁ (+/-) _min were either inactive in the conditionally “k-1” “Minimization Zone” , or two arguments are active in it at the same time. But argument structures are possible when only one positive argument ¹ ( ⁺ S _{i + 1} ) _k-1 or conditionally negative argument ¹ ( ¹ S _{i + 1} ) _{k-1 is} active in the conditionally “k-1” “Minimization Zone”, and activation of the argument in the conditionally “k” “Minimization Zone” is also performed for this situation; therefore, we will form a functional structure (385).

     Option 2

From the analysis of the functional structure (385) it follows that the “Necessary conditions” for activating the resulting argument of the sum ( ⁺ S _i ) _k are presented in it by the logical function f ₁ (}) - OR as a positive argument ¹ ( ⁺ S _{i + 1} ) _{k -1} , and conditionally negative argument ¹ ( ^- S _{i + 1} ) _k-1 conditionally "k-1""Minimizationzones", which is included in the logical function system f ₁ (&) - And together with the input argument of activated zero ( ^{± 0} S _i ) _k-1 . At the same time, the logical function f ₂ (}) - OR with the input arguments “Activation condition” is also included in the system of the logical function f ₁ (&) -, but two possible variants of the arguments of the terms can be included in it (386),

since the active conditionally negative argument (^-n & m_{i + 1})_k-2 conditionally "I-2" discharge can be included in the system of logical function f_one(&) - And only with a positive argument^one(⁺S_{i + 1})_k-1, and a positive argument (⁺n & m_{i + 1})_k-2 conditionally "I-2" discharge can be included in the system of logical function f₂(&) - And only with conditionally negative argument^one(^-S_{i + 1})_k-1. Therefore, in the functional structure of the two possible options (384) and (385), which we write in the form of a graphic-analytical expression (387)

it is necessary to introduce two additional structures (386) so that the procedure for converting arguments in accordance with the inverse arithmetic axiom “+2” “-1” → “+1” is correctly implemented. As a result, a functionally complete structure of logical functions will be formed with possible options for activating the argument of the resulting sum ( ⁺ S _i ) _k and it will include four possible combinations of possible arguments of the terms that cannot be combined, since the “Permissive Situation” was analyzed. And a “Prohibitive situation” is possible, when the procedure for converting arguments to the conditionally “k” “Minimization Zone” is performed taking into account possible “Prohibitory arguments”, and such arguments are directly related to possible local transfers of arguments from the conditionally “k-1” “Minimization Zones” . Therefore, we write down the possible structures of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min , in which local transfer is activated and for them we write the structure of logical functions (388),

in which two functional structures with output logical functions f ₁ (&) - NAND and f ₂ (&) - NAND with positive input arguments are introduced into the system of a logical function f ₁ (&) - AND. And similar functional structures with conditionally negative input arguments in expression (388) are written in the form of transformed arguments ↓ ( ^-11 S ⁱ _{i + 1} ) _k and ↓ ( ^{+10 | 1} S ^{i + 1} _{i + 1} ) _k , since their functional the structures are the structures of the "Conditionally negative channel of the adder" i "category", and we write them in the form of expression (389).

It should be noted that the functional structure of “ ⁺ Complex argument” ( ^{(± 1x1) +} S ^{i + 1} _i ) _k and “ ^- Complex argument” ( ^{(± 1x1) -} S ^{i + 1} _i ) _k in conditionally “k” The “minimization zone” can also be minimized, because if we return to the analysis of the functional structure (370), writing it in the form of the expression (390)

and functional structure (371), writing it in the form of expression (391),

then to activate these arguments, it is necessary to include four additional functional structures in the mathematical model of the adder ^± f (Σ _RU ) _min for activating the transformed arguments ( ⁺ n _{i + 1} & ^- m _i ) _k , ( ⁺ m _{i + 1} & ^- n _i ) _k , ( ⁺ n _i & ^- m _{i + 1} ) _k and ( ⁺ m _i & ^- n _{i + 1} ) _k , as well as the logical function f ₁ (}) - OR. And if we consider that the functional structures (247) and (248) should be included in the mathematical model of the adder ^± f (Σ _RU ) _min , writing them in the form of analytical expressions (292),

and included functional structures (249) and (250), writing them in the form of analytical expressions (293)

with technological cycle ∆t_Σ→ 2 ∙ f (&) - And, equal to two conditional logical functions f (&) - And, then the functional structures (390) and (391) can be excluded from the mathematical model of the adder^±f (Σ_RU)_min, but "⁺Complex argument (^{(± 1x1) +}S^{i + 1} _i)_k»In the structure of logical functions (388) can be written using two converted arguments^one(⁺S_{i + 1})_k conditionally "i + 1" discharge and^one(^-S_i)_kconditionally "i" discharge expressions (292) and (293). As a result, we write the adjusted structure of logical functions (388) in the form of an analytical expression (294),

and write down the corrected structure of logical functions (389) in the form of an analytical expression (295),

с функциональной цифровой связью (≡), под которой будем понимать функциональную цифровую связь либо непосредственно самих преобразованных аргументов функциональных структур (292) и (293) и в этом случае технологический цикл ∆t_Σ → 5∙f(&)-И структуры логических функций (394) и (395) будет соответствовать пяти условным логическим функциям f(&)-И. Либо под входным аргументом и функциональной цифровой связью (≡) будем понимать совокупность самих входных аргументов функциональных структур (292) и (293), и в этом случае технологический цикл ∆t_Σ → 4∙f(&)-И структуры логических функций (394) и (395) будет соответствовать четырем условным логическим функциям f(&)-И. Поэтому функциональные структуры (394) и (395) запишем в виде аналитических выражений (396)in which the system of logical functions f ₁ (&) - AND NOT and f ₁ (&) - AND NOT converted arguments

with functional digital communication (≡), by which we mean functional digital communication or directly converted arguments of functional structures (292) and (293) themselves and in this case the technological cycle ∆t _Σ → 5 ∙ f (&) - AND structures of logical functions (394) and (395) will correspond to five conditional logical functions f (&) - And. Or, by an input argument and functional digital communication (≡) we mean the set of input arguments of the functional structures (292) and (293) themselves, in which case the technological cycle ∆t _Σ → 4 ∙ f (&) - AND the structures of logical functions (394 ) and (395) will correspond to four conditional logical functions f (&) - And. Therefore, we write the functional structures (394) and (395) in the form of analytical expressions (396)

and in the form of analytical expressions (397)

Based on the results obtained, it follows that the optimal structure of the logical functions of the mathematical model of the adder ^± f ₁ (Σ _RU ) _min can be formed at the level of symbolism of the combined structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min , which will significantly minimize the number of functional input structures in the analytical expression of the mathematical model of the adder ^± f ₁ (Σ _RU ) _min . Since if we return to the re-analysis of the pre-formed structure of the logical functions of the “Positive channel of the adder“ i ”discharge” (368), writing it taking into account the corrected symbology of the input argument ¹ ((“ ^± 0”) S _{i + 1} ) _k → ¹ ( ^{± 0} S _{i + 1} ) _k and ¹ ((“ ^± 0”) S _i ) _k → ¹ ( ^{± 0} S _i ) _k in the form of a graphoanalytic expression (398),

where the input arguments ( ^-10 S _{i + 1} ) _k and ¹ ( ^{± 0} S _i ) _k in the conditionally “k” “Minimization Zone” are formed by functional structures (399),

and the input argument ( ^-11 S ⁱ _{i + 1} ) _{k is} formed by the functional structure (400),

which is at the level of the combined structure of the arguments of the terms^±[S_i] f_one(+/-)_min fully corresponds to the minimized structure (401) with the output logical function f_one(&) - And, then the structure of logical functions (398) can be significantly minimized. And this minimization is due to the fact that as input arguments (^-10S_{i + 1})_kand^one(^{± 0}S_i)_k in expression (399), and  the input argument in the expression (401) is formed by the logical function f (&) - AND, which can be combined with the logical function f (&) - And, forming the resulting argument (⁺S_i)_k. But in order to minimize the structure of logical functions (398), it is necessary to introduce a unifying input logical function f₂(}) - OR to combine the corresponding “Conditions of activation”, the “Complex argument” of which is positionally located in the conditionally “k-1” “Zone of minimization” and their technological cycle ∆t_Σ→ 1 ∙ f (&) - And should not exceed one conditional logical function f (&) - And. Therefore, on the one hand, we write the functional structure (400) in the form of an analytical expression (402),

which introduced the "Complex argument" (^-elevenS^{i + 1} _i)_k≡ ↑ and which represents the collection of input arguments of the logical function f_one(}) - OR, on the other hand, form the functional structure (403)

by means of which, in the conditionally “k-1” “Minimization Zone”, inactive zero arguments “± 0” → “+1” “- 1” conditionally “i-1” of the digit are converted into the active argument ( ^{± 0} S _i ) _{k-1 of the} active logical zero “± 0” “+ 1” “- 1” → “± 0” and in this functional structure the technological cycle ∆t _Σ → 1 ∙ f (&) - And does not exceed one conditional logical function f (&) - And . As a result, the structure of logical functions (398) with the active arguments of the same name conditionally “k” “Minimization zone” taking into account the functional structure (399) can be written in the form of two functional structures (404) and (405),

in which “Feature 2” is the simultaneous sequence of conditionally negative arguments in the conditionally “k” “Minimization Zone” and the resulting argument ( ^-11 S ^{i + 1} _i ) _k activates the functional structure (406)

with the technological cycle ∆t _Σ → 2 ∙ f (&) - AND, which corresponds to two conditional logical functions f (&) - And, but with the output logical function f ₁ (}) - OR. A “Feature 1” is the sequence of active and inactive argument ¹ ( ^- S _{i + 1} ) _k and ¹ ( ^{± 0} S _i ) _k in the conditionally “k” “Minimization Zone”, and the resulting arguments ¹ ( ^- S _{i + 1} ) _k and ( ^{± 0} S _i ) _k activate the functional structures of expression (399),

which for the resulting combined conditionally negative argument ¹ ( ^-10 S ^{i + 1} _i ) _k we write in the form of an analytical expression (407),

with the technological cycle ∆t _Σ → 2 ∙ f (&) - And, which also corresponds to two conditional logical functions f (&) - And, but with the output logical function f ₁ (&) - And. Moreover, in the combined structure of the arguments of the terms ± [S _i ] f ₁ (+/-) _min in the conditionally “k” “Minimization Zone”, “Complex argument” ¹ ( ^-01 S ^{i + 1} _i ) _k and ¹ ( ^{-1 +1} S ^{i + 1} _i ) _k ; therefore, we write the functional structure that activates the conditionally negative argument ¹ ( ^-01 S ^{i + 1} _i ) _k in the form of an analytical expression (308)

and a functional structure (391) that activates the argument in the form of an analytical expression (409).

Functional similar structures have positive “Complex arguments” ( ⁺¹¹ S ^{i + 1} _i ) _k , ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k , ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k and ¹ ( ^{+ 1- 1} S ^{i + 1} _i ) _k , which we write in the form of an analytical expression (409),

the functional structure that activates the positive argument ( ⁺¹⁰ S ^{i + 1} _i ) _k , we write in the form of an analytical expression (410),

and the functional structure that activates the positive argument ( ⁺⁰¹ S ^{i + 1} _i ) _k , we write in the form of an analytical expression (411),

and the functional structure (390), activating the argument ( ^{+ 1-1} S ^{i + 1} _i ) _k , we write in the form of an analytical expression (412).

A necessary similar and sufficient “Activation Condition” of one of the terms or the argument of their transformation into conditionally “k” “Minimization Zone” is also the “Complex argument” ( ^{± 1} S _{i + 1} ) _k-1 “i + 1” bits or the argument ( ^{± 1} S _i ) _k-1 “i” of the discharge in conditionally “k-1” “Minimization zones” that correspond to the active logical zero argument “+1” “- 1” → “ ^± 0 ¹ ”, and write their functional structures in the form of analytical expressions (413).

It should be noted that as an argument (^{± 1}S_{i + 1})_k-1 active logical zero "+1" "- 1" → "^±0^one»Of expression (413), and the argument (^{± 0}S_{i + 1})_k-1 inactive logical zero "^±0 "expressions (403) are equally probable in the structure of the arguments of the terms^±[n_i] f_one(+/-)_min  and^±[m_i] f_one(+/-)_min, and they are a necessary and sufficient “Condition for activation” of either one of the arguments of the terms or the argument of the procedure for their transformation into conditionally “k” “Zone of minimization”. And when you consider that the argument (^{± 0}S_{i + 1})_k-1 inactive logical zero "^±0 "of expression (403) has the technological cycle Δt_Σ→ 1 ∙ f (&) - And, equal to one conditional logical function 1 ∙ f (&) - And, therefore, it can be included in the system of the logical function f_one(}) - OR expression (413), which we write in the form of an analytical expression (414).

It should be noted that the necessary and sufficient “Activation conditions” category of arguments in the conditionally “k” “Minimization Zone” can also include the following functional structures.

      1. Functional structure (415),

activating conditionally negative “Complex argument” ¹ (| -1x + 1 | ^- S ^{i + 1} _i ) _k-1 in conditionally “k-1” “Minimization zone”, in which the input arguments

can be entered into the output system of the logical function f ₁ (}) - OR expressions (414) in the form of argument ¹ (| -1x + 1 | ^- S ^{i + 1} _i ) _k-1 “Activation conditions”. Since the structure of the arguments in the conditionally “k-1” “minimization zone” is minimized with the resulting argument activated in the conditionally “i-1” category, as a result, we write the functional structure (414) in the form of an analytical expression (416)

    2. Functional structure (417),

activating the positive "Complex argument" ¹ (| + 1x-1 | ⁺ S ^{i + 1} _i ) _k-1 in the conditionally "k-1""Minimizationzone", in which the input arguments

can be entered into the output system of the logical function f ₁ (}) - OR expressions (416) in the form of argument ¹ (| + 1x-1 | ⁺ S ^{i + 1} _i ) _k-1 “Activation conditions”. Since the structure of the arguments in the conditionally “k-1” “Minimization Zone” is minimized by activating the resulting argument in the conditionally “i-1” category, as a result, we write the functional structure (416) as an analytical expression (418).

       3. The functional structure (376), which we write in the form of an analytical expression (419),

activating by means of the logical function f ₁ (} &) - OR NOT “Complex argument” ( ^{(± 0х0) ±} S ^{i + 1} _i ) _k-1 inactivity of all terms in the conditionally “k-1” “Minimization zone”, which also we introduce into the structure of logical functions (418), as a result, we write it in the form of an analytical expression (420).

It should be noted that the generated functional structure (420) is a “condition for activation” as positive arguments of the terms^±[n_i] f_one(+/-)_min  and^±[m_i] f_one(+/-)_min, and conditionally negative arguments of the terms, when in the conditionally “k” “Minimization Zone” two arguments are simultaneously active and they are transformed in accordance with the procedure of logical differentiation d_one/ dn⁺ → f_one(⁺← ↓_-)_{d / dn}  or d₂/ dn^- → f₂(^-← ↑⁺)_{d / dn} or in accordance with the inverse arithmetic axioms “+2” “-1” → “+1” and “-2” “+1” → “-1”. And also in situations of activity of one of the arguments in the conditionally “k” “Minimization Zone”, but when the argument is active (^{± 1, ± 0, ± 0x0}| -1x + 1 |, | + 1x-1 | S^{i + 1} _i)_{k + 1} “Conditions of activation” in conditionally “k + 1” “Zone of minimization”.

Situation 1. In the conditional “k” “Minimization Zone” only the positive argument ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _{k is} conditionally “i” of the discharge with the technological cycle ∆t _Σ → 2 ∙ f (&) - And in the logical system functions f ₁ (&) - And the functional structure (421),

in which the technological cycle ∆t _Σ → 4 ∙ f (&) - And corresponds to four conditional logical functions f (&) - And. It should be noted that if we return to the analysis of the functional structure (411), the positive argument ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k , writing it in the form of the analytical expression (422),

then to minimize the analytical expression of the adder ^± f (Σ _RU ) _min conditionally "k""Minimizationzones" it is advisable not to combine the same logical functions f ₂ (&) - And expressions (422) with the logical function f ₁ (&) - And expressions ( 421), since this combination will not lead to the minimization of the technological cycles ∆t _Σ → 4 ∙ f (&) - And of the general functional structure by which the positive resulting argument of the sum ( ⁺ S _i ) _{k of} conditionally “i” discharge is activated.

Situation 2. In conditionally “k” “Minimization Zone” only positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _{k is} conditionally “i + 1” of discharge with the technological cycle ∆t _Σ → 2 ∙ f (&) - And in logical function system f ₁ (&) - AND functional structure (423).

Situation 3. In conditionally “k” “Minimization Zone” only conditionally negative argument ¹ ( ^-01 S ^{i + 1} _i ) _{k is} conditionally “i” of the discharge with the technological cycle ∆t _Σ → 2 ∙ f (&) - And in the system logical function f ₁ (&) - And the functional structure (424),

which activates the conditionally negative argument of the resulting sum ( ^- S _i ) _k conditionally "i" discharge.

Situation 4. In conditionally “k” “Minimization Zone” only conditionally negative argument ¹ ( ^-10 S ^{i + 1} _i ) _{k is} conditionally “i + 1” of discharge with the technological cycle ∆t _Σ → 2 ∙ f (&) - И in the system of the logical function f ₁ (&) - AND the functional structure (425),

which activates the conditionally negative argument of the resulting sum ( ^- S _{i + 1} ) _k conditionally "i + 1" category.

     Further, if we return to the functional structure (420) “Conditions of activation”, writing it taking into account the functional structure (423) in the form of a graphic-analytical expression (426),

then the functional input structure “Activation conditions” with the output logical function f ₁ (} &) - OR NOT correctly activates the resulting positive sum argument ( ⁺ S _{i + 1} ) _k conditionally “i + 1 in conditionally“ k ”“ Minimization zone ” "Discharge. Since even if a local transfer is possible in the previous “Minimization Zones”, its argument will be activated in the conditionally “i + 1” category of the conditionally “k-1” “Minimization Zones”. But if we write down the argument structure of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min in the form of a graph-analytical expression of the form (429)

and activate the functional structure of expression (428), then the structure of the arguments in the conditionally “k-1” “Minimization Zone” has a “Defect”, since it does not correspond to the logic of the formation of the structure of conditionally minimized arguments. Therefore, in the logical function system f ₁ (&) - And expressions (428), it is necessary to introduce “Additional conditions” for activating the resulting argument of the sum ( ⁺ S _{i + 1} ) _k and they are formed by the functional structure (429) and (430) with output logical functions f ₁ (&) - NAND and f ₂ (&) - NAND, in the system of which the arguments “Situation 1” and “Situation 2” are included, and since they are equally probable, therefore, we introduce these functional structures into the system of the logical function f ₂ (}) - OR and write the structure of logical functions (431)

and it has a technological cycle ∆t _Σ → 4 ∙ f (&) - And, corresponding to four conditional logical functions f (&) - And. But if you write the vector structure (432)

transfer of the functional structure with the output logical function f ₂ (&) - AND through the system of the logical function f ₁ (}) - OR and transfer of the logical function f ₁ (&) - NOT through the system of the logical function f ₂ (}) - OR, write functional structure (432) with the output logical function f ₁ (&) - And, in the system of which “Complex arguments” (( ⁺ n & m _i ) _k-1 ) & ( ⁺ n & m _{i + 1} ) _k-2 , (( ⁺ n & m _i ) _k-1 ) & ( ⁺ n _{i + 1} & m _i ) _k-2 and (( ⁺ n & m _i ) _k-1 ) & ( ⁺ m _{i + 1} & n _i ) _{k-2 are} also generated by one logical function f ₀ (&) - AND NOT. As a result, the minimized functional structure (432) has a technological cycle ∆t _Σ → 2 ∙ f (&) - And, which corresponds to two conditional logical functions f (&) - And.

    Based on the results obtained from the structure of logical functions (420), which we write in the form of an analytical expression (433)

it is necessary to exclude the functional structure with the output logical function f ₁ (} &) - OR NOT, since it does not correspond to the category of necessary and sufficient “Activation conditions” of the argument in the conditionally “k” “Minimization Zone” and write it in the form of an analytical expression (434 )

And if we return to the vector structure (432), writing it without the output logical function f ₁ (&) - NOT in the form of the expression (435)

and carry out the transfer of the functional structure with the output logical function f ₂ (}) - AND through the system of the logical function f ₁ (}) - OR, then we write the functional structure (435) with the output logical function f ₁ (}) - OR, in the system of which "Complex arguments" (( ⁺ n & m _i ) _k-1 ) & ( ⁺ n & m _{i + 1} ) _k-2 , (( ⁺ n & m _i ) _k-1 ) & ( ⁺ n _{i + 1} & m _i ) _k-2 and (( ⁺ n & m _i ) _k-1 ) & ( ⁺ m _{i + 1} & n _i ) _{k-2 are} formed by the functional structure (436).

and functional structures (437).

As a result, the procedure for converting the arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _{min of} expression (428) can be written as a graph-analytical expression (437),

in which in the conditionally “k” “Minimization Zone” the positive argument of the resulting sum ( ⁺ S _{i + 1} ) _{k is} conditionally “j + 1” of the discharge of the functional structure (438), since in the system of the logical function f ₁ (&) - And the argument is not active ( ^{± 1, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _{k-1 of the} necessary and sufficient “Activation conditions” of expression (434). But the conditionally negative argument of the resulting sum ( ^- S _i ) _k conditionally “j” of the discharge of the functional structure is active (439), since in the logical function system f ₂ (&) - And is active as an input positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k , the functional structure with the output logical function f ₂ (}) is also active - OR, since the Complex argument is active in its system (( ⁺ n & m _i ) _k-1 ) & ( ⁺ m _{i + 1} & n _i ) _{k -2} conditionally "k-1""Zone of minimization." It should be noted that the functional structure with the output logical function f ₂ (}) - OR expression (439), which activates the argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 “Activation conditions” can be formed and in conditionally “k” “Zone of minimization” in the form of expression (440),

resulting argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _{k of} which is a conditionally negative argument of the resulting sum ( ^- S _i ) _{k of} conditionally “i” discharge. Since if we write the graphoanalytic expression (441),

then the positive argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k ↑ of the functional structure with the output logical function f ₁ (}) - OR through the output logical function f ₂ (}) - OR activates the conditionally negative argument of the resulting sum ( ^- S _i ) _k conditionally “i” discharge. In this case, the input argument ↓ ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 conditionally “is included in the system of the logical function f ₁ (&) - And, which activates in the conditionally“ k + 1 ”“ Minimization zone ” k-1 "" Minimization zones ", it should be noted that if the" Complex argument "(( ⁺ n & m _i ) _k ) & ( ⁺ n & m _{i + 1} ) _k-1 in the logical function system f ₁ (}) - OR of expression (441) uniquely activates the transformed argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k ↑, then the “Complex arguments” of the simultaneous activity of two consecutive positive arguments (( ⁺ n & m _i ) _k ) & ( ⁺ n _{i + 1} & m _i ) _k-1 and (( ⁺ n & m _i ) _k ) & ( ⁺ n _{i + 1} & m _i ) _k-1 in conditionally “k-1” “Zone min imizations ”should be further analyzed. Since their transformation logic substantially depends on the activity of the arguments in the conditionally “k-2” “Minimization Zone” and one of the possible argument structures in this zone is the structure of the local transfer of conditionally negative arguments, which we write in the form of a graphic-analytical expression (442).

From the analysis of the logical-dynamic process of transforming the arguments in the combined structure of the terms ^± [S _i ] f ₁ (+/-) _{min of} expression (442), it follows that if the conditionally negative sum argument ( ^- S _i ) _k with the active argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k ↑ of the logical function f ₁ (}) - OR, then the transformation into conditionally “k-1” “Minimization zone” must be performed taking into account the possible activity of the conditionally negative local transfer argument from the conditionally “k-2” “Minimization Zones”.

Since in the conditionally “k-1” “Minimization Zone” of expression (442) a “non-standard” structure of conditionally negative arguments is formed with the need for local transfer of the argument from the conditionally “i” bit to the conditionally “i + 1” bit, therefore it will form a functional structure by which activate the conditionally negative argument of the sum ( ^- S _{i + 1} ) _k . It should be noted that this argument can be activated in the following situations:

      Situation 1. A conditionally negative argument is active (^-n & m_{i + 1})_k-1 and^one(^-elevenS^{i + 1} _i)_k-1, and we write this situation in the form  graphoanalytic expression (443).

      Situation 2. Conditionally negative argument is active^one(^-10S^{i + 1} _i)_k-1and a conditionally negative argument is active (^-n & m_{i + 1})_k-2 or^one(^-elevenS^{i + 1} _i)_k-2 in the conditionally "k-2" "minimization zone", and we write this situation in the form  graphoanalytic expression (444).

      Situation 3. Conditionally negative argument is active^one(^-10S^{i + 1} _i)_k-1and^one(^-10S^{i + 1} _i)_k-2and a conditionally negative argument is active (^-n & m_{i + 1})_k-2 or^one(^-elevenS^{i + 1} _i)_k-2 in the conditionally "k-2" "minimization zone", and we write this situation in the form  graphoanalytic expression (445).

      Situation 4. Three consecutive conditionally negative arguments are active.^one(^-10S^{i + 1} _i)_k-1,^one(^-10S^{i + 1} _i)_k-2 and^one(^-10S^{i + 1} _i)_k-3, and we write this situation in the form  graphoanalytic expression (446),

it should be noted that the activity of three consecutive conditionally negative arguments ¹ ( ^-10 S ^{i + 1} _i ) _k-1 , ¹ ( ^-10 S ^{i + 1} _i ) _k-2 and ¹ ( ^-10 S ^{i + 1} _i ) _k-3 is a necessary and sufficient condition for activating a conditionally negative argument of the sum ( ^- S _{i + 1} ) _{k of} conditionally “i + 1” discharge. Since if we form a graphoanalytic expression (447),

then it follows that for the formation of a conditionally negative local transfer argument in the conditionally “k-1” “Minimization Zone”, the activity of three consecutive conditionally negative arguments ¹ ( ^-10 S ^{i + 1} _i ) _k-1 , ¹ ( ^{- 10} S ^{i + 1} _i ) _k-2 and ¹ ( ^-10 S ^{i + 1} _i ) _k-3 , since such a sequence is unpredictable.

      Situation 5. Two consecutive conditionally negative arguments are active^one(^-10S^{i + 1} _i)_k-1 and^one(^-10S^{i + 1} _i)_k-2 and the argument is active (^{± 1, ± 0x0}| -1x + 1 |, | + 1x-1 | S^{i + 1} _i)_k-3 in the conditionally “k-3” “minimization zone”, and we write this situation either in the form  graphoanalytic expression (448),

or in the form of a graphoanalytic expression (449).

From a comparative analysis of the logical-dynamic transformation processes of the combined structure of the arguments of the terms (448) and (449) it follows that the functional structure of activating the conditionally negative argument of the sum ( ^- S _{i + 1} ) _k taking into account the conversion procedure in the conditionally “k-1” “Zone minimizing the expression (449) can be minimized. And this minimization at the first stage may include the functional structure of the first situation (443) and the functional additional input structure with the input logical function f ₃ (&) - And expressions (450),

the system of which includes two “Complex arguments” ( ^- nVm _{i + 1} ) _k-2 and ( ⁺ nVm _{i + 1} ) _k-2 , and their combination corresponds to the fact that in the conditionally “k-2” “Minimization Zone” is active conditionally negative argument is conditionally “i + 1” of the category and the positive argument in this category is not active. And if we take into account the unifying feature of the input arguments ( ^- n & m _{i + 1} ) _k-1 and ¹ ( ^-11 S ^{i + 1} _i ) _k-1 , and we write this feature in the form of a functional structure (451)

then we write down the structure of logical functions (450) in a minimized form in the form of an analytical expression (452),

in which two "Complex arguments" ( ^- nVm _{i + 1} ) _k-1 and ( ⁺ nVm _{i + 1} ) _k-1 are included in the system of the logical function f ₁ (&) - And and their combination also corresponds to what is conditionally “K-1” “Zone of minimization” conditionally negative argument of conditionally “i + 1” category is active and positive argument in this category is not active. It should be noted that the input functional structures with the output logical functions f ₁ (&) - And and f ₂ (&) - And combine the "Complex argument" ¹ ( ^-10 S ^{i + 1} _i ) _k-1 , and it allows write the structure of logical functions (452) as a minimized functional structure (453)

to activate a conditionally negative argument of the resulting sum ( ^- S _{i + 1} ) _k with “Condition argument” ( ⁺ nVm _{i + 1} ) _k-2 , which in the situation of an active logical zero “+1” “- 1” → “ ^± 0 ¹ »Expressions (454)

excludes the activation of the argument of the resulting sum ( ^- S _{i + 1} ) _k , since in the system of the logical function f ₁ (&) - And the positive input argument ( ⁺ nVm _{i + 1} ) _k-2 in the conditionally “k-2” “Zone minimization. " A similar situation exists in graphoanalytic expression (455),

in which also the inactive “Argument of the condition” ( ⁺ nVm _{i + 1} ) _k-2 excludes the activation of the argument of the resulting sum ( ^- S _{i + 1} ) _k . But if the argument of the resulting sum ( ^- S _{i + 1} ) _{k is} activated, and it is activated in accordance with the arithmetic axiom “-1” → “-2” “+1” in the conditionally “k-1” “Minimization Zone”, there should be the positive argument of the resulting sum ( ⁺ S _{i + 1} ) _{k-1 is} activated. And we write this situation in the form of graphoanalytic expression (456),

in which the “Condition Argument” ( ^{± 0} S _i ) _k-1 , formed by the functional structure (457), is included in the logical function system f ₁ (&) - And.

And if we return to the analysis of the functional structure (423), writing it in the form of the expression (458),

in which when activating a positive resulting argument of the sum ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge, the “Complex argument” ( ^{± 1, ± 0, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k-1 , formed by the functional structure (420), which can be written as an analytical expression (459).

It should be noted that the “Feature” of the structure of logical functions (459) is a functional input structure with an output logical function f ₂ (} &) - OR NOT, and its converted argument ( ^{± 0} S _{i + 1} ) _{k-1 is} included in the logical function system f ₁ (&) - And expressions (456), which together with the functional structure (458) can be written as an analytical expression (460),

by means of which the positive resulting argument of the sum ( ⁺ S _{i + 1} ) _k conditionally “i + 1” bits in the conditionally “k” “Minimization zone” is activated. It should also be noted that the “Feature” of the structure of logical functions (459) with the output logical function f ₂ (} &) is OR NOT and is the functional affiliation in the conditionally “k” “Minimization Zone” only conditionally “i + 1 "Discharge. And if we consider that in the structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min positive and conditionally negative arguments are equally probable, then the functional structure (453),

which activates the conditionally negative argument of the sum ( ^- S _{i + 1} ) _k conditionally “i + 1” of the discharge in the conditionally “k” “Minimization Zone”, for a similar structure of arguments of the opposite sign, we write the functional structure in the form of an analytical expression (461)

and introduce it into the system of the logical function f ₁ (}) - OR expressions (460). And if we return to the analysis of graphoanalytic expression (437), writing it in the form of expression (462),

in which the “Activation Condition” of argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k in the logical function system f ₁ (&) - And is the input argument ( ^{± 1, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k-1 , in which, in comparison with the argument ( ^{± 1, ± 0, ± 0х0} | -1х + 1 |, | + 1х-1 | S ^{i + 1} _i ) _k-1, one from possible situations ( ^± 0 _{i + 1} ) _k-1 inactivity of arguments in conditionally “i + 1” category. And this exception led to the need to form an additional functional structure (434),

as a result, in the structure of logical functions of the mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k” “Minimization zones” it is necessary to include the functional structure (433), which we write in the form of an analytical expression (463)

with the input logical function f ₂ (} &) - OR NOT. But if we introduce the functional structure (432) into the system of a logical function f ₁ (&) - And expressions (462),

then this logical function in expression (464)

not correctly activated, since either the input argument (( ⁺ n & m _i ) _k-1 ) & ( ⁺ n _{i + 1} & m _i ) _k-2 or the input argument (( ⁺ n & m _i ) _k-1 ) is not active in its system & ( ⁺ m _{i + 1} & n _i ) _k-2 "Conditions of activation", which are formed by the logical function f ₁ (&) - AND-NOT. In this case, the input arguments ( ^{± 1, ± 0, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k-1 and ( ^{± 1, ± 0, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _{k + 1 of the} logical function f ₂ (&) - And exclude one of the possible situations ( ^± 0 _{i + 1} ) _k-1 inactivity of the arguments in the conditionally “i + 1” category "k-1""Zoneminimization". As a result, the structure of the logical functions of the mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k” of the “Minimization Zone” includes only one functional structure (463). In this case, the functional structure with the output logical function f ₁ (&) - And expressions (464) is written with the converted argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 ↑ with a changed level of the analog signal, since the structure of the arguments is possible terms ^± [S _i ] f ₁ (+/-) _{min of} expression (456),

 which we write either in the form of a graphoanalytic expression (466),

either in the form of a graphoanalytic expression (467),

And if it is similar to the functional structure (432),

which activates to form the converted positive argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 ↑ with a changed level of the analog signal, write the functional structure (468)

with the conditionally negative argument converted ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 ↑ with the changed analog signal level and enter the conditionally negative argument ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k-1 ↑ and positive argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 ↑ with a changed level of the analog signal of expression (464) into the logical function system f ₁ (&) - And expressions (466) and (467) respectively, then we write the correct functional structure (466) in the form of an analytical expression (469),

and write the correct functional structure (467) in the form of an analytical expression (470).

And if we take into account the logic of the formation of a conditionally minimized structure of the arguments of the terms^±[n_i] f_one(+/-)_min  and^±[m_i] f_one(+/-)_min, according to which in the "Zone of minimization" can be activated only one argument, then when forming the combined structure of the terms^±[S_i] f_one(+/-)_min in each “minimization zone” only two arguments can be active. And in this situation, with the activity in the conditionally “k-1” “minimization zone”, expressions (469) and (470) at the same time two arguments of the conditionally “i” discharge lead to the situation in which the system of the logical function f_one(&) - And these expressions input argument (^{± 0}S_{i + 1})_k-1 redundant. But since the mathematical model of the adder is being formed^±f (Σ_RU)_min conditionally “k” of the “Minimization Zone”, therefore, its structure of logical functions should include only functional structures by which the arguments of the resulting sum are activated. And in this regard, we write the procedure for activating the resulting arguments of the sum of terms (469) in the form of analytical expressions (471) and (472),

in which the conditionally negative argument ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k activates the functional structure (473),

and similar analytic expressions (474) and (475)

for the arguments of the terms of the opposite sign.

     From a comparative analysis of the logical-dynamic processes of transformation of the arguments of the terms^±[S_i] f_one(+/-)_min of expressions (472) and (475) it follows that the active argument^one(^-10S^{i + 1} _i)_kand^one(⁺¹⁰S^{i + 1} _i)_k in conditionally "k"_one The “minimization zone” is correctly transformed only using the arithmetic axioms “-1” → “-2” “+1” and “+1” → “+2” “–1”, and the “Activation condition” in this situation is activity argument^one(^{+0.11 | 11}Sⁱ|_{i + 1})_k-1  in "k-1" "Zone of minimization" of double local transfer. But other situations are possible in which the active argument^one(^-10S^{i + 1} _i)_kand^one(⁺¹⁰S^{i + 1} _i)_k in conditionally "k"  The "minimization zone" is correctly transformed only using the same arithmetic axioms. So for a conditionally negative argument^one(^-10S^{i + 1} _i)_k  the transformation using the arithmetic axiom “-1” → “-2” “+1” will be written in the form of a graphic-analytical expression (476),

and in the form of a graphoanalytic expression (477).

And for a positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k , we write the transformation using the arithmetic axiom “+1” → “+2” “- 1” in the form of a graphoanalytic expression (478),

and in the form of a graphic-analytical expression (479).

But if we return to the analysis of the procedure for transforming the arguments of the terms and (282)

and taking into account the adjusted logic of the formation of functional structures, write a graphoanalytic expression (480)

to activate a positive argument of the sum ( ⁺ S _i ) _k conditionally “i” of the discharge or graphoanalytic expression (481)

to activate a positive argument of the sum of ( ⁺ S _{i + 1} ) _k conditionally “i + 1” bits, then on the one hand, taking into account the logical-dynamic process of converting a positive argument to the sum of ( ⁺ S _{i + 1} ) _k conditionally “i + 1” bits in conditionally “k” “Zone of minimization” of expression (475)

in the combined structure of the terms ^± [S _i ] f ₁ (+/-) _min in the conditionally “k-1” “Zone of minimization” “Complex argument” ( ^{± 1, ± 0, ± 0x0} | -1x + 1 |, | + 1x-1 | ^{i + 1} _i ) _{k-1 is} active because the arguments in the conditionally “i + 1” category are not active and its activity will lead to the activation of a positive argument of this category, which leads to a “Defect” in the “k” “Minimization Zone ". Therefore, from the structure of logical functions (463)

"K-1""Minimizationzones" it is necessary to exclude the functional structure with the input logic function f ₂ (} &) - OR NOT, which activates the converted argument ( ^{± 0} S _{i + 1} ) _k-1 . As a result, the structure of the logical functions of the mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k-1” “Minimization zones” can be written as the structure of logical functions (482),

and the structure of the logical functions of the mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k” “Minimization zones” can be written as the structure of logical functions (483),

It should be noted that the transformed argument ( ^{± 1, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k should be the argument “Conditions of activation” in conditionally “k” “Zone of minimization” , but the totality of the arguments ¹ (| + 1x-1 | ⁺ S ^{i + 1} _i ) _k and ¹ (| -1x + 1 | ^- S ^{i + 1} _i ) _k (484)

are not an “Activation Condition”, therefore they are “Excessive arguments” forming a “Defect” when the argument of the resulting sum ( ⁺ S _i ) _{k is} conditionally “i” of the discharge, and they should be excluded from the logical function system f ₁ (}) - OR expressions (483), and the functional structure of the argument “Activation conditions” in the conditionally “k” “Minimization zone” we write in the form of an analytical expression (485)

and the structures of logical functions (463) can be written in the form of an analytical expression (486)

with an input transformed argument of the structure of logical functions (485). Since if we write the functional structure (487),

and functional structure (488),

by means of which the transformation of arguments into the conditionally “k” “minimization zone” is implemented using the inverse arithmetic axioms “-2” “+1” → “-1” and “+2” “-1” → “+1”, then they activate conditionally negative argument of the resulting sum ( ^- S _i ) _k and positive argument of the resulting sum ( ⁺ S _i ) _k conditionally “i” of the category. Moreover, if we write the functional structure (489),

and functional structure (490),

which also activate the resulting argument of the sum ( ^- S _i ) _k and ( ⁺ S _i ) _k , they can be written together with functional structures (487) and (488) in the form of a general analytical expression (491).

and in the form of a general analytical expression (492).

But if we write the graphoanalytic expression (493),

then the activity of the argument ( ^{± 1, ± 0x0} S ^{i + 1} _i ) _k in the conditionally “k” “Minimization Zone” allows you to activate f _1-3 (&) - And the argument of the resulting sum ( ⁺ S _i ) _k conditionally “ i "discharge in three situations. It should be noted that the input arguments in curly brackets ({...}) can be combined in the logical function system f ₂ (}) - OR, but in this case the technological cycle ∆t _Σ → 5 ∙ f (&) - And such structure of logical functions will correspond to five conditional logical functions f (&) - And. It also makes sense to note that the number of possible options for activating the argument of the resulting sum ( ⁺ S _i ) _k conditionally “i” the discharge with the active argument ( ^{± 1, ± 0x0} S ^{i + 1} _i ) _k can be supplemented by writing the procedure for its activation in expression (494),

in the structure of the terms S _i ] f ₁ (+/-) _min which positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _{k-1 is} active in the conditionally “k-1” “Minimization Zone”, and in the conditionally “k-2 »“ Minimization zone ”the local transfer argument is active, written in the system as input arguments ( ⁺ n & m _{i + 1} ) _k-2 , ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k-2 and ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 . It should be noted that the number of possible options for activating the positive argument of the resulting sum ( ⁺ S _i ) _{k of} conditionally “i” discharge with the active argument ( ^{± 1, ± 0x0} S ^{i + 1} _i ) _k can also be supplemented by analyzing the graphoanalytic expression (495)

writing down its logical-dynamic process of converting the arguments of the terms S _i ] f ₁ (+/-) _min in the previous “k-1” - “k-5” “minimization zones” with respect to the conditionally “k” ₁ “minimization zones”, in which the procedure for converting positive arguments is implemented using the arithmetic axiom “+1” → “+2” “- 1”, and the result of this conversion is a conditionally negative argument of the resulting sum ( ^- S _i ) _{k of} conditionally “i” bits to conditionally “k” ₂ “Minimization zone”, and this argument activates the functional structure (496) with the output logic second function f ₂ (k) - E. Moreover, from the analysis of the entire sequence of positive arguments in the previous “k-1” - “k-5” “Minimization Zones”, it follows that, to activate the conditionally negative argument of the resulting sum ( ^- S _i ) _{k, the} conditionally “i” discharge into the logical function system f ₂ (&) - And it’s enough to include only two input arguments ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 . And in conditionally “k” ₁ “Minimization zone”, the positive argument of the resulting sum ( ⁺ S _i ) _k conditionally “i” of the discharge activates the functional structure (498) with the output logical function f ₁ (&) - And, in the system of which, in addition to the argument ( ^{± 1, ± 0x0} S ^{i + 1} _i ) _k , two consecutive arguments ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-2 are included. Moreover, from the analysis of the logical-dynamic process of activating the arguments of the resulting sums (496), it follows that the functional structures (498) and (499) that activate the conditionally negative argument ( ^- S _i ) _k and ( ^- S _{i + 1} ) _{k are} conditionally “ i ”and“ i + 1 ”categories have common“ Activation conditions ”. As a result, the positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-2 conditionally “k-2” of the “Minimization Zone” of the expression (497), we introduce into the totality of the arguments of the “Additional Condition” of the expression (494), which is the “Positive Adder Channel "I" discharge "and write down its functional structure (500),

as well as the functional structure (501) of the "Positive channel of the adder" i + 1 "category" with the output logical function f ₃ (&) - And, the system of which includes input arguments ( ^{± 1, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k-1 , ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k and ¹ ( ^-01 S ^{i + 1} _i ) _k “Activation condition” of the positive argument of the resulting sum ( ⁺ S _{i +1} ) _k conditionally “i + 1” discharge.

     The “Conditionally negative channel of the adder“ i ”category” has a similar functional structure except for the sign of the arguments, which we write in the form of an analytical expression (502),

as well as the functional structure (503) of the "Conditionally negative channel of the adder" i + 1 "category" with the output logical function f ₃ (&) - And, the system of which includes input arguments ( ^{± 1, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k-1 , ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k and ¹ ( ^-01 S ^{i + 1} _i ) _k “Activation condition” of the positive argument of the resulting sum ( ⁺ S _{i + 1} ) _k conditionally “i + 1” category. Since if the logical-dynamic process of converting the positive arguments of the terms ⁺ [S _i ] f ₁ (+/-) _{min of the} expression (495) is written for a similar structure of conditionally negative arguments of the terms ^- [S _i ] f ₁ (+/-) _min in the form graphoanalytic expression (504),

then the logic of the formation of functional structures (506) - (508) and (496) - (499) is equivalent, and they correctly activate the resulting arguments of the sum, as well as functional structures (472), (475), (497) and (506) . Therefore, we redistribute them between the adder channels and write “The positive adder channel of the“ i ”category” in the form of a structure of logical functions (509),

in which the “Feature” is a functional input structure with output logical functions f _1-6 (&) - And with two groups of input arguments, while the first group includes the arguments ( ⁺ n & m _{i + 1} ) _k , ( ^- n & m _{i + 1} ) _k and ( ^{± 1, ± 0x0} | -1x + 1 |, | + 1x-1 | S ^{i + 1} _i ) _k conditionally “k” ₂ “Minimization zones”, and the second group includes two arguments ( ⁺ n & m _{i +1} ) _k-1 and ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k-1 conditionally “k-1” ₂ “Minimization zones”, which with a technological cycle ∆t _Σ → 4 ∙ f (&) - And four conditional logical functions f (&) - And form six functional structures, and if these arguments are combined in a logical functions f ₂ (&) - And and f ₃ (&) - And and write the functional structure (510),

then the technological cycle ∆t _Σ → 5 ∙ f (&) - And will correspond to five conditional logical functions f (&) - And.

     Next, we write the “Positive channel of the adder“ i + 1 ”discharge" in the form of a structure of logical functions (511),

 "Conditionally negative channel of the adder" i "discharge" in the form of a structure of logical functions (512),

and "Conditionally negative channel of the adder" i + 1 "discharge" in the form of a structure of logical functions (513),

in which, as in the structure of logical functions (511) of the "Positive channel of the adder" i + 1 "category" Feature "is a functional input structure with output logical functions f _1-2 (&) - And with a group of input arguments ( ^- n & m _i ) _k-1 and ¹ ( ^-11 S ^{i + 1} _i ) _k and a common input argument ¹ ( ^-01 S ^{i + 1} _i ) _k .

Further, to form a functionally complete mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k” “Minimization zones”, we analyze the possible structures of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min , which activate the resulting argument of the sum in the conditionally "I" discharge. And for this, we return to the analysis of the functional structure (491) and (492), which in the conditionally “k” “Minimization Zone” activate the resulting argument ( ^- S _i ) _k and ( ⁺ S _i ) _k using the inverse arithmetic axioms “-2 "" +1 "→" -1 "and" +2 "" -1 "→" +1 "and we write it in the form of an analytical expression (514)

and in the form of an analytical expression (515).

And given that the “Positive channel of the adder“ i ”discharge” and the “Conditionally negative channel of the adder“ i ”discharge” are equivalent in structure of logical functions, except for the signs of the arguments, it makes sense to analyze the possible structures of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min , which activate the resulting positive argument of the sum ( ⁺ S _i ) _k in the conditionally “i” category. Therefore, from the analysis of the logical-dynamic process of transforming arguments (515) it follows that the number of possible options for activating a positive argument of the sum ( ⁺ S _i ) _k in the conditionally “i” category can be significantly increased. Since if we write a functional structure with an output logical function f _1-3 (}) - OR expressions (509), writing it in the form of an analytical expression (516),

then from a comparative analysis of the input arguments of the expression (515) and (516) it follows that their functional structures can be combined and written in the form of an analytical expression (517),

which includes six possible combinations of input arguments, activating the positive argument of the sum ( ⁺ S _i ) _k in the conditionally “i” category. As a result, in the expression (509) of the "Positive channel of the adder" i "category" we replace the input functional structure with the output logical function f _1-3 (}) - OR by the functional structure with the output logical function f _1-8 (}) - OR (517) and write its structure of logical functions in the form of a graphoanalytic expression (518)

in which the “Feature” is the recording of two initial structures of the arguments of the terms ^{± 1} [S _i ] ₁ and ^{± 1} [S _i ] ₂ .

We write down a similar adjusted functional structure that activates the conditionally negative argument of the sum ( ^- S _i ) _k in the conditionally “i” category in the form of an analytical expression (519)

and enter into the “Conditionally negative channel of the adder“ i ”discharge” and write the adjusted structure of logical functions in the form of an analytical expression (520).

It should be noted that the active arguments ¹ ( ^{+ 1x-1} S ^{i + 1} _i ) _k and ¹ ( ^{-1x + 1} S ^{i + 1} _i ) _k can be activated in the conditionally “i + 1” category, so by functional structure (521)

the positive argument ( ⁺ S _{i + 1} ) _{k is} activated, and by means of the functional structure (522)

the conditionally negative argument ( ^- S _{i + 1} ) _{k is} activated. And if we take into account that the combined structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _{min is} multivariant and the local end-to-end transfer can be formed in the graphoanalytic expression (523)

with the activation of the positive argument ( ^- S _{i + 1} ) _k and in the graphic-analytical structure (524)

with the activation of a conditionally negative argument ( ^- S _{i + 1} ) _k .

A similar situation is formed when converting the arguments ¹ ( ^-11 S ^{i + 1} _i ) _k and ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k into the conditionally “k” “Minimization Zone” when the local transfer argument with the opposite sign is active into the conditionally “K-1” “Zone of minimization”, and the logical-dynamic process of converting arguments can be written in the form of graph-analytical expressions.

For the conditionally negative argument ¹ ( ^-11 S ^{i + 1} _i ) _k and the positive local transfer argument from the conditionally “k-1” “Minimization Zones”, we write the argument conversion procedure in the form of a graph-analytical expression (525).

Moreover, if we return to the analysis of the functional structure with the output logical function f ₁ (&) - And the "Positive channel of the adder" i + 1 "category" of expression (511), writing it in the form of an analytical expression (526),

then the “Feature” of the system of input arguments of the logical function f ₁ (&) - And (526) is the input argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 conditionally “k-2” “Minimization zones” for two input arguments ¹ ( ^-11 S ^{i + 1} _i ) _k and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 , one of which is also included in the logical function system f ₁ (&) - And expressions (525). Therefore, the functional structures (525) and (526) can be combined into one analytical expression (527),

at the same time, an “Additional argument” is introduced into the set of input arguments ^one(⁺⁰¹S^{i + 1} _i)_k, which also activates the positive argument of the sum (⁺S_{i + 1})_k with active input argument^one(⁺¹⁰S^{i + 1} _i)_k-1   conditionally "k-1" "Minimization zones" and the active positive argument of local transfer⁺S_{d / dn}(⁺←⁺)_k-2from conditionally “k-2” “Minimization zones”. As a result, the corrected structure of the logical functions of the “Positive channel of the adder“ i + 1 ”discharge" (511) can be written in the form of a graphic-analytical expression (528).

It should be noted that in the adjusted analytical expression (528) into the functional input structure with the output logical function f_1-3(&) - And, which activates the combined structure of the arguments of the terms^{± 1}[S_i]₇ into the system of "Complex arguments" (⁺n & m_i)_k-1   and^one(⁺¹¹S^{i + 1} _i)_k-1, optional argument introduced^one(^{+0.11 | 11}Sⁱ|_{i + 1})_k-1  “Activation conditions” of the argument^one(⁺⁰¹S^{i + 1} _i)_k  in conditionally “k” “minimization zone”, but no argument is entered^one(⁺¹⁰S^{i + 1} _i)_k-1. Since if we write the graphoanalytic expression (529),

then there are three possible structures of the arguments of the terms ^{± 1} [S _i ] ₈ , ^{± 1} [S _i ] ₁₁ and ^{± 1} [S _i ] ₁₂ , which correctly activate the resulting positive argument of the sum ( ⁺ S _{i + 1} ) _k , but the structures of the arguments of the terms ^{± 1} [S _i ] ₁₃ and ^{± 1} [S _i ] ₁₄ activate the “Defect”. It should be noted that the number of logical functions f _1-3 (&) - And in expression (528) can be minimized to one logical function f ₁ (&) - And, if the system of "Complex arguments" is introduced into the system of the logical function f ₁ (}) - OR and write the analytic expression (530)

and in such a record of the functional structure with the transformed argument of the local end-to-end transfer ⁺ S _{d / dn} ( ⁺ ← ⁺ ) _k-1 , the structure of the logical functions of the entire “Positive channel of the adder“ i + 1 ”discharge” will be substantially minimized. Since on the one hand the functional structure in the output logical function f _1-6 (&) - And

we write in the form of a structure of logical functions (532),

then the technological cycle ∆t _Σ → 5 ∙ f (&) - And the transformation of the arguments will correspond to the five conditional logical functions f (&) - And. Since the mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k” “Zone of minimization” is being formed, then to minimize the analytical expression of its functional structure, various “Complex arguments” “Activation conditions” will be included in the system of their common set, under which, in in particular, it implies the logical function f ₁ (}) - OR.

Returning to the analysis of the functional structure (531) with the output logical function f _1-6 (&) - And, which converts the input arguments ( ⁺ n & m _i ) _k and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k to the conditionally “k” “ Minimization zone ”and, in accordance with additional structures of the arguments of the terms ^{± 1} [S _i ] ₉ - ^{± 1} [S _i ] _{9, we} correct it and write it in the form of an analytical expression (533).

    From the analysis of the analytical expression (533) it follows that the additional functional structures with the input logical function f_1-12(^one&) - And and f_1-12(²&) - And including a set of input arguments of the same sign can be minimized and written by means of a common transformed conditionally negative argument^one(^-VS^{i + 1} _i)_k-2 "^-Functional structure  (534)

and a general converted positive argument^one(⁺S^{i + 1} _i)_k-2 "⁺Functional structure  (535)

which include the logical function f ₁ (}) - OR with input arguments of the same sign as in the converted argument ( ^-V S ^{i + 1} _i ) _k-2 and ( ^{+ V} S ^{i + 1} _i ) _k-2 , and also include the logical function f ₁ (} &) - OR NOT with arguments of the opposite sign, while the technological cycle ∆t _Σ → 2 ∙ f (&) - And the transformation of the arguments corresponds to two conditional logical functions f (&) - And. It should be noted that the converted arguments ( ^-V S ^{i + 1} _i ) _k-2 and ( ^{+ V} S ^{i + 1} _i ) _k-2 can also be activated when in the conditionally “k-1” “Zone of minimization” the conditionally negative argument ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k-2 and the positive argument ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _{k-2 are} ^activated . And if in the structure of logical functions (533) we replace the conditionally negative and positive system of input arguments of the input logical function f _1-12 ( ¹ &) - And and f _1-12 ( ² &) - And, then we write the minimized structure of logical functions in the form of an analytical expression (536),

which can be introduced into the system of the logical function f ₂ (}) - OR expressions (528), but it is not functionally complete. Since the structure of the arguments of the terms ^{± 1} [S _i ] ₁ - ^{± 1} [S _i ] ₃ (537) is possible

which, through the functional structure (537) with the output logical function f_1-8(&) - And also activate a positive argument (⁺S_{i + 1})_k conditionally "i + 1" discharge. It should be noted that in the “Activation Condition” the set of input conditionally negative arguments can be replaced by “Complex argument” ^one(^-VS^{i + 1} _i)_k-2 functional structure (534), resulting in a mathematical model of the adder^±f (Σ_RU)_min   The “positive channel of the adder“ i + 1 ”discharge” conditionally “k” “Minimization zone” taking into account the functional structures (536) and (537) can be written in the form of an analytical expression (538).

From the analysis of the graph-analytical expression (538) it follows that the combination of the combined structures of the terms ^{± 1} [S _i ] ₁ - ^{± 1} [S _i ] ₁₄ includes the “Unanalysed structure” ^{± 1} [S _i ] ₃ , which includes a conditionally negative argument ( ^- n & m _i ) _k-2 conditionally “k-2” “Minimization zones” and conditionally negative argument ¹ ( ^-10 S ^{i + 1} _i ) _k-3 conditionally “k-3” “Minimization zones” and the logic of transforming their “Complex argument ”(( ^- n & m _i ) _k-2 ) & ¹ ( ^-10 S ^{i + 1} _i ) _{k-3 is} equivalent to the logic of the“ Complex argument ”transformation ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 under the condition pass through argument activity nose _{^{+ S d / dn (+ ←}} +) k- ₃ of conditionally «k-3""minimizationZones". But the analyzed structure of the arguments to the activation of the argument of the resulting sum ( ⁺ S _{i + 1} ) _{k is} not relevant, because in this situation, in the functional input structure with the output logical function f _1-6 (&) - And the generalized conditionally negative argument ¹ ( ^{- V} S ^{i + 1} _i ) _k-2 , which correctly activates the argument of the resulting sum ( ⁺ S _{i + 1} ) _k and this procedure with the technological cycle ∆t _Σ → 4 ∙ f (&) - And implements six logical functions f ₁ ( &)-AND. And if you write down the functional structure with the output logical function f _1-12 (&) - And in the form of a graphic-analytical expression (539),

then to implement the procedure for converting arguments with the technological cycle ∆t _Σ → 4 ∙ f (&) - And you need twelve logical functions f ₁ (&) - And. But their number could be minimized if the additional argument ( ⁺ n & m _i ) _{k-2 of} conditionally “i” category, which does not apply to the system of “Complex arguments” of local transfer ⁺ S _{d / dn} ( ⁺ ← ⁺ ) _k-2 categories of the local transfer argument ⁺ S _{d / dn} ( ⁺ ← ⁺ ) _k-2 , and such an inclusion will minimize the functional structure (539) and can be written in this situation in the form of an analytical expression (540)

with one “ ⁺ Complex argument” ¹ ( ^{+ V} S ^{i + 1} _i ) _k-2 with the technological cycle ∆t _Σ → 4 ∙ f (&) - And and two logical functions f ₁ (&) - And. It should be noted that the resulting positive argument of the sum ( ⁺ S _{i + 1} ) _k in the conditionally “k” “Minimization Zone” is correctly activated, but the logic of converting the argument of the terms ^{± 1} [S _i ] ₅ to the conditionally “k-2"" The minimization zone "has been substantially changed, since in this zone the positive argument ( ⁺ n & m _i ) _k-2 conditionally" i "of the discharge in this case must be converted by means of" Double local transfer "to correctly activate the conditionally negative argument as in conditionally" k-1 "" Zone of minimization ", where the argument ( ^- S _i ) _{k-1 is} activated , and in the conditionally “k-2” “minimization zone”, where the argument ( ^- S _{i + 1} ) _{k is} activated. A similar situation exists in graphoanalytic expression (541),

in which a positive argument is activated both in the conditionally “k” “Minimization Zone”, where the sum argument is active ( ⁺ S _i ) _k , and in the conditionally “k-1” “Minimization Zone”, where the sum argument is active ( ⁺ S _{i + 1} ) _k . But before adjusting the logical-dynamic process of converting arguments in the "Positive channel of the adder" i + 1 "category" of expression (538), we return to the analysis of the procedure for converting arguments in the "Positive channel of the adder" i "category" expression (518), writing it in the form of graphoanalytic expression (542).

From the analysis of the combined structures of the arguments of the terms ^{± 1} [S _i ] ₁ - ^{± 1} [S _i ] ₁₂ (542) and the input arguments of the structure of logical functions, by means of which the positive argument of the sum ( ⁺ S _i ) _k is activated, it follows that, on the one hand, the functional input structures with the output logical function f ₁ (&) - And and f ₂ (&) - And can be combined, since they have a common input argument ¹ ( ^-10 S ^{i + 1} _i ) _k , and the input conditionally negative argument ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _{k-1 of the} logical function f ₂ (&) - And is included in the extended set of input arguments by the logical function f ₁ ( &)-AND. On the other hand, if we adjust the structure of logical functions (542) and write it in the form of an analytical expression (543),

then a functional input structure with output logic f_1-12(&) - And with a positive input argument^one(⁺¹⁰S^{i + 1} _i)_k-1 conditionally “k-1” of the “Minimization Zone” is a multivariate structure that activates the positive resulting argument of the sum (⁺S_i)_kbecause in her "Prerequisites"  two additional arguments are included (⁺n & m_{i + 1})_k and (^-n & m_{i + 1})_k. But when you consider that the arguments of the “Prerequisite” can be combined using the logical function f_one(}) - OR → (V_one), since the additional arguments (⁺n & m_{i + 1})_k and (^-n & m_{i + 1})_k can be introduced into the system of functional structure (485) with the output logical function f_one(}) - OR and written as an analytical expression (544).

It should be noted that the resulting argument is of the form

written in the structure of logical functions (544) in the form of a set of three “Complex arguments” for understanding its semantic content in graphoanalytic expressions of the logical-dynamic process of transforming the arguments of the terms ^± [n _i ] f ₁ (+/-) _min and ^± [m _i ] f ₁ (+/-) _min → ^± [S _i ] f ₁ (+/-) _min and the technological cycle ∆t _Σ → 2 ∙ f (&) - And its activation corresponds to two conditional logical functions f (&) - And .

Similarly, the “Transfer Condition“ ← ²⁺ ” _k-2 ” in the functional input structure (543) with the output logic function f _1-12 (&) - And can be minimized, since the arguments ( ⁺ n & m _{i +1} ) _k-2 and ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 , and write the functional structure of such a union in the form of an analytical expression (545),

which also has a positive resulting argument

written as a combination of two "Complex arguments". Except for the signs of the arguments, the functionally similar structure has the resulting conditionally negative argument in the form of a combination of two “Complex arguments”

“Transfer conditions“ ← ^2- ” _k-2 ”, which is activated by the functional structure (546).

And if we take into account the fact that the positive resulting argument of the sum ( ⁺ S _i ) _k , as well as the resulting conditionally negative argument of the sum ( ^- S _i ) _k , can be activated with the active argument of the conditionally negative term ¹ ( ^-01 S ^{i + 1} _i ) _k and ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and the positive term ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1, respectively, in situations where either functional structure (547)

either the functional structure is active (548)

and take into account that the functional structures (547) and (548) have an output logical function f ₁ (}) - OR, then to minimize the structure of logical functions of the mathematical model of the adder ^± f (Σ _RU ) _min conditionally "k""Minimizationzones", then the input arguments of these functional structures can be introduced into the system of the same logical output functions f ₁ (}) - OR and f ₂ (}) - OR expressions (545) and (546) and written in the form of an analytical expression (549)

to activate conditionally negative arguments of the terms ¹ ( ^-01 S ^{i + 1} _i ) _k and ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and analytical expression (550)

for the positive arguments of the terms ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 , and the resulting “ ⁺ Complex arguments” (549) as a set of arguments (551)

 and "^-Complex arguments ”(550) as a set of arguments (552)

are  the correct “Activation Condition” of the positive argument^one(⁺⁰¹S^{i + 1} _i)_k and conditionally negative argument^one(^-01S^{i + 1} _i)_k in the conditionally “k” “minimization zone” without their transformation. But the totality of arguments (551) and (552) is functionally incomplete, since the input arguments of the “Complex argument” (^{± 1, ± 0x0}| -1x + 1 |, | + 1x-1 | S^{i + 1} _i)_k-2 inactive logical zero "^±0^{i + 1} _i"_k-2 and active logical zero “+1” “- 1” → “^±0^one"Graphoanalytic expression (553).

Therefore, analytical expressions "⁺Integrated Arguments (549) we write in the form of a functional structure (554),

and the analytical expression “ ^- Complex arguments” (550) can be written in the form of a functional structure (555).

It should be noted that the functional structures (554) and (555) are also functionally incomplete, since the input category “ ⁺ Complex argument” ( ⁺¹¹ S ^{i + 1} _i ) _{k-2 of the} analytical expression also belongs to the category of “Activation conditions” 556)

and input arguments “ ^- Complex argument” ( ^-11 S ^{i + 1} _i ) _k-2 analytical expression (557)

therefore, the analytical expressions of the aggregate "⁺Integrated Arguments (554) we write in the form of a functional structure (558),

and the analytical expression of the set “ ^- Complex arguments” (555) can be written in the form of a functional structure (559).

It should be noted that the conditionally positive set of “ ⁺ Complex arguments” (558), if they are written in the form of a graph-analytical expression (560),

then the functional structure (561) correctly activates not only the positive argument ( ⁺ S _i ) _k , but also the conditionally negative argument ( ^- S _i ) _k in the alternating sequence of positive and conditionally negative arguments of the terms in the conditional “k-1” “k-2 "" Zones of minimization. " We write down a similar functional structure for the conditionally negative set “ ^- Complex arguments”, which we will write in the form of a graphic-analytical expression (562),

in which not only the positive argument ( ⁺ S _i ) _k , but also the conditionally negative argument ( ^- S _i ) _k in the alternating sequence of positive and conditionally negative arguments of the terms in the conditional “k-1” “k-2” “Zones” minimization. " It should be noted that the “Feature” of functional structures (561) and (562) is a conditionally negative argument ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and a positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _{k- 1} conditionally “k-1” “Minimization zones”, which do not change their sign when activating both the positive argument of the sum ( ⁺ S _i ) _k and the conditionally negative argument of the sum ( ⁺ S _i ) _k , as was previously assumed.

Based on the results obtained, it follows that on the one hand in the structure of logical functions (543) the functional structure with the output logical function f _1-12 (&) - And → f _1-2 (&) - And minimized to two logical functions f _{1- 2} (&) - And, on the other hand, an additional functional structure can be formed with two successively active arguments, one of which is activated in the conditionally “k” “Minimization Zone” ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k or ¹ ( ^{+ 1x-1} S ^{i + 1} _i ) _k or ¹ ( ^-11 S ^{i + 1} _i ) _k , and the second argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _{k-1 is} activated in the conditionally “k-1” “Minimization zone "And uh and functional structures can be written as analytical expressions (556), (557) and (558).

It should be noted that the analytical record of the “Positive channel of the adder“ i ”discharge” can be minimized, since on the one hand the structure of logical functions (557) and (558) includes the general “Necessary conditions”, therefore these structures of logical functions can be written in the form of an analytical expression with the general “Prerequisites”. On the other hand, if we introduce a positive “ ⁺ Complex argument” (( ⁺ Comp) S ^{i + 1} _i ) _k-2 and a conditionally negative “ ^- Complex argument” (( ⁺ Comp) S ^{i + 1} _i ) _k-2 , then they essentially functionally refer to the “Positive channel of the adder“ i ”category” and the “Conditionally negative channel of the adder“ i ”category”, therefore the analytical expressions (556), (557) and (558) of the “Positive channel of the adder“ i ” discharge ”in graphoanalytic expression (559) we write in the form of three analytical expressions (560), (561) and (562).

And “Conditionally negative channel of the“ i ”discharge adder” taking into account the “Features” of the functional structures and expression (520) in the graph-analytical expression corrected (563), we write in the form of analytical expressions (564), (565) and (566).

It should be noted that since the graphoanalytic expressions (559) and (563) include the positive “ ⁺ Complex argument” (( ⁺ Comp) S ^{i + 1} _i ) _k-2 and the conditionally negative “ ^- Complex argument” (( ⁺ Comp ) S ^{i + 1} _i ) _k-2 conditionally “k-2” “Minimization zones”, and if we take into account that a mathematical model of the adder ^± f (Σ _RU ) _min conditionally “k” “Minimization zones” is formed. Therefore, in the structure of the logical functions of the "Positive channels of the adder" i + 1 "and" i "discharge" and "Conditionally negative channels of the adder" i + 1 "and" i "discharge" conditionally "k""Minimizationzones" should include such functional structures that activate the “ ⁺ Complex argument” (( ⁺ Comp) S ^{i + 1} _i ) _k and the conditionally negative “ ^- Complex argument” (( ⁺ Comp) S ^{i + 1} _i ) _k . Therefore, the "Positive channel of the adder" i "discharge" (559) we write in the form of the structure of logical functions (567), (568) and (569),

and “Conditionally negative channel of the adder“ i ”category” (563) we write in the form of the structure of logical functions (570), (571) and (572)

Further, if we return to the analysis of the structure of the arguments of the terms ^{± 1} [S _i ] ₁ and ^{± 1} [S _i ] _{2 of the} graphoanalytic expression (541), in which the conditionally negative argument “ ^- Transfer conditions“ ← ^2- ” _k-2 ” from conditionally "i-2" discharge, writing it in the form of expression (573)

and the procedure for activating the positive argument “ ⁺ Transfer conditions“ ← ²⁺ ” _k-2 ” from the conditionally “i-2” category, writing it in the form of a graphic-analytical expression (574),

then sequential structures of conditionally negative arguments ( ^- n & m _i ) _k-1 and ¹ ( ^-10 S ^{i + 1} _i ) _k-2 , as well as sequential structures of positive arguments ( ⁺ n & m _i ) _k-1 and ¹ ( ⁺¹⁰ S ^{i +1} _i ) _k-2 , which are positionally located between the "minimization zones", have ambiguous transformation logic. Since if the procedure for converting the combined structure of the positive arguments of the terms is written as a logical-dynamic process (575),

and the procedure for converting the combined structure of conditionally negative arguments of the terms written as a logical-dynamic process (576),

then they present three possible situations.

      Situation 1. The structure of the positive arguments of the terms (577)

and the structure of conditionally negative arguments of terms (578),

in which “ ⁺ Transfer conditions“ ← ²⁺ ” _k-2 ” and “ ^- Transfer conditions“ ← ^2- ” _k-2 ” are absent, and in this situation a conditionally negative argument ( ^- S _i ) _k can be activated in accordance with procedure (577) and the positive argument ( ⁺ S _i ) _k in the conditionally “k” “Minimization Zone” are transformed in accordance with the procedure (578), and this logic of generating the resulting sum correctly activates the structure of the conditionally minimized sum. But if we take into account that the combined structures of the arguments of the terms are multivariant, then the transformation of the arguments of the terms 577) and (578) must be performed in accordance with the logical-dynamic process (579)

and in accordance with the logical-dynamic process (580),

in which only the positive argument ( ⁺ n & m _i ) _k and the conditionally negative argument ( ^- n & m _i ) _k , and the positive argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and conditionally are transformed in the conditionally “k” “Minimization Zone” negative argument ¹ ( ^-10 S ^{i + 1} _i ) _{k-1 is} not correctly converted. In this case, both resulting arguments of expression (579) functionally belong to the "Positive channel of the adder" i + 1 "category" (538), and the conversion of the input arguments is performed in accordance with the functional structure (537), which we write down taking into account the adjusted "graphoanalytic information technology" in the form of graphoanalytic expression (581)

with a set of input conditionally negative arguments ¹ ( ^-V S ^{i + 1} _i ) _k-2 conditionally “k-2” “Minimization zones”. Moreover, the feature of the “Generalized argument” ¹ ( ^-V S ^{i + 1} _i ) _k-2 is that it can be formed by means of an independent functional structure (582),

which includes the input logical function f ₁ (} &) - OR NOT with conditionally negative arguments and the logical function f ₂ (} &) - OR NOT with positive arguments. As a result, we write the functional structure (581) in the form of a minimized analytical expression (583),

in which the “Excessive argument” ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k is included in the system of the logical function f _1-6 (&) - And. A similar “Excessive argument” is also included in the functional structure of the “Conditionally negative channel of the adder“ i + 1 ”category, which we write in the form of an analytical expression (584),

the positive argument ¹ ( ^{+ V} S ^{i + 1} _i ) _{k-2 is} formed by means of an independent functional structure (585).

It should be noted that the “Redundancy of the argument” ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k and ¹ ( ^-10 S ^{i + 1} _i ) _{k is} directly related to the unified logic of converting the arguments of the terms in the “Positive channel of the adder“ i + 1 "Discharge" and "Conditionally negative channel of the adder" i + 1 "discharge", and in the "Positive channel of the adder" i "discharge" and "Conditionally negative channel of the adder" i "discharge". And if we return to the previously formed “Positive channel of the adder“ i ”category” of expression (518), writing it without taking into account the functional structures (567) - (569) in the form of a graphoanalytic expression (586)

then the conversion of the arguments of the terms^{± 1}[S_i]₆  performs a functional structure with an output logical function f_one(&) - And, in the system of which two consecutive conditionally negative arguments are included^one(^-10S^{i + 1} _i)_k and^one(^-10S^{i + 1} _i)_k-1, and it implements the procedure for activating the resulting positive argument of the sum (⁺S_i)_k conditionally "i" discharge. And the functional structure (584) of the "Conditionally negative channel of the adder" i + 1 "category" with two consecutive conditionally negative arguments^one(^-10S^{i + 1} _i)_k and^one(^-10S^{i + 1} _i)_k-1 implements the procedure for activating the resulting conditionally negative argument of the sum (^-S_{i + 1})_k conditionally "i + 1" discharge, which is unacceptable. Therefore, the "Positive channel of the adder" i + 1 "discharge" (538) will be written in the form of graphoanalytic expression (587).

And if we return to the previously formed “Conditionally negative channel of the adder“ i ”category” of the expression (520), writing it without taking into account the functional structures (570) - (572) in the form of a graphic-analytical expression (588)

then the conversion of the arguments of the terms^{± 1}[S_i]₆  performs a functional structure with an output logical function f_one(&) - And, in the system of which two consecutive positive arguments are included^one(⁺¹⁰S^{i + 1} _i)_k and^one(⁺¹⁰S^{i + 1} _i)_k-1implements the procedure for activating the resulting conditionally negative argument of the sum (^-S_i)_k conditionally "i" discharge. And the functional structure (583) of the "Positive channel of the adder" i + 1 "category" with two consecutive positive arguments^one(⁺¹⁰S^{i + 1} _i)_k and^one(⁺¹⁰S^{i + 1} _i)_k-1 implements the procedure for activating the positive resulting argument of the sum (⁺S_{i + 1})_k conditionally "i + 1" discharge, which is unacceptable. Therefore, we write the “Conditionally negative channel of the adder“ i + 1 ”discharge” in the form of a graphoanalytic expression (589).

From a comparative analysis of the logical-dynamic processes of transforming the arguments of the possible structures of the terms (586) - (589) it follows that, in essence, the procedure for activating the resulting argument of the sum in the conditionally “k” “minimization zone” can be divided into two categories, when in the conditionally “K-1” or “k-2” “Minimization zone” or the positive local transfer argument “Yes” is activated ⁺ Transfer argument ”→ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 or ((Yes ⁺ ← ⁺⁾ S ^{i + 1,} _{i) k-2,} or conditionally active negative argument local transfer «« Not ^»- argument transferability and ^{»→ ((Not - ← -} ) S i + ^1, _{i) k-1} or ^{((Yes - ← -) S} i + ^1, _{i) k-2.} Moreover, in the "Positive channel of the adder" i + 1 "category" of expression (587) and the "Conditionally negative channel of the adder" i + 1 "category" of expression (589) there is a "Feature" and it consists of three options for converting positive arguments ( ⁺ n & m _i ) _k and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k and conditionally negative arguments ( ^- n & m _i ) _k and ¹ ( ^-10 S ^{i + 1} _i ) _k , which are active in the conditionally “k” “Minimization Zone” and which have the equivalent “information content” and therefore must be jointly included in all functional structures, and as “Conditions for activation” should be formed "Integrated Case" (590).

It should be noted that “Yes” ^{+, -} Transfer argument ”and“ “Not” ^{+, -} Transfer argument ”should have a common set of input arguments with mutually opposite information content, because if“ Yes ” ^{+, -} Transfer argument ”, then in this situation“ Not ” ^{+ is} active ^{, -} Transfer argument”. And since “Yes” ^{+, is the} Transfer Argument, in essence, it represents both the active sequential structure of the local transfer arguments and the alternating structure of active and inactive arguments of the possible transfer, and we write down such structures of the arguments of the terms in the form of a graphoanalytic expression (591) .

Moreover, functional structures with an output logical function f ₁ (&) - And and f ₂ (&) - And have a technological cycle ∆t _Σ → 2 ∙ f (&) - And, corresponding to two conditional logical functions f (&) - And . Since the input positive arguments ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _{k-2 are} formed by the logical function f ₁ (&) - And and f ₂ (&) - And , and their general functional structure can be written either in the form of an analytical expression (593),

or in the form of a minimized analytical expression (594).

And the combined functional structure that activates the conditionally negative argument ^-101 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k-1 can be} written either in the form of an analytical expression (595),

or in the form of a minimized analytical expression (596).

But alternating structures of active and inactive arguments of a graphoanalytic expression can also be attributed to a potential transfer (595)

Moreover, functional structures with an output logical function f ₁ (&) - And and f ₂ (&) - And have a technological cycle ∆t _Σ → 1 ∙ f (&) - And, corresponding to one conditional logical function f (&) - And . Since the positive input arguments ( ⁺ n & m _i ) _k-1 and ( ⁺ n & m _i ) _{k-2 are} also formed by the logical function f ₁ (&) - And and f ₂ (&) - And, and write their general functional structure either in the form of an analytical expression (596),

or in the form of a minimized analytical expression (597).

And the combined functional structure that activates the conditionally negative argument ^-2 (Yes ^- ← ^- ) S ^{i + 1} _i ) _{k-1 can be} written as an analytical expression (598),

or as a minimized analytical expression (599).

And if we take into account that the combined structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _{min is} multivariant, then “Yes” ^{+, -} Transfer Argument can activate the following functional structures.

Functional structure 1. Sequential alternation of positive "Complex arguments" ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and ( ⁺ n & m _i ) _k-2 and conditionally negative "Complex arguments" ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and ( ^- n & m _i ) _k-2 in the graph-analytical expression (600),

in which we write the functional structure either in the form of an analytical expression (601),

or in the form of a minimized analytical expression (602).

And the combined functional structure that activates the conditionally negative argument ^-3 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k-1 can be} written as an analytical expression (603),

or in the form of a minimized analytical expression (604).

Functional structure 2. Sequential alternation of positive "Complex arguments" ( ⁺ n & m _i ) _k-1 and ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-2 and conditionally negative "Complex arguments" ( ^- n & m _i ) _k-1 and ¹ ( ^-10 S ^{i + 1} _i ) _k-2 in the graph-analytical expression (605),

in which we write the functional structure either in the form of an analytical expression (606),

or in the form of a minimized analytical expression (607).

And the combined functional structure that activates the conditionally negative argument ^-4 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k-1 can be} written as an analytical expression (608),

or in the form of a minimized analytical expression (609).

Moreover, if we take into account that “Yes” ^{+, - the} Transfer Argument ”can also be activated in the conditionally“ k-1 ”“ Minimization Zone ”by means of the set of arguments ⁺⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _{k -1} and ^-0 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 in the graph-analytical expression (610)

and the same set of arguments ⁺⁵ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ^-5 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 , positionally located in the conditionally “k- 2 ”“ Minimization zone ”may activate additional“ Yes ” ^{+, -} Transfer argument”.

Functional structure 3. Sequential alternation of positive "Complex arguments" ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k-2 and conditionally negative "Complex arguments" ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and ¹ ( ^-11 S ^{i + 1} _i ) _k-2 in the graph-analytical expression (611),

in which functional structures have a technological cycle ∆t _Σ → 3 ∙ f (&) - And, corresponding to three conditional logical functions f (&) - And. Since if we write down the structure of the logical functions of the “Complex argument” ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k-2 in the form of an analytical expression (612),

then only this functional structure has a technological cycle ∆t _Σ → 2 ∙ f (&) - And, corresponding to two conditional logical functions f (&) - And. But if we perform the transformation of the structure of logical functions (612) in accordance with the vector structure (613),

as well as in accordance with vector structures (614),

then the resulting structure of logical functions, which we write in the form of a minimized analytical expression (615)

also has a technological cycle ∆t _Σ → 2 ∙ f (&) - And, corresponding to two conditional logical functions f (&) - And, but with an output logical function f ₁ (&) - And. As a result, the functional structure (611) activating the positive argument ⁺⁵ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _{k-1 can be} written either in the form of an analytical expression (616),

or in the form of a minimized analytical expression (617).

And the combined functional structure that activates the conditionally negative argument ^-5 (Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 , we write in the form of an analytical expression (618),

or in the form of a minimized analytical expression (619).

Functional structure 4. Sequential alternation of positive "Complex arguments" ( ⁺ n & m _i ) _k-1 and ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-1 and conditionally negative "Complex arguments" ( ^- n & m _i ) _{k- 1} and ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 in the ^{graph-analytical} expression (620),

in which functional structures have a technological cycle ∆t _Σ → 3 ∙ f (&) - And, corresponding to three conditional logical functions f (&) - And. Since if we write down the structure of logical functions of the positive “Complex argument” ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 in the form of an analytical expression (621),

and the structure of the logical functions of the conditionally negative “Complex argument” ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _{k-2 is} written in the form of an analytical expression (622),

then only these functional structures have a technological cycle ∆t _Σ → 2 ∙ f (&) - And, corresponding to two conditional logical functions f (&) - And. But if you perform the transformation of the structure of the logical functions “Yes” ^{+, -} Transfer argument ”(620) in accordance with the vector structure (623),

and in accordance with the vector structure (624),

then we write either the structure of logical functions (625)

either minimized analytic expression (626)

with the technological cycle ∆t _Σ → 2 ∙ f (&) - And, which corresponds to two conditional logical functions f (&) - And, and also for activating the conditionally negative argument ^-4 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1, we write either the structure of logical functions (627)

 or minimized analytic expression (628).

Functional structure 5. Sequential alternation of positive “Complex arguments” ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 and conditionally negative “Complex arguments” ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k-2 in the ^{graph-analytical} expression (629),

in which functional structures have a technological cycle ∆t _Σ → 3 ∙ f (&) - And, corresponding to three conditional logical functions f (&) - And. But if you perform a transformation of the structure of the logical functions “Yes” ^{+, -} Transfer argument ”(629) for positive arguments ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 and ¹ ( ^{+0.11 | 11} S ⁱ | _{i + 1} ) _k-2 in accordance with the vector structure (630),

where by the input positive “Complex argument” ¹ { ⁺¹⁰ S ^{i + 1} _i } _k-1 we mean the set of input arguments (631),

since they are included in the system of the input logical function f ₁ (&) - And, and for conditionally negative arguments ¹ ( ^-10 S ^{i + 1} _i ) _k-1 and ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _{k- 2} in accordance with the vector structure (632),

where under the input conditionally negative "Complex argument" {^-10S^{i + 1} _i}_k-1 we will also understand the set of input arguments (633),

we’ll write it down for a positive Complex argument ” {⁺¹⁰S^{i + 1} _i}_k-1 either minimized analytic expression (634)

with a technological cycle ∆t _Σ → 2 ∙ f (&) - And, which corresponds to three conditional logical functions f (&) - And, or we write down the structure of logical functions (635).

It should be noted that the functional structure (635) also has a technological cycle ∆t_Σ→ 3 ∙ f (&) - And, corresponding to the three conditional logical functions f (&) - And, but this technological cycle does not change when the resulting conditionally negative sum argument (^-S_i)_k in conditionally “k” “Minimization Zone”, if the transformed positive argument of the term^one(⁺¹⁰S^{i + 1} _i)_k we also write in the form of a "Comprehensive argument" {⁺¹⁰S^{i + 1} _i}_k   (636).

As a result, the non-minimized functional structure that activates the resulting conditionally negative argument of the sum ( ^- S _i ) _k in the conditionally “k” “Minimization Zone” is written in the form of an analytical expression (637),

And after transferring the functional structure with the output logical function f ₁ (&) - AND through the logical function system f ₁ (}) - OR and after combining the logical functions, we write the minimized functional structure (638)

with a technological cycle ∆t _Σ → 3 ∙ f (&) - And, which corresponds to three conditional logical functions f (&) - And. We write down a similar functional structure that activates the resulting positive argument of the sum ( ⁺ S _i ) _k in the conditionally “k” “Minimization Zone” in the form of an analytical expression (638.1),

in which also the technological cycle ∆t _Σ → 3 ∙ f (&) - And corresponds to the three conditional logical functions f (&) - And. Moreover, the structure of logical functions that activates the resulting positive argument of the sum ( ⁺ S _i ) _k in the conditionally “k” “minimization zone” is written in the form of an analytical expression (639).

And the structure of logical functions that activates the resulting conditionally negative argument of the sum ( ^- S _i ) _k in the conditionally “k” “Minimization Zone” is written in the form of an analytical expression (640).

From the analysis of graphoanalytic expressions (639) and (640) it follows that the system of the output logical function f ₁ (}) - OR and f ₃ (}) - OR includes "Excessive structures" with the output logical function f ₂ (&) - AND and f ₃ (&) - And the “Redundant arguments” ( ⁺ n _{i + 1} ) _k-3 and ( ⁺ m _{i + 1} ) _k-3 conditionally “k-3” “Minimization zones”, and the functional structure ( 639) can be written either in the form of an analytical expression (641)

either as a minimized analytical expression (642)

either as a non-minimized analytical expression (643),

but with the technological cycle ∆t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And. And the functional structure (640), activating the conditionally negative argument of the resulting sum ( ^- S _i ) _k , can be written either in the form of an analytical expression (644),

either as a minimized analytical expression (645)

either as a minimized analytical expression (646),

but with the technological cycle ∆t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And. And such a minimization of functional structures (639) and (640) is possible, because if we return to the analysis of “Functional structure 1” of expression (601) and (603), writing down a functional structure (601) for a similar situation or in the form of a graphoanalytic expression (647) ,

either as a minimized analytical expression (648)

where under the system of input arguments { ^-10 S ^{i + 1} _i } _k-1 and { ^-0.11 S ^{i + 1} _i } _k-2 with the symbol ^- (Yes ^- ← ^- ) ₃

and the functional link (=), which is included in the system of the logical function f ₁ (&) - And, we will understand the simultaneous supply of written arguments that activate the third conditionally negative argument ^-3 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k- 1} local “Yes” ^- Transfer argument ”with the technological cycle ∆t _Σ → 3 ∙ f (&) - And, corresponding to the three conditional logical functions f (&) - And;

either as a non-minimized analytical expression (649),

but with the technological cycle ∆t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And, and the functional structure (603), activating the conditionally negative argument of the resulting sum ( ^- S _i ) _k, writing it either in the form of a graphic-analytical expression (650),

either as a minimized analytical expression (651)

either as a minimized analytical expression (652),

then from the graph-analytical expressions (647) - (652) it follows that for the correct conversion of the arguments in the conditionally “k” “Minimization Zone” it is enough to analyze the activity of the arguments in the conditionally “k-2” “Minimization Zone”. But if we write down for the positive sequence of arguments the terms ( ⁺ n & m _i ) _k , ( ⁺ n & m _i ) _k-1 , ... ( ⁺ n & m _i ) _kg in the form of a graphoanalytic expression (653)

with an active local transfer argument in conditionally "k-1"₂ “Zone of minimization” and graphoanalytic expression (654)

without an active local carry argument in conditionally "k-1"₂ “Zone of minimization”, as well as graphoanalytic expression (655)

without an active local carry argument in conditionally "k-1"₂ "Minimization Zone", but with sequential positive arguments included^one(⁺¹⁰S^{i + 1} _i)_k-3 and^one(⁺¹⁰S^{i + 1} _i)_k-4 and similar procedures for converting conditionally negative arguments of terms (^-n & m_i)_k, (^-n & m_i)_k-1, ... (^-n & m_i)_kg in the form of a graphic-analytical expression (656),

with an active local transfer argument in conditionally "k-1"₂ “Zone of minimization” and graphoanalytic expression (657)

without an active local carry argument in conditionally "k-1"₂ “Zone of minimization”, as well as graphoanalytic expression (658)

without an active local carry argument in conditionally "k-1"₂ "Zone of minimization", but with consecutive conditionally negative arguments enabled^one(^-10S^{i + 1} _i)_k-3 and^one(^-10S^{i + 1} _i)_k-4 and similar procedures for converting conditionally negative arguments of terms (^-n & m_i)_k, (^-n & m_i)_k-1, ... (^-n & m_i)_kg in the form of a graphoanalytic expression (658), then from an analysis of the logical-dynamic process of transforming the arguments of the combined structure of the terms^±[S_i] f_one(+/-)_min and^±[S_i] f₂(+/-)_minit follows that for the correct conversion of the arguments in the conditionally “k” “Minimization Zone” it is sufficient to analyze the activity of the arguments in the conditionally “k-1” “Minimization Zone”. It should be noted that in graphoanalytic expressions (653) - (658), the combined structures of the terms were analyzed^±[S_i] f_one(+/-)_minand ^±[S_i] f₂(+/-)_min, in the structure of which the sequence of arguments is written of a single sign of either positive arguments or conditionally negative arguments, but sequential combined argument structures with alternating signs are possible and the logic of transformation of such sequences has a “Feature”. And if we write down the logical-dynamic process of converting such arguments in the form of a graphoanalytic expression (659)

and in the form of graphoanalytic expression (660)

then from the analysis of the vector structure of the logical-dynamic process of converting the combined structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min it follows that for the correct conversion of the arguments into the conditionally “k” “minimization zone” it is not enough to analyze the activity of the arguments conditionally "k-1""Zone of minimization." And only the analysis of the arguments in the conditionally “k-2” “Minimization Zone” allows the correct activation of the argument of the resulting conditionally minimized sum ^± [S _i ] f ₃ (+/-) _min , since the argument conversion procedure has “ ⁺ Feature” and “ ^“ Feature.” It should be noted that for the correct conversion of arguments in the conditionally “k” “minimization zone” there can be two options.

Option 1. Concrete argument ⁺ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 and ^- ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 positive local transfer (661)

and the specific argument ^is (Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 conditionally negative carry (662)

      Option 2. Not a specific structure of the arguments in the conditionally “k-2” “Minimization Zone”, by means of which the local transfer argument is generated, but its sign component, ie "⁺Generalized Argument ^one(^{+ V}S^{i + 1} _i)_k-2expressions (585)

 and "^-Generalized Argument ^one(^-VS^{i + 1} _i)_k-2expressions (664).

It should be noted that the functional structures (663) and (664) with the output logical function f ₂ (} &) - OR NOT have a technological cycle ∆t _Σ → 2 ∙ f (&) - AND conversion of arguments corresponding to two logical functions f (&) - And, but have a singularity. Since if we write the analytical expressions (663) and (664) in the form of a structure of logical functions (666),

then after transferring the logical functions f ₂ (&) - NOT and f ₄ (&) - NOT through the system of logical functions f ₃ (}) - OR and f ₆ (}) - OR they change their logical properties in the expression (667)

by the properties of the logical functions f ₁ (&) - And and f ₂ (&) - And, and after replacing the sequential logical f ₁ (& ₁ = & _2.1 ) and f ₁ (& ₂ = & _4.1 ) with equivalent functional connections f ₁ (=) and f ₂ (=) and the union of the logical functions f _2.2 (&) - NOT and f _4.2 (&) - NOT with the logical functions f ₂ (}) - OR and f ₄ (}) - OR, which will result to the formation of logical functions f ₁ (} &) - OR NOT and f ₂ (} &) - OR NOT in analytical expressions (668).

It should be noted that the “Feature” of analytical expressions (668) are the output logical functions f ₁ (&) - And and f ₂ (&) - And, which can be output logical functions when the resulting argument of the sum is activated. And if we take into account that the mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization Zones” is being formed, then in this “Minimization Zone” the input functional structures of expression (668) must be entered, which can be written either in the form of analytical expressions (669),

or as a system of “ ^± Complex arguments” (670).

with the technological cycle ∆t _Σ → 1 ∙ f (&) - And. It should be noted that the technological cycle of the system of arguments (670) is less than the technological cycle of functional structures (661) and (662) by one conditional logical function f (&) - And, which ultimately allows the mathematical model of the adder ^± f ₁ ( Σ _RU ) _min conditionally “k” “Minimization zones” with the technological cycle ∆t _Σ → 3 ∙ f (&) - And, which corresponds to three conditional logical functions f (&) - And. And when forming functional structures that activate the resulting argument of the sum, we will write the arguments ↓ ¹ ( ^{+ V} S ^{i + 1} _i ) _k-2 and ↓ ¹ ( ^-V S ^{i + 1} _i ) _k as the input “ ^± Generalized argument” _-2 . And if we return to the semantic content of similar arguments ¹ ( ^{+ V} S ^{i + 1} _i ) _k-2 and ¹ ( ^-V S ^{i + 1} _i ) _k-2 introduced in expression (533), we write it in the form of analytical expressions ( 671)

then the technological cycle ∆t _Σ → 2 ∙ f (&) - And corresponds to two conditional logical functions f (&) - And, and in its semantic content are equivalent to “ ^± Complex arguments” (670). At the same time, the feature of the information content “ ^± Complex arguments” ↓ ¹ ( ^{+ V} S ^{i + 1} _i ) _k-2 and ↓ ¹ ( ^-V S ^{i + 1} _i ) _k-2 , as expressions (670) and (671) is positive argument and conditionally negative argument ¹ ( ⁺⁰¹ S ^{i + 1} _i ) _k-2 and ¹ ( ^-01 S ^{i + 1} _i ) _k-2 , which significantly changes the logic of transformation of arguments into conditionally “k” “Minimization Zone”. Because if we write the graphoanalytic expression (672)

with an active argument of local end-to-end transfers and graphoanalytic expression (673),

Without an active argument of local end-to-end transfers, then there is uncertainty in the procedure for generating the argument of the resulting sum in the subsequent “Minimization Zones”. But if the combined structure of the arguments of the terms (673) is corrected and written down either in the form of a graphic-analytical expression (674),

where {⁺¹⁰S^{i + 1} _i}_k  and {⁺¹⁰S^{i + 1} _i}_k-1  - a set of arguments that activate the resulting argument^one(⁺¹⁰S^{i + 1} _i)_k;

and in the form of graphoanalytic expression (675)

with the technological cycle t _Σ → 3 ∙ f (&) - And, corresponding to the three conditional logical functions f (&) - And, and in a minimized analytical form expressions (674) and (675) we write in the form of a functional structure (676)

with four output logical functions f _1-4 (&) - And and with a technological cycle t _Σ → 3 ∙ f (&) - And, corresponding to three conditional logical functions f (&) - And, or in the form of graphoanalytic expression (677)

also with four output logical functions f _1-4 (&) - And, but with a technological cycle t _Σ → 4 ∙ f (&) - And, corresponding to four conditional logical functions f (&) - And. But if we write down all possible active and inactive arguments in the conditionally “k-2” “minimization zone” in the form of a graphoanalytic expression (678)

and in the form of a graphoanalytic expression (679),

then the correct activation of the conditionally negative argument of the resulting sum ( ^- S _i ) _k in expressions (676) and (677) is possible both with a positive local transfer argument ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 , and with conditionally negative local transfer argument ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 . Since if we return to the analysis of the procedure for transforming the combined structure of the arguments of the terms (660), writing it in the form of a graphic-analytical expression (680),

then conversion of positive arguments (⁺n & m_i)_kV (⁺¹⁰S^{i + 1} _i)_k  in the conditionally “k” “minimization zone” with the activity of positive arguments (⁺n & m_i)_k-1V (⁺¹⁰S^{i + 1} _i)_k-1    with local transfer arguments ((Not⁺←⁺) S^{i + 1} _i)_k-2 and ((Not^-←^-) S^{i + 1} _i)_k-2 expressions (678) and (679) is independent of the activity of the arguments in the conditionally “k-2” “minimization zone”. Therefore, the input argument ↓^one(^{+ V}S^{i + 1} _i)_k-2  in functional structures (676) and (677) is the “Redundant argument”, and we write these functional structures in the form of an analytical expression (681)

with four output logical functions f _1-4 (&) - And and with the technological cycle t _Σ → 3 ∙ f (&) - And, or in the form of graphoanalytic expression (682)

and with the technological cycle t _Σ → 4 ∙ f (&) - And, which activate the conditionally negative resulting argument ( ^- S _i ) _k conditionally “i” of the discharge in the conditionally “k” “Minimization zone”.

We write similar functional structures that activate the positive resulting argument ( ⁺ S _i ) _{k of} conditionally “i” bits in the conditionally “k” “Minimization Zone” in the form of an analytical expression (683)

with four output logical functions f _1-4 (&) - And and with the technological cycle t _Σ → 3 ∙ f (&) - And, or in the form of graphoanalytic expression (684)

and with the technological cycle t _Σ → 4 ∙ f (&) - And. Both functional structures (683) and (684) correctly activate the positive resulting argument ( ⁺ S _i ) _k in the conditionally “i” category, because if we return to the analysis of the procedure for converting the combined structure of the arguments of the terms (659), writing it in the form of a graphoanalytic expression ( 685)

then the conversion of conditionally negative arguments ( ^- n & m _i ) _k V ( ^-10 S ^{i + 1} _i ) _k to the conditionally “k” “minimization zone” when conditionally negative arguments ( ^- n & m _i ) _k-1 V ( ^-10 S ^{i +1} _i ) _k-1 , taking into account the arguments of local transfer ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 expressions (678) and (679) does not depend on the activity of the arguments in the conditionally “k-2” “minimization zone”.

    Further, if we return to the analysis of the graphoanalytic expression "Positive channel of the adder" i + 1 "category" (586), then on the one hand it is necessary to exclude the expression (686) from it,

since based on the results obtained, the conversion of positive arguments ( ^- n & m _i ) _k V ( ^-10 S ^{i + 1} _i ) _k in the conditionally “k” “Minimization Zone” with the activity of positive arguments ( ^- n & m _i ) _k-1 V ( ^-10 S ^{i + 1} _i ) _k-1 , the conditionally negative argument ( ^- S _i ) _k conditionally “i” of the discharge in the conditionally “k” “Minimization zone” should be activated. On the other hand, in the "Positive channel of the adder" i + 1 "discharge" (586) included the functional structure (687)

which, taking into account the logical-dynamic process of transformation of arguments (682), which can be written in the form of a graphic-analytical expression (688)

should also be excluded from this channel, because if we adjust the procedure for converting the arguments of the terms (687)  taking into account the functional structure (688), writing it in the form of a graphic-analytical expression (689)

and in the form of graphoanalytic expression (690),

from the analysis of which it follows that the functional structure (690) has a “Defect”, since it does not take into account the possible active local transfer argument from the conditionally “k-2” “Minimization Zones”, which leads to the activation of two consecutive arguments into the conditionally “k-1” "Zone of minimization." Therefore, for the correct transformation of the arguments of the terms into a system of logical functions f_1-4(&) - And functional structures (689) and (690) we introduce an additional "" Not "^-Transfer Argument ((Not^-←^-) S^{i + 1} _i)_k-1 and "Yes"^-Transfer Argument ”((Yes^-←^-) S^{i + 1} _i)_k-2 and write them in the form of an analytical expression (691)

and in the form of an analytical expression (692).

At the same time, “Yes” ^{is the} Transfer Argument ”((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 can be activated in the following situations, which we write in the form of a graphic-analytical expression (693),

in which all possible "Complex arguments" of local transfer ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k-2 are} introduced into the system of the logical function f ₁ (}) - and its activation will correspond to three conditional logical functions f (& ) -A, which will lead to an increase in the technological cycle t _Σ → 5 ∙ f (&) - And the procedure for generating the resulting argument of the conditionally negative sum ( ^- S _{i + 1} ) _{k of} expression (692) to five conditional logical functions f (&) - AND. And to form the “Complex argument” of the local transfer ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 into the functional structure (693) we introduce the output logical function f ₁ (&) - NOT and write it in the form of an analytical expression ( 694)

in which we carry out the transfer of the introduced function through the logical function system f ₁ (}) - OR. As a result of such a transfer, the logical properties of the logical function f ₁ (}) - OR are changed to the properties of the logical function f ₁ (&) - AND in the analytical expression (694.1),

in this case, after combining the transferred logical function f_one(&) - NOT with the input "Complex arguments" they also changed their logical properties and the symbols of their formation are recorded with a changed level of the analog signal. And when you consider that the argument ((Not^-←^-) S^{i + 1} _i)_k-2formed by the logical function f_one(&) - And, must be entered in expression (691)    into the system of the same logical function, therefore, the technological cycle t_Σ→ 1 ∙ f (&) - And and t_Σ→ 2 ∙ f (&) - And the functional structure (694) is determined by the technological cycle of formation of its input arguments. As a result, if we write the functional structure (691) in the form of an analytical expression (695),

then the maximum technological cycle t_Σ→ 4 ∙ f (&) - And activating the resulting conditionally negative argument (^-S_i)_k will correspond to four conditional logical functions f (&) - And. It should be noted that the technological cycle t_Σ→ 4 ∙ f (&) - And activating the resulting conditionally negative argument (^-S_i)_k in the functional structure (695) is directly related to positive input arguments (⁺¹⁰S^{i + 1} _i)_k and (⁺¹⁰S^{i + 1} _i)_k-1  and a conditionally negative argument (^-10S^{i + 1} _i)_k-2 with a changed level of an analog signal, technological cycle t_Σ→ 2 ∙ f (&) - And which corresponds to two conditional logical functions f (&) - And. Therefore, let us return to an additional analysis of the functional structure (407), writing it in the form of a graphoanalytic expression (696)

and functional structure (410), writing it in the form of a graphic-analytical expression (697)

which in a minimized form can be written in the form of analytical expressions (696) and (697) with the input “Complex argument” (⁺nVm_{i + 1}) V (⁺nVm_i) V (^-nVm_i)_k (698)

with output logic f_one(} &) - OR NOT and with the input "Complex argument" (^-nVm_{i + 1}) V (⁺nVm_i) V (^-nVm_i)_k (699)

with output logic function f ₂ (} &) - OR NOT.

Further, if the output logic function f ₁ (&) is NOT entered into the functional structure (696), which activates without changing the level of the analog signal, then the functional structure (700) will be formed,

which activates the resulting conditionally negative argument (^-10S^{i + 1} _i)_k with a changed analog signal level. And if you carry out the transfer of the functional structure with the output logical function f_one(&) - And through the system of the logical function f_one(}) - OR and write the analytical expression (701),

and also perform, in accordance with the vector structure, the sequential transfer of the function f ₁ (&) - NOT through the logical function system f ₁ (}) - OR, f _1.1 (&) - And and f _1.2 (&) - And, and then combine with input “Complex arguments”, and write down the functional structure (702),

then in the system of logical functions f ₁ (}) - OR and f ₂ (}) - OR input conditionally negative argument ( ^- n & m _{i + 1} ) _k belongs to the category "Features". Since if the functional structure (702) is written for conditionally “k-2” “Minimization zones” in the form of expression (703)

and introduce it into the functional structure (694), writing in the form of a structure of logical functions (704),

then in the system of logical functions f ₁ (}) - OR and f ₂ (}) - OR conditionally negative input argument ( ^- n & m _{i + 1} ) _k-2 , formed by the logical function f (&) - AND, is “Redundant argument ”, Taking into account that the“ Priority argument ”is included in the functional structure (694), the input conditionally negative argument ( ^- n & m _{i + 1} ) _k-2 , formed by the logical function f (&) is NAND, and only its activity allows activate the resulting argument ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 . Therefore, we write the functional structure (702) in the form of an analytical expression (705),

in which we perform the reverse transfer of the functional structure of the same name with the output logical function f ₁ (}) - OR and f ₂ (}) - OR through the logical function system f ₁ (&) - AND and write the minimized analytical expression (706),

and after the transfer of the logical functions f ₁ (&) - NOT and f ₂ (&) - NOT through the system of the logical function f ₁ (&) - And we will write either in the form of a minimized analytical expression (707)

with the input logical function f ₁ (} &) - OR NOT, or in the form of a minimized analytical expression (708)

and introduce the functional structure (694) into the system, writing it in the form of a graphic-analytical expression (709).

From the analysis of the input arguments of the functional structure (709) it follows that it includes conditionally negative arguments of the same name, which are formed by three logical functions f ₁ } &) - OR-NOT, f (}) - OR and f (&) - AND- NOT, therefore, we will conduct an additional analysis of the possible redundancy of conditionally negative arguments. And for this, we carry out the transfer of the functional structure with the output additional logical function f _1.1 (&) - AND with the input conditionally negative argument ( ^- n & m _i ) _k-2 through the logical function system f ₁ (}) - OR and write the structure of the logical functions (710 ),

from the analysis of which it follows that functional input structures with output logical functions f _1.1 (&) - And - f _1.3 (&) - And allow you to correctly activate the resulting argument ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 for the absence of a local conditionally negative transfer argument; therefore, we write the functional structure (709) in the form of an analytical expression (711),

and the functional structure of the "Conditionally negative channel of the adder" i "discharge" (691) we write in the form of an un minimized analytical expression (712),

where ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k and ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 - “Complex argument” conditionally “k” and “k-1” “Minimization zones” with the technological cycle t _Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And. But the functional structure (712) can be adjusted before the technological cycle t _Σ → 4 ∙ f (&) - And four conditional logical functions f (&) - And, if you carry out the transfer of the logical function f ₁ (&) - And through the input logical system functions f ₁ (}) - OR, but it is advisable at the first stage of synthesis of a functionally complete mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization zones” not to minimize the structure of logical functions (712) by the technological cycle, but write in the form of a minimized analytical expression (713).

Since at the technological cycle level t _Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And on the one hand, the number of functional structures for possible various transformations of a particular argument in the conditionally “k” “Minimization Zone” is minimized, with on the other hand, the analytical form used for writing various “Complex arguments”, combined with the graphic-analytical structure of the logical-dynamic process of transforming the arguments of the terms ^± [S _i ] f ₁ (+/-) _min , has a completely simple semantic content that will allow the formation of to have a functionally complete mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k-1” “Minimization zones”. So, in particular, the analytical form for writing the “Complex argument” ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k , which includes two positional structures of the arguments and the logic of their conversion corresponds to one arithmetic axiom “+1” → “+ 2 "" - 1 ", since these arguments have the equivalent" information content ", as well as the introduced" Complex argument "((Not ^- ← ^- ) S ^{i + 1} _i ) _{k-2 of} conditionally negative local transfer with minimized semantic content eliminates a sufficiently large number of possible options for such a transfer, which include functional structure (711)

activating the resulting conditionally negative argument ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 , a similar "information quality" has the conditionally negative "Complex argument" ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k- 2} in graphoanalytic terms (693).

Moreover, a similar “information quality" has a positive argument ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 in the functional structure (714),

which is active when the positive argument ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 local transfer of the functional structure is inactive (715).

       Further, if we return to the additional analysis of the functional structure (713), writing it in the form of a graphic-analytical expression (716)

then with the activity of the positive “Complex argument” ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k and ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 into the logical function system f ₁ ( &) - And the conditionally negative argument ((Not ^- ← ^- ) S ^{i + 1} _i ) _{k-2 of the} “Necessary condition” is included. Since if we write down the logical-dynamic process of converting the combined structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min with the active positive argument ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k to the conditionally “k” “Zone of minimization” and the active conditionally negative argument ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 in the conditionally “k-2” of “Zone of minimization” in the form of a graphoanalytic expression (717),

then in this situation, the conditionally negative argument of the resulting sum ( ^- S _{i + 1} ) _{k of the} conditionally “i + 1” discharge will be activated and it will be activated only with the active conditionally negative argument ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k- 2} . Since if we write down the logical-dynamic process of converting the combined structure of the arguments of the terms ^± [S _i ] f ₁ (+/-) _min with the active argument ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k to the conditionally “k” “ Minimization zone ”and with an active positive“ Complex argument ”((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 in the conditionally“ k-2 ”“ Minimization zone ”in the form of a graphic-analytical expression (718),

then in this situation, as well as in the graphoanalytic expression (716)

the conditionally negative argument of the resulting sum ( ^- S _i ) _{k of} conditionally “i” discharge will be activated. Therefore, the input arguments ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-2 functional structures (718) and (719) must be combined in the system logical function f ₂ (}) - OR, functional structures are written in the form of an analytical expression (720),

      A "Positive channel of the adder" i "discharge" has a similar functional structure and we write it in the form of an analytical expression (721)

and the "Positive channel of the adder" i + 1 "discharge" has a similar structure and it in accordance with the expression (717)

we write in the form of an analytical expression (723)

It should be noted that the procedure for converting the arguments of the terms in (722) and (723) with alternating arguments ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k has a “Feature” of activating the arguments of the resulting sum in the conditionally “k” “Zone of minimization” and in the conditionally “k-1” “Zone of minimization” if we write down the procedure for converting the arguments ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 in the form of a graphoanalytic expression (724),

then in this situation, the positive argument of the resulting sum ( ⁺ S _i ) _{k of} conditionally “i” discharge will be activated. And if we write down the procedure for converting the arguments ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k and ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 in the form of a graphoanalytic expression (725),

then in this situation, the conditionally negative argument of the resulting sum ( ^- S _i ) _{k of} conditionally “i” discharge will be activated. It should be noted that the input "Complex argument" ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k and ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k directly relates to the category of argument ( (Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k of} local transfer, which also includes the argument ( ⁺¹¹ S ^{i + 1} _i ) _k and ( ^{- 11} S ^{i + 1} _i ) _k with two consecutive active arguments and the argument ( ⁺¹⁰ S ^{i + 1} _i ) _k and ( ^-10 S ^{i + 1} _i ) _k , as well as the arguments ( ⁺ n & m _{i + 1} ) _k and ( ^- n & m _{i + 1} ) _k . As a result, the argument ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _{k of the} local transfer can be written in the form of the expression (726),

from the analysis of which it follows that if the arguments ( ⁺¹¹ S _{i + 1} ) _k and ( ^-11 S _{i + 1} ) _k are active in the conditionally “k” “Minimization Zone”, then they relate to the “Activation condition” of the local transfer argument ( (Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 from conditionally “k-1” “Minimization zones” and they are included in the functional structure ( 727)

into the general system of the logical function of the expression (567) together with the “Complex argument” ( ^{± 1, ± 0x0} S ^{i + 1} _i ) _k . As for the “Complex argument” ( ⁺¹¹ S ^{i + 1} _i ) and ( ^-11 S ^{i + 1} _i ), the logic of their transformation has its own “Feature”, which is written in the “Positive channel of the adder“ i ”category” as functional structure (688), which we write in the form of a graphical analytical expression (728),

where is the system of input arguments ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1 and ( ^{± 1, ± 0х0} | -1х + 1 | , | + 1x-1 | S ^{i + 1} _i ) _k-1 corresponds to the “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally "k-1" of the "Minimization zone", and in the "Conditionally negative channel of the adder" i "discharge" is written in the form of a functional structure (691), which we write in the form of graph-analytical expression (729),

where is also the input argument system^one(⁺⁰¹S^{i + 1} _i)_k-1,^one(^-01S^{i + 1} _i)_k-1 and (^{± 1, ± 0x0}| -1x + 1 |, | + 1x-1 | S^{i + 1} _i)_k-1 matches the "Complex argument" ((Not⁺←⁺) S^{i + 1} _i)_k-1and ((Not^-←^-) S^{i + 1} _i)_k-1 conditionally "k-1" "Zone of minimization." And the system of "Complex arguments" ((Not⁺←⁺) S^{i + 1} _i)_k-1and ((Not^-←^-) S^{i + 1} _i)_k-1 conditionally "k-1" "Zone of minimization", essentially  belongs to the category of argument ((Not^±←^±) S^{i + 1} _i)_k-1, which includes the semantic content - “the absence of any transfers” from the conditionally “k-1” “Minimization Zones”. It should be noted that the "Complex argument" ((Not^±←^±) S^{i + 1} _i)_k-1 conditionally "k-1" "Minimization zones" is formed in accordance with the functional structure (730)

by means of the logical function f ₁ (&) - And, and if we write the functional structure conditionally “k-1” of the “Minimization Zone”, activating the conditionally negative argument ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1 in the form of graph-analytical expressions (731)

and the functional structure of the conditionally “k-1” “Minimization Zones”, activating the positive argument ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 in the form of a graphic-analytical expression (732),

then the “Complex argument” ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-1 “absence of any transfers” in the conditionally “k-1” “Minimization Zone” can be written as an analytical expression (733),

and if we take into account that the “Complex argument” ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-1 “the absence of any transfers” in the functional structure of the “Positive channel of the adder“ i ”category” (728) is included in the logical function system f _1-6 (&) - And, after combining the same logical functions in the expression (734),

then, on the one hand, the number of functional structures is minimized three times, on the other hand, the technological cycle t _Σ → 4 ∙ f (&) - And the activation of the positive argument ( ⁺ S _i ) _k conditionally “i” the discharge will correspond to four conditional logical functions f ( &)-AND. In this case, the functional structure of the “Positive channel of the adder“ i ”discharge” (728) with the “Complex argument” ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-1 “absence of any transfers” can be written as a minimized analytical expression (735 ),

in which the "Complex argument" ((Not ^± ← ^± ) S ^{i + 1} _i ) _{k-1 is} written as a system of transformed input arguments (736),

similarly, we write the functional structure of the “Conditionally negative channel of the adder“ i ”category” (729) in the form of a minimized analytical expression (737).

It should be noted that the “Complex argument” ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-1 in the form of a system of transformed input arguments (736) functionally belongs to the conditionally “k-1” “minimization zone”, and since the mathematical model of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization zones” is formed, then we can write it either as a set of arguments (738)

conditionally “k” of the “Zone of minimization”, or in the form of a functional structure (739).

Since the logic of converting the arguments into conditionally “k” of the “Minimization Zone” has been significantly changed in connection with the transformation of the “Complex argument” ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k and ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k , which includes two positional structures of the arguments and the logic of their transformation corresponds to the arithmetic axiom “+1” → “+2” “- 1” and “-1” ← “-2” “+ 1”, because these arguments have an equivalent "informational contents", so we can write functional structures for their correct conversion of the active argument ^{((Not ± ← ±) S} i + ^1, _{i) k-1} "absent e all transfers. " For the "Positive channel of the adder" i + 1 "discharge" and "Conditionally negative channel of the adder" i + 1 "discharge" we write the functional structure (740),

and functional structure (741).

     Further, if we return to the analysis of functional structures (721) and (724), writing down the functional structure (721) in the form of an analytical expression (742),

in which the input argument ((Not⁺←⁺) S^{i + 1} _i)_k-2written as an argument ((Not^±←^±) S^{i + 1} _i)_k-2, functional structure (724) in the form of an analytical expression (743),

then the functional structure of the "Positive channel of the adder" i "discharge" at this stage of its synthesis, we write in the form of a graphic-analytical expression (744),

and the "Positive channel of the adder" i + 1 "discharge", taking into account the functional structure (723) and (740), we write in the form of graphoanalytic expression (745).

At the same time, “Conditionally negative channel of the adder“ i ”category, taking into account the functional structures (737) and (720), as well as the functional structure

we write in the form of a graphoanalytic expression (746),

and “Conditionally negative channel of the adder“ i + 1 ”discharge”, taking into account the functional structures (717) and (741), we will write in the form of a graphic-analytical expression (747).

Further, if we return to the analysis of the previously formed functional structure of the “Positive channel of the adder“ i ”category” of the expression (586) and the functional structure of the “Conditionally negative channel of the adder“ i ”category” of the expression (588), in which, as a separate procedure for converting the combined structure terms ^± [S _i ] f ₁ (+/-) _{min the} functional structure is written ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k = f ₁ (}) - OR = ( ⁺ S _i ) _k (586), ¹ and the functional structure ^{(+0.11 | 11} S _ⁱ | ⁱ _{+ 1) k} = f ₃ (}) - OR = ^(- S _{i) k} (588), the arguments given corrected logic conversion Comrade makes sense to conduct a further analysis on the correctness of these functional structures. And for this, we write the functional structure ¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k = f ₁ (}) - OR = ( ⁺ S _i ) _k (586) in the form of a graph-analytical expression (748),

where ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 is the “transfer argument” formed by the functional structure (749);

¹ ( ^{-0.11 | 11} S ⁱ | _{i + 1} ) _k - “Complex argument” formed by the functional structure (750);

and write the functional structure of the "Positive channel of the adder" i "category" of the expression (742) in the form of a graphical analytical expression (751),

in which the “Feature” is the input conditionally negative argument ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k-1 conditionally “k-1” of the “Minimization zone” in the logical function system f ₃ (&) - And and to activate the positive resulting argument of the sum ( ⁺ S _i ) _k , the “Necessary condition” is included in the system of this function in the form of two arguments ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-2 and ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 conditionally "k-2""Minimizationzones". Since if the positive argument ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 is the “transfer argument” is activated in the conditionally “k-2” “Minimization Zone”, then in accordance with the functional structure of the “Positive Adder Channel“ i +1 "category" of expression (745)

the positive argument ( ⁺ S _{i + 1} ) _{k of} conditionally “i + 1” discharge will be activated. And if we return to the analysis of the functional structure (748) and, taking into account the functional structure (750), write the graphoanalytic expression (752)

and carry out the transfer of "Complex arguments" through the logical function system f ₁ (}) - OR, then we write the analytical expression (753), (753)

in which we replace the input argument ( ^- n & m _i ) _k with "Complex argument" ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k and write the adjusted analytical expression (754)

then the “Feature” of the functional structure (754) is the correct activation of the positive argument of the sum ( ⁺ S _i ) _k with the active positive “transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 . Since the set of active arguments is “Activation Conditions”, and we minimize them in the form of “Complex argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 → ( ^-11 S ^{i + 1} _i ) _k , allows you to activate the conditionally minimized positive argument of the resulting sum ( ⁺ S _{i + 1} ) _k-1 in the conditionally “k-1” “Minimization Zone”, and write such an activation either in the form of a graphic-analytical expression (755.1)

in which the conditionally negative "Complex argument" ( ^-11 S ^{i + 1} _i ) _{k is} written as a set of arguments ( ^- n _{i + 1} & m _i ) _k and ( ^- m _{i + 1} & n _i ) _k , or as a graphoanalytic expression (755)

with a positive additional input argument ( ⁺⁰¹ S ^{i + 1} _i ) _k and ¹ ( ^{+ 1х-1} S ^{i + 1} _i ) _k , which also activates the positive argument of the sum ( ⁺ S _{i + 1} ) _k . And if we return to the analysis of the functional structure of the "Positive channel of the adder" i + 1 "category" of expression (586),

where the positive argument of the sum ( ⁺ S _{i + 1} ) _{k of} conditionally “i + 1” discharge is also activated, then in the logical function system f _1-4 (&) - And the input argument ¹ ( ⁺¹⁰ S ^{i + 1} _i ) _{k- 1} due to the changed logic of argument conversion, it belongs to the category “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 , which is activated in the conditionally “k-1” “Minimization zone”. It should be noted that the logical positive function f _1-4 (&) - And also introduced the input positive " ⁺ Complex transfer argument" ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 conditionally "k-2 »“ Minimization zones ”as a“ Prerequisite ”, since if the conditionally negative“ ^- Complex transfer argument ”((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 is active in this“ Minimization zone ”, then a positive argument the sum ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge in accordance with the graphic-analytical expression (757),

in accordance with graphoanalytic expression (757),

in accordance with graphoanalytic expression (758)

cannot be activated, but will be activated positive argument to the sum (⁺S_i)_k conditionally “i” discharge in accordance with the changed logic of transformation of arguments of the combined structure of terms^±[S_i] f_one(+/-)_min. And if we combine the functional structures (757) - (759), then we write the minimized analytical expression (760),

at the same time, the functional structure (756), taking into account the combination “Complex argument” (^{+ 01, -11, + 1x-1}S^{i + 1} _i)_k expressions (760) we write in the form of an analytical expression (761).

Since the generated functional structure (760) correctly activates the resulting argument of the sum ( ⁺ S _i ) _{k of} conditionally “i” discharge, therefore, we introduce it into the “Positive channel of the adder“ i ”discharge” (744) and write the joint graphoanalytic expression (762),

it should be noted that in a functional structure with an output logical function f ₃ (&) - And the input conditionally negative argument ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k-1 can be replaced by “ ^- Complex argument transfer ”((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally“ k-1 ”“ Minimization zones ”and in this case, when the input argument ¹ ( ^-11 S ^{i + 1} _i ) _k-1 in In this zone, the resulting argument of the sum ( ⁺ S _i ) _{k of} conditionally “i” discharge will also be activated. And the "Positive channel of the adder" i + 1 "discharge", taking into account the functional structure (755) and (761), we write in the form of graphoanalytic expression (763),

in which also in the functional structure with the output logical function f ₂ (&) - And the input conditionally negative argument ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k-1 can be replaced by " ^- Complex transfer argument" ( (Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally "k-1" of the "Minimization zone" and in this case, when the input argument ¹ ( ^-11 S ^{i + 1} _i ) _k-1 is also active in this zone the resulting argument of the sum of ( ⁺ S _{i + 1} ) _k conditionally “i + 1” bits will be activated. It should be noted that the technological cycle t _Σ → 6 ∙ f (&) - And the procedures for activating the resulting argument of the sum ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge will correspond to six conditional logical functions f (&) - And, since the activation of the “Complex argument” (Not ^± ← ^± ) V ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 corresponds to the technological cycle t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And. And to shorten the technological cycle t _Σ → 4 ∙ f (&) - And the procedures for activating the resulting argument of the sum ( ⁺ S _{i + 1} ) _k conditionally “i + 1” of the discharge to four conditional logical functions f (&) - And you need a functional structure with the output logical function f ₂ (&) - And write in the form of an analytical expression (764)

with two functional structures and with input arguments ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-2 and ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 .

Functional similar structures should be introduced into the “Conditionally negative channel of the adder“ i ”discharge” and “The conditionally negative channel of the adder“ i + 1 ”discharge, since the positive and conditionally negative combined structures of the arguments of the terms ^± [S _i ] f ₁ (+ / -) _{min are} equally probable, therefore the structure of the logical functions of the "Positive channel of the adder" i "discharge" (760)

for the "Conditionally negative channel of the adder" i "discharge" we write in the form of an analytical expression (765).

since the logical-dynamic process of converting the input conditionally negative argument ¹ ( ^-01 S ^{i + 1} _i ) _k can be written in the form of a graphic-analytical expression (766),

the logical-dynamic process of converting the input positive argument ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k can be written in the form of a graphic-analytical expression (767),

and the logical-dynamic process of converting the input argument ¹ ( ^{-1x + 1} S ^{i + 1} _i ) _k can be written in the form of a ^{graphic-analytical} expression (768),

And the structure of the logical functions of the "Positive channel of the adder" i + 1 "discharge" (755)

for the "Conditionally negative channel of the adder" i + 1 "discharge" we write in the form of an analytical expression (769)

and the structure of the logical functions of the "Positive channel of the adder" i + 1 "category" (761)

for the "Conditionally negative channel of the adder" i "category" write either in the form of an analytical expression (770)

with the technological cycle t _Σ → 6 ∙ f (&) - And the transformation of the arguments of the terms six conditional logical functions f (&) - And, or in the form of a minimized analytical expression (771)

with the technological cycle t _Σ → 4 ∙ f (&) - And the transformation of the arguments of the terms four conditional logical functions f (&) - And. As a result, the “Conditionally negative channel of the adder“ i ”bits” of expression (746), taking into account the functional structure (765), we write in the form of a graphoanalytic expression (772)

where also in the functional structure with the output logical function f ₃ (&) - AND the input conditionally negative argument ( ⁺ n & m _i ) V ( ⁺¹⁰ S ^{i + 1} _i ) _k-1 can be replaced by “ ⁺ Complex transfer argument” (( Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 conditionally “k-1” “Minimization zones” and in this case when the input argument ¹ ( ⁺¹¹ S ^{i + 1} _i ) _k-1 is activated in this zone the resulting conditionally negative argument of the sum ( ^- S _i ) _k conditionally "i" discharge. In this case, the “Conditionally negative channel of the adder“ i + 1 ”category" of expression (747), taking into account the functional structures (769) and (771), we write in the form of graphoanalytic expression (773).

     Further, if we return to the functional structure of the “Positive channel of the adder“ i ”category" (567), writing it in the form of graphoanalytic expression (774),

in which, on the one hand, we perform the indicated equivalent replacements of the input arguments, on the other hand, we correct the logical-dynamic process of transforming the combined argument structures of the terms ^± [S _i ] f ₁ (+/-) _min , then write the corrected graph-analytical expression (775).

It should be noted that the “Feature” of the functional structure (775) is the two input “Complex arguments” ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-2 and ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 conditionally “k-2” “Minimization zones”, with activity of which the positive resulting argument ( ⁺ S _i ) _k conditionally “i” of the discharge can be activated. Since if we write the graphoanalytic expression (776),

then in the conditionally “i” bit “k” of the “Minimization Zone” both the positive argument ( ⁺ S _i ) _k and the conditionally negative argument ( ^- S _i ) _k , which form the active logical zero “+1” “–1 "→" ^± 0 ¹ ". Therefore, only the inactivity “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 in the conditionally “k-2” “Minimization zone” can be activated by the positive resulting argument of the sum ( ⁺ S _i ) _k , and if we return to the analysis of input arguments of the functional structure (775), then the set of arguments (777)

can be written using “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-2 with a changed level of the analog signal, the functional structure of which can be written in the form of a graphic-analytical expression (778),

and after transferring the logical function f ₁ (&) - NOT through the system of the logical function f ₁ (}) - OR and combining the transferred logical function f ₁ (&) - NOT with the input function "Complex arguments", we write the functional structure (779)

with output logic function f ₂ (&) - And with input “Complex arguments” with changed levels of analog signals. And if we return to the analytical expression of the “Positive channel of the adder“ i ”category” (775) and introduce the functional structure (779) into the system of the logical function f ₁ (&) - And, after combining the same logical functions f ₁ (&) - И and f ₂ (&) - And we write the corrected graphoanalytic expression (780)

with the technological cycle t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And. And if we write “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 with a changed analog signal level in the form of an analytical expression (781),

then the “Conditionally negative channel of the adder“ i ”discharge” has a similar functional structure, which we write in the form of a graphoanalytic expression (782),

where also instead of the totality of arguments (783)

in the logical function system f ₁ (&) - And “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 with a changed level of the analog signal is introduced. It should be noted that “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 with a changed level of the analog signal can be entered into the functional structure of the “Conditionally negative channel of the adder“ i ”discharge” ( 772) and “Conditionally negative channel of the adder“ i + 1 ”category” (773), and “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 with a changed analog signal level can be entered into the functional structure of the "Positive channel of the adder" i "discharge" (762) and the "Positive channel of the adder" i + 1 "discharge" (763), which will allow the procedure for converting the arguments of the terms is performed with the technological cycle t _Σ → 4 ∙ f (&) - And, which corresponds to four conditional logical functions f (&) - And. Therefore, the "Positive channel of the adder" i "discharge" (762), taking into account the functional structure (780), we write in the form of a graphic-analytical expression (784),

and “Conditionally negative channel of the adder“ i ”discharge” (772), taking into account the functional structure (782), we write in the form of a graphic-analytical expression (784),

A similar replacement of the sets of input arguments is performed in the "Positive channel of the adder" i + 1 "category" (763) we write it in the form of graph-analytical expression (785)

and in the "Conditionally negative channel of the adder" i + 1 "discharge" (773) and write it in the form of graphoanalytic expression (786).

Moreover, from the analysis of the functional structure of the “Positive channel of the adder“ i + 1 ”discharge" (785), which we write in the form of graphoanalytic expression (787)

it follows that a “Complex argument” ( ^-11 S ^{i + 1} _i ) _k-1 conditionally “k-1” “Minimization zones” with a changed level of an analog signal should be introduced into the system of a logical function. Since if we write down the procedure for converting the arguments of the terms with the active argument ( ^-11 S ^{i + 1} _i ) _k-1 in the conditionally “k-1” “Minimization Zone” in the form of the expression (788),

then the positive argument of the sum ( ⁺ S _i ) _k in the conditionally “i” category will be activated correctly, and the functional structure (787) in this situation will form a “Defect”. And if we return to the analysis of the functional structure “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally “k-1” of the “Minimization Zone”, writing it in the form of a graphic-analytical expression (789),

then the “Excessive arguments” should be excluded from the logical function system, since the conditionally negative argument ( ^-11 S ^{i + 1} _i ) _k-1 and ( ^- n & m _{i + 1} ) conditionally “k-1” “Minimization zones” allows any transfers of the argument from the conditionally “k-2” “Minimization Zones” and these transfers allow us to form the correct conditionally minimized structure of the arguments of the resulting sum. Therefore, the functional structure “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally “k-1” “Minimization zones” can be written in the form of two analytical expressions (790) and (791)

with the output logical function f ₁ (}) - OR and f ₂ (}) - OR, which activate " ^- Complex transfer argument" ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 with "Information content "- in the conditionally" k-1 "" Minimization zone "only one conditionally negative argument is active and" ^- Complex transfer argument " ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 with" Information content "- in the conditionally “k-1” “minimization zone” two conditionally negative arguments are active. And these “Complex arguments” allow the functional structure (787) to be written in the form of an analytical expression (792),

and write the functional structure (788) in the form of an analytical expression (793)

without the input “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-2 conditionally “k-2” “Minimization zones”, because “ ^- Complex transfer argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 in the conditionally “k-1” “Minimization Zone” with two conditionally negative arguments allows you to activate the argument of the resulting sum in this “Minimization Zone”. Therefore, the "Positive channel of the adder" i "discharge" (784), taking into account the functional structure (793), we write in the form of a graphic-analytical expression (794),

and the "Positive channel of the adder" i "discharge" (785), taking into account the functional structure (792), we write in the form of a graphic-analytical expression (795),

     A similar adjustment of the functional structure is performed in the "Conditionally negative channel of the adder" i + 1 "category" (786), which we write in the form of a graphic-analytical expression (796),

where " ⁺ Complex transfer argument" ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 conditionally "k-1" of the "Minimization zone" activates the functional structure (797),

and a functional structure similar to expression (788) that activates the conditionally negative argument of the resulting sum ( ^- S _i ) _{k is} written in the form of an analytical expression (799).

As a result, "Conditionally negative channel of the adder" i + 1 "discharge" (786), taking into account the adjusted functional structure (796) we write in the form of a graphic-analytical expression (800),

a "Conditionally negative channel of the adder" i "discharge" (784), taking into account the functional structure (799) we write in the form of graphoanalytic expression (801),

Since all possible argument structures of the combined structure of the terms ^± [S _i ] f ₁ (+/-) _min were analyzed, and they functionally belong to two categories, in one of them, the arguments are converted to the conditionally “k” “Minimization Zone” taking into account the fact that in the conditionally “k-1” “Minimization Zone” there is no “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and there is no “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 , and in the second combined structure, the transformation of arguments in the conditionally “k” “Minimization Zone” is performed taking into account the activity of quiet arguments. Therefore, the mathematical model of the "Positive channel of the adder" i "discharge" conditionally "k""Minimizationzones" of expression (794) can be written either in the form of a mathematical model (802)

with a functional input structure with an output logical function f ₂ (}) - OR, or in the form of a structure of logical functions (803),

in which the functional structure with the output logical function f ₂ (}) - OR expressions (802) is excluded from the logical function system and written in the form of a “Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k . Since this functional structure functionally belongs to both the “Positive channel of the adder“ i ”category” and the “Conditionally negative channel of the adder“ i ”category” and write it down either as a separate analytical expression (804),

or, taking into account the structure of logical functions (544), we write in the form of a graphoanalytic expression (805)

And the mathematical model of the “Positive channel of the adder“ i + 1 ”discharge" (795) is also written in the form of a structure of logical functions (806),

with input “Complex arguments” ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k and ( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k , which are also included in the functional structure of “Positive channel of the adder "i" category ", therefore, we write their functional structures for the argument ( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k in the form of an analytical expression (807),

and for the argument ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k in the form of an analytical expression (808),

in which the output “Complex arguments” ( ^- n & m _i ) V ( ^-10 S ^{i + 1} _i ) _k ↑ and ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k ↑ have the same “Information content”. Therefore, the "Positive channel of the adder" i "category" of expression (803) can be written in the form of a structure of logical functions (809),

in which the “Complex argument” ((Not ^± ← ^± ) S ^{i + 1} _i ) _{k-1 is} conditionally “k-1” the “Minimization zones” of expression (803) in the logical function system f ₃ (&) - AND the adjusted expression ( 809) is written as two converted arguments ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1 . Since if we return to the analysis of the “Complex argument” ((Not ^± ← ^± ) S ^{i + 1} _i ) _k-1 - “The absence of any transfers” in the conditionally “k-1” “Minimization Zone” of expression (733), writing it in the form of the structure of logical functions (810),

then in the logical function system f ₁ (&) - And this expression includes two functional structures that activate the positive “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and the conditionally negative “Complex argument” ( (Not ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally "k-1""Minimizationzones". And if we take into account that these two functional structures in the expression (809) are also included in the logical system of the same name f ₃ (&) - And, then the functional structure of the positive “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 conditionally “k-1” “Minimization zones” can be written in the form of an analytical expression (811),

and the functional structure of the conditionally negative “Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally “k-1” of the “Minimization Zone” can be written as an analytical expression (812).

But since the mathematical model of the conditionally “k” “Minimization Zones” is being formed, therefore, the functional structure of the positive “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k conditionally “k” of the “Minimization Zones” will be written for this minimization zone in the form of an analytical expression (813),

and the functional structure of the conditionally negative “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k conditionally “k” of the “Minimization Zone” for this minimization zone can be written in the form of an analytical expression (814).

And the mathematical model of the “Positive channel of the adder“ i + 1 ”discharge” (806), taking into account the adjustment of the input arguments and the “Positive channel of the adder“ i ”discharge”, we write in the form of a structure of logical functions (815),

in which also the "Complex argument" ((Not^±←^±) S^{i + 1} _i)_k-1 conditionally "k-1" "Minimization zones" of expression (806) in the system of logical function f₈(&) - And the adjusted expression (815) is written as two converted arguments ((Not⁺←⁺) S^{i + 1} _i)_k-1 and ((Not^-←^-) S^{i + 1} _i)_k-1. It should be noted that in the "Positive channel of the adder" i + 1 "category" of expression (815) also included "Complex argument" ⁺¹¹((Yes⁺←⁺) S^{i + 1} _i)_k-1conditionally "k-1" "Minimization zones", which functionally relate to this adder channel. But since the mathematical model of conditionally “k” “Minimization zones” of “Positive adder channels” (816) and “Conditionally negative adder channels” (817) and (818) is being formed,

in which the structure of logical functions is equivalent to the structure of logical functions of “Positive Adder Channels” (816) with the exception of signs of input arguments. It should be noted that the "Feature" of the "Positive channel of the adder" i + 1 "category" (815) and the "Conditionally negative channel of the adder" i + 1 "category" (818) are the input positive "Complex argument" ⁺¹¹ ((( Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and input conditionally negative argument ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally “k-1” “Minimization zones”, which is functionally only belongs to these channels. Therefore, in the analytical expression (815), it is necessary to introduce the functional structure of the positive “Complex argument” ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k conditionally “k” of the “Minimization zone” and this argument in accordance with the expression (798) , writing it in the form of a graphic-analytical expression (819)

activates the functional structure with the output logical function f ₂ (}) - OR with the input converted argument ( ⁺ n & m _{i + 1} ) _k-1 and two input arguments ( ⁺ n _{i + 1} & m _i ) _k-1 and ( ⁺ n _i & m _{i + 1} ) _k-1 , which, to minimize the analytical record, we will write as a set of transformed arguments { ⁺¹¹ S ^{i + 1} _i } _k in the analytical expression (820).

And in the analytical expression “Conditionally negative channel of the adder“ i + 1 ”category” (818), it is necessary to introduce the functional structure of the “Complex argument” ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 conditionally “k-1 "" Zones of minimization "and this argument in accordance with the expression (791), writing it in the form of a graphic-analytical expression (821)

we also write in the form of an analytical expression (822).

As a result, we write the structure of the logical functions of the “Positive channel of the adder“ i + 1 ”discharge" (815) in the form of a graphoanalytic expression (823),

where { ⁺¹¹ S ^{i + 1} _i } _k-1 is a positive set of transformed arguments and it is activated by a set of functional structures, which for the “Complex argument” ( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _{k is} written as an analytical expression (824)

and from which the totality of functional structures (825),

recorded for the conditionally “k-1” “Minimization Zones” activates a positive set of transformed arguments { ⁺¹¹ S ^{i + 1} _i } _k-1 . And the structure of the logical functions of the "Conditionally negative channel of the adder" i + 1 "discharge" (818) can be written in the form of a graphic-analytical expression (825),

where { ^-11 S ^{i + 1} _i } _k-1 is a conditionally negative set of transformed arguments, which activates the set of functional structures of the expression (807) and which for the conditionally “k-1” “Minimization Zones” we write in the form of an analytical expression (826) .

It should be noted that in the “Positive channel of the adder“ i + 1 ”discharge” (823) and in the “Conditionally negative channel of the adder“ i + 1 ”discharge” the functional structures with the output logic function (825) are written with the converted positive argument ^{+ 11} ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 ↑ and the transformed conditionally negative argument ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 ↑. Since the conditionally negative argument ^-11 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k-1 ↑ is included in the logical function system f ₄ (&) - And the “Positive channel of the adder“ i ”category" (809), which we write in the form of a graphoanalytic expression (827),

in this case, the procedure of activating the functional structure with the output logical function f ₃ (&) - And and the input arguments ( ^{+ 01, -11, + 1х-1} S ^{i + 1} _i ) _k , ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1, we write in the form of a graphic-analytical expression (828).

And the transformed positive argument ⁺¹¹ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 ↑ is included in the logical function system f ₄ (&) - And “Conditionally negative channel of the adder“ i ”category” of expression (817) and we will write it in the form of a graphic-analytical expression (829),

in this case, the procedure of activating the functional structure with the output logical function f ₃ (&) - And and the input arguments ( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k , ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k-1 and ((Not ^- ← ^- ) S ^{i + 1} _i ) _k-1, we write in the form of a graphic-analytical expression (830).

      Based on the results obtained, the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” (816) conditionally “k” of the “Minimization zone” can be written in the form of a structure of logical functions (831)

with the general functional structure (807), by means of which the “Complex argument” ( ^{+ 01, -11, + 1x-1} S ^{i + 1} _i ) _k ↑ and { ⁺¹¹ S ^{i + 1} _i } _k ↑ are activated, which we write in the form of graphoanalytic expression (832).

And the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ”of the discharge” (817) conditionally “k” of the “Minimization zone” will be written in the form of the structure of logical functions (833),

with the general functional structure (824), by means of which the “Complex argument” is activated ( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k ↑ and { ^-11 S ^{i + 1} _i } _k ↑, which we write in the form of graphoanalytic expression (834).

In this case, the general functional structures of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization zones” are functional structures that activate the following “Complex arguments”:

Functional structure 1. “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k (835).

Functional structure 2. “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k (836).

Functional structure 3. “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k , which, taking into account the transformed argument ( ⁺ n & m _{i + 1} ) _k and taking into account the functional structure (837),

an activating set of arguments { ⁺¹¹ S ^{i + 1} _i } _k with a changed level of the analog signal, and also taking into account the converted argument ( ^{± 0х0} S ^{i + 1} _i ) _{k of the} functional structure (838),

forms the structure of logical functions (838).

Functional structure 4. “Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k , which, taking into account the transformed arguments ( ^- n & m _{i + 1} ) _k and taking into account the functional structure (839),

an activating set of arguments { ^-11 S ^{i + 1} _i } _k with a changed level of the analog signal, and also taking into account the transformed argument ( ^{± 0х0} S ^{i + 1} _i ) _{k of the} functional structure (838), forms the structure of logical functions (840).

Functional structure 5. “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k without changing the level of the analog signal, which activates the structure of logical functions (841).

Functional structure 6. “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k without changing the level of the analog signal, which activates the structure of logical functions (842).

Functional structure 7. “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal activates the functional structure (843).

Functional structure 8. “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal activates the functional structure (844).

Functional structure 9. “Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k “Activation conditions” of the local transfer argument in conditionally “k” “Minimization zone” activates the functional structure (845).

It should be noted that the technological cycle ∆t_Σ→ 3 ∙ f (&) - AND  functional input adder structures^±f_one(Σ_RU)_minthat perform the procedure for converting conditionally minimized structures of the arguments of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_min in the conditionally “k” “minimization zone” and “Complex arguments” are activated, corresponds to the three conditional logical functions f (&) - And, and the technological cycle ∆t_Σ→ 2 ∙ f (&) - AND  functional output structures of the adder^±f_one(Σ_RU)_minthat perform the conversion process of "Complex arguments" and activate the resulting positive arguments of the sum (⁺S_i)_k and (⁺S_{i + 1})_k and conditionally negative arguments to the sum (^-S_i)_k and (^-S_{i + 1})_k, corresponds to two conditional logical functions f (&) - And, as a result, the technological cycle ∆t_Σ→ 3 ∙ f (&) - AND  functional structures of the adder^±f_one(Σ_RU)_min corresponds to ∆t_Σ → 5 ∙ f (&) - And the five conditional logical functions f (&) - And.

     Further, the synthesized mathematical models of the functional output structures of the "Positive channel of the adder" i "and" i + 1 "category" (815) and (818), which we write in the form of analytical expressions (846)

and synthesized mathematical models of the functional output structures of the “Conditionally negative channel of the adder“ i ”and“ i + 1 ”category” (817) and (818), which we write in the form of analytical expressions (847)

The first option can be written by other logical functions. It should be noted that since the structures of the logical functions of the two channels are equivalent, therefore, rather formalized transformations of the logical functions should be performed, for example, in the mathematical model of the “Positive channel of the adder“ i ”and“ i + 1 ”discharge” (846).

Option 2. For the synthesis of mathematical models of the functional output structures of the "Positive channel of the adder" i "and" i + 1 "category" (846) of the second option, we replace the functional input connections f (=) of the logical function f ₁ (}) - OR and f ₂ (}) - OR to the corresponding functions of double changing the level of the analog signal f ₁ (& ₁ = & ₂ ) in accordance with the graphic-analytical structure (848).

And write down the graphoanalytic expression (849),

in which we combine the input logical functions f ₁ (&) - And - f ₁₀ (&) - And with the logical functions f ₁ (&) - And, which are transformed in the expression (850)

into logical functions f ₁ (&) - AND NOT - f ₁₀ (&) - AND NOT. And after transferring the logical functions f ₂ (&) - AND in expression (849) through the output logical function f ₁ (}) - OR and f ₂ (}) - OR they change their logical properties to the properties of the logical function f ₁₁ (&) -AND NOT and f ₁₂ (&) - AND NOT.

     The functional structure of the “Conditionally negative channel of the adder“ i ”and“ i + 1 ”category” (847) has a similar structure of logical functions, which we write in the form of analytical expressions (851).

     Since formalized transformations were performed in the analytical expressions (850) and (1851), therefore, to check the correctness of the “Complex argument” transformations in them, we will form vector structures for activating logical functions and write them in the form of a graphic-analytical expression (852),

in the form of graphoanalytic expression (853)

in the form of graphoanalytic expression (854)

and in the form of a graphoanalytic expression (855),

from the analysis of which it follows that the positive resulting arguments of the sum ( ⁺ S _i ) _k and ( ⁺ S _{i + 1} ) _k and the conditionally negative arguments of the sum ( ^- S _i ) _k and ( ^- S _{i + 1} ) _k for the corresponding input structures Complex arguments ”in the conditionally“ k ”“ minimization zone ”are activated correctly, because in the systems of output logic functions f ₁₁ (&) - AND-NOT, f ₁₂ (&) - AND-NOT and f ₂₃ (&) - AND-NOT , f ₂₄ (&) - AND-NOT active input logic functions f ₁ (&) - AND-NOT - f ₆ (&) - AND-NOT, f ₇ (&) - AND-NOT - f ₁₀ (&) -And NOR f ₁₃ (k) - aND-NO - f ₁₈ (k) - aND-NO element ₁₉ and f (k) - aND-NO - f ₂₂ (k) - aND-NO, so formalized analytic transformation exp Nij (850) and (851) have been performed correctly.

Option 3. For the synthesis of the mathematical model of the functional output structures of the “Positive channel of the adder“ i ”and“ i + 1 ”category” (846) of the third option, we will correct in the expression (849) the transfer of the logical function f ₁ (&) - NOT in accordance with the graphic-analytical expression (856).

As a result of transferring the logical functions f ₂ (&) - NOT in the expression (856) through the output logical function f ₁ (}) - OR and f ₂ (}) - OR they change their logical properties to the properties of the logical function f ₁ (&) -AND NOT and f ₂ (&) - AND NOT. And as a result of the transfer of logical functions f ₁ (&) - NOT through the system of logical functions f ₁ (&) - AND - f ₁₀ (&) - And they change their logical properties to the properties of logical functions f ₁ (}) - OR - f ₁₀ (}) - OR, and the further transfer of logical functions f ₁ (&) - NOT through the input "Complex arguments" they change their level of the analog signal in the analytical expression (857),

which is the mathematical model of the adder output structure ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization zones”.

     The functional structure of the “Conditionally negative channel of the adder“ i ”and“ i + 1 ”discharge” (847), which we write in the form of analytical expressions (858), has a similar structure of logical functions.

It should be noted that since the levels of analog signals are changed in the analytical expressions (857) and (858) in the input “Complex arguments”, we therefore introduce the output logical function f ₁ (&) - NOT, which changes their level, into the corresponding functional structures analog signal, and perform a formal union with the output logical function of the corresponding functional structure of the "Complex argument" and write the corrected functional structure.

Functional structure 1. “Complex argument” ( ^{+ 01, -11, + 1x-1} S ^{i + 1} _i ) _k with a changed level of the analog signal of the analytical expression (832) with the output logic function f ₁ (&) - DO NOT write in the form structures of logical functions (859),

which, after combining the logical function f ₁ (&) - NOT with the output logical function f ₂ (}) - OR we will write in the form of a graphic-analytical expression (860) with the output logical function f ₂ (} &) - OR NOT. It should be noted that the functional structure (860) functionally relates only to the output structures of the "Positive channels of the adder" i "and" i + 1 "discharge".

Functional structure 2. “Complex argument” ( ^{-01, + 11, -1x + 1} S ^{i + 1} _i ) _k with a changed level of the analog signal of the analytical expression (834) with the output logic function f ₁ (&) - DO NOT write in the form structures of logical functions (861),

which, after combining the logical function f ₁ (&) - NOT with the output logical function f ₂ (}) - OR we will write in the form of a graphoanalytic expression (862)

with output logic function f ₂ (} &) - OR NOT. It should be noted that the functional structure (860) functionally relates only to the output structures “Conditionally negative channels of the adder“ i ”and“ i + 1 ”of the discharge”.

In this case, the general functional structures of the adder ^± f ₁ (Σ _RU ) _min conditionally “k” “Minimization zones” are functional structures that activate the following “Complex arguments”:

Functional structure 3. “ ⁺ Complex transfer argument” ⁺¹⁰ ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _{k of the} corrected expression (835) can be written as a graph-analytical expression (863).

with output logic function f ₂ (} &) - OR NOT.

Functional structure 4. “ ^- Complex transfer argument” ^-10 ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal of the corrected expression (836), we write in the form of a graphic-analytical expression (864).

with output logic function f ₂ (} &) - OR NOT.

Functional structure 5. “Complex argument” ((Not ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal of expression (838), which can be written as a graph-analytical expression (865)

with the output logical function f ₁ (&) - AND NOT.

Functional structure 6. “Complex argument” ((Not ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal of expression (840) and we write it in the form of a graphoanalytic expression (866)

with the output logical function f ₁ (&) - AND NOT.

Functional structure 7. “ ⁺ Complex transfer argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k without changing the level of the analog signal, which activates the structure of logical functions (841) and we write it in the form of a graphic-analytical expression (867)

with output logical function f ₁ (}) - OR.

Functional structure 8. “ ^- Complex transfer argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k without changing the level of the analog signal, which activates the structure of logical functions (842), and write it in the form of a graphic-analytical expression (868)

with output logical function f ₁ (}) - OR.

Functional structure 9. “ ⁺ Complex argument” ((Yes ⁺ ← ⁺ ) S ^{i + 1} _i ) _k with a changed level of the analog signal (843), the activation of which can be written as a graph-analytical expression (869)

with the output logical function f ₁ (&) - And.

Functional structure 10. “ ^- Complex argument” ((Yes ^- ← ^- ) S ^{i + 1} _i ) _k with a changed level of the analog signal (844), which can be written as a graphic-analytical expression (890)

with the output logical function f ₁ (&) - And.

Functional structure 11. “Complex argument” ( ^{± 11.0, ± 1, ± 0x0} S ^{i + 1} _i ) _k “Activation conditions” of the local transfer argument in conditionally “k” “Minimization zone” with a changed level of the analog signal of the corrected expression (845) and write it down in the form of a graphic-analytical expression (891)

with output logic function f ₂ (} &) - OR NOT.

It should be noted that the technological cycle ∆t_Σ→ 3 ∙ f (&) - AND  functional input adder structures^±f_one(Σ_RU)_minthat perform the procedure for converting conditionally minimized structures of the arguments of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_min in the conditionally “k” “minimization zone” and “Complex arguments” are activated, corresponds to the three conditional logical functions f (&) - And, and the technological cycle ∆t_Σ→ 2 ∙ f (&) - AND  functional output structures of the adder^±f_one(Σ_RU)_minthat perform the conversion process of "Complex arguments" and activate the positive resulting arguments of the sum (⁺S_i)_k and (⁺S_{i + 1})_k and conditionally negative arguments to the sum (^-S_i)_k and (^-S_{i + 1})_k, corresponds to two conditional logical functions f (&) - And, as a result, the technological cycle ∆t_Σ→ 3 ∙ f (&) - AND  functional structures of the adder^±f_one(Σ_RU)_min corresponds to ∆t_Σ → 5 ∙ f (&) - And the five conditional logical functions f (&) - And.

    Further, since formalized transformations were performed in the analytical expressions (857) and (858), therefore, to check the correctness of the “Complex argument” transformations in them, we form vector structures for activating logical functions and write them in the form of a graphoanalytic expression (892),

as graphoanalytic expression (893)

as graphoanalytic expression (894)

and in the form of a graphoanalytic expression (895),

from the analysis of which it follows that the resulting positive arguments of the sum ( ⁺ S _i ) _k and ( ⁺ S _{i + 1} ) _k and conditionally negative arguments of the sum ( ^- S _i ) _k and ( ^- S _{i + 1} ) _k for the corresponding input structures Complex arguments ”in the conditionally“ k ”“ minimization zone ”are activated correctly, since in the systems of output logical functions f ₁ (&) - AND-NOT, f ₂ (&) - AND-NOT and f ₃ (&) - AND-NOT , f ₄ (&) - AND-NOT active input logic functions f ₁ (}) - OR - f ₆ (}) - OR, f ₇ (}) - OR - f ₁₀ (}) - OR, f ₁₁ ( }) - OR - f ₁₆ (}) - OR and f ₁₇ (}) - OR - f ₂₀ (}) - OR, therefore, formalized transformations of analytical expressions (857 ) and (858) were executed correctly.

Option 4. For the synthesis of the mathematical model of the functional output structures of the “Positive channel of the adder“ i ”and“ i + 1 ”category” (846) of the fourth option, we will correct in the expression (849) the transfer of logical functions f ₁ (&) - NOT and f ₂ ( &) - NOT in accordance with the graphic-analytical expression (896).

As a result of transferring the logical functions f ₁ (&) - NOT through the system of input logical functions f ₁ (&) - And - f ₁₀ (&) - And they change their logical properties to the properties of the logical functions f ₁ (}) - OR - f ₁₀ (}) - OR, and the further transfer of logical functions f ₁ (&) - NOT through the input "Complex arguments" they change their level of the analog signal in the analytical expression (857), and the union of the corrected logical functions f ₁ (}) - OR - f ₁₀ (}) - OR with the corresponding logical function f ₂ (k) - NOT in the expression (896), they change their logical properties on the properties of the log iCal functions f ₁ (&}) - NOR - f ₁₀ (} &) - NOR the analytical expression (897).

     The functional structure of the “Conditionally negative channel of the adder“ i ”and“ i + 1 ”category” (847), which we write in the form of analytical expressions (898), has a similar structure of logical functions.

     Since formalized transformations were performed in the analytical expressions (897) and (898), therefore, to check the correctness of the “Complex argument” transformations in them, we will form vector structures for activating logical functions and write them in the form of a graph-analytical expression (899),

in the form of graphoanalytic expression (900)

in the form of graphoanalytic expression (901)

and in the form of graphoanalytic expression (902),

from the analysis of which it follows that the positive resulting arguments of the sum ( ⁺ S _i ) _k and ( ⁺ S _{i + 1} ) _k and the conditionally negative arguments of the sum ( ^- S _i ) _k and ( ^- S _{i + 1} ) _k for the corresponding input structures Complex arguments ”in the conditionally“ k ”“ minimization zone ”are activated correctly, because in the systems of output logical functions f ₁ (}) - OR, f ₂ (}) - OR and f ₃ (}) - OR and f ₄ (}) -OR active input logic functions f ₁ (} &) - OR-NOT - f ₆ (} &) - OR-NOT, f ₇ (} &) - OR-NOT - f ₁₀ (} &) - OR-NOT, ₁₁ f (&}) - NOR - f ₁₆ (} &) - NOR ₁₇ and f (&}) - NOR - f ₂₀ (} &) - NOR so formalized conversion anal cally expressions (897) and (898) have been performed correctly.

      Using the invention allows to form a process for converting conditionally minimized argument structures of analogue terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) with the procedure for simultaneously converting the arguments of the terms by means of arithmetic axioms of the ternary number system f_RU(+ 1.0, -1).

Claims (5)

1. The method of forming the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1) (Russian logic), according to which in the “Positive channel of the adder“ i ”category” and “Conditionally negative channel of the adder“ i ”category” conditionally “k” “Minimization zones” perform simultaneous analysis the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minthrough functional structures

with output logical functions f₅(}) - OR and f₆(}) - OR, in the system of which positive arguments of analog signals are included (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative arguments of analog signals (^-n_i)_k  and (^-m_i)_k conditionally “i” of the discharge “k” “Minimization zones”, activating the positive “Complex argument” (⁺nVm_i)_kand conditionally negative "Complex argument" (^-nVm_i)_k and by means of functional structures with output logical functions f_one(} &) - OR NOT, f₃(} &) - OR NOT and f_one(&) - AND-NOT kind

in the "Positive channel of the adder" i "discharge", in the system of which include the positive arguments of the analog signals (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative arguments of analog signals (^-n_i)_k and (-m_i)_k conditionally “i” of the discharge “k” “Minimization zones” and activate the generalized “Complex argument” (^-Comp) s^{i + 1} _i)_k and⁺(^±Comp) s^{i + 1} _i)_k and the positive “Comprehensive Argument” (⁺n & m_i)_k with a changed level of the analog signal, and through functional structures with output logical functions f₂(} &) - OR NOT, f_four(} &) - OR NOT and f₂(&) - AND-NOT kind

in the "Conditionally negative channel of the adder" i "discharge", the system of which also includes the positive arguments of the analog signals (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative arguments of analog signals (^-n_i)_k  and (^-m_i)_k conditionally “i” of the discharge “k” “Minimization zones”, activate the generalized “Complex argument” (⁺Comp) s^{i + 1} _i)_k and^-(^±Comp) s^{i + 1} _i)_kwhich are fed to the corresponding functional input connections of the input logical functions f_one(&) - And - f₆(&) - And in the "Positive channel of the adder" i "category" and served on the corresponding functional input connections of the input logical functions f_eleven(&) - And - f₁₆(&) - And in the “Conditionally negative channel of the adder“ i ”bits” conditionally “k” “Minimization zones”, which are included in the system of output logical functions f_one(}) - OR and f₃(}) - OR in accordance with an analytical expression of the form

 and by which they activate the positive argument of the resulting sum (⁺S_i)_k and the conditionally negative argument of the resulting sum (^-S_i)_kcharacterized in that for the simultaneous analysis of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin accordance with the graphoanalytic expression of the form

Where

      and

      - a positive argument and a conditionally negative argument, respectively;

      and

     - positive double argument and conditionally negative double argument in conditionally “i” and “i + 1” categories, respectively;
in each conditionally “k” “Minimization Zone”, which includes two consecutive bits - conditionally “i” discharge and conditionally “i + 1” discharge and activate the following “Complex arguments”:
  ▶ "⁺Complex argument ”(⁺⁰¹S^{i + 1} _i)_k  activate through the functional structure of graphoanalytic expression of the form

 with input logic functions f₅(}) - OR, f_one(} &) - OR NOT and f_one(&) - AND NOT and output logic function f₂₁(&)-AND;
    ▶ "^-Complex argument ”(^-01S^{i + 1} _i)_k  activate through the functional structure of the species

with input logic functions f₆(}) - OR, f₂(} &) - OR NOT and f₂(&) - AND NOT and output logic function f₂₂(&)-AND;
    ▶ "⁺Complex argument ”(⁺¹⁰S^{i + 1} _i)_k  activate through the functional structure of graphoanalytic expression of the form

with input logic functions f₇(}) - OR, f₃(} &) - OR NOT and f₃(&) - AND NOT and output logic function f₂₃(&)-AND;
Where

    and

   - the transformed positive and conditionally negative resulting argument, which are activated by applying the arithmetic axioms of the ternary number system f_RU(+ 1.0, -1);
    ▶ "^-Complex argument ”(^-10S^{i + 1} _i)_k  activate through the functional structure of graphoanalytic expression of the form

with input logic functions f₈(}) - OR, f_four(} &) - OR NOT and f_four(&) - AND NOT and output logic function f₂₄(&)-AND;
    ▶ "⁺Complex argument ”(⁺¹¹S^{i + 1} _i)_k  without changing the level of the analog signal activate through the functional structures of graphoanalytic expression of the form

with input logic functions f₂₅(&) - And and f₂₆(&)-AND;
    ▶ "⁺Complex argument ”(⁺¹¹S^{i + 1} _i)_k  with a changed level of the analog signal activate through functional structures of the form

with input logic functions f₅(&) - NAND and f₆(&) - AND NOT;
    ▶ "^-Complex argument ”(^-elevenS^{i + 1} _i)_k → {^-elevenS^{i + 1} _i}_k  without changing the level of the analog signal activate through the functional structures of graphoanalytic expression of the form

with input logic functions f₂₇(&) - And and f₂₈(&)-AND;
    ▶ "^-Complex argument ”(^-elevenS^{i + 1} _i)_k → {^-elevenS^{i + 1} _i}_k   with a changed level of the analog signal activate through functional structures of the form

with input logic functions f₇(&) - NAND and f₇(&) - AND NOT;
    ▶ "⁺Complex argument ”(⁺n & m_i)_k  activate through the functional structure of graphoanalytic expression of the form

 with output logic f_29th(&)-AND;
    ▶ "^-Complex argument ”(^-n & m_i)_k  activate through the functional structure of graphoanalytic expression of the form

with output logic f_thirty(&)-AND;
     ▶ "⁺Complex argument ”(⁺n & m_{i + 1})_k  activate through the functional structure of graphoanalytic expression of the form

 with output logic f₃₁(&)-AND;
     ▶ "^-Complex argument ”(^-n & m_{i + 1})_k  activate through the functional structure of graphoanalytic expression of the form

with output logic f₃₂(&)-AND;
     ▶ "^±Complex argument ”(^{+ 1x-1}S^{i + 1} _i)_k→ {^{+ 1x-1}S^{i + 1} _i}_kactivate through functional structures of graphoanalytic expression of the form

 with input logic functions f₃₃(&) - And and f₃₄(&)-AND;
    ▶ "^±Complex argument ”(^{-1x + 1}S^{i + 1} _i)_k→ {^{-1x + 1}S^{i + 1} _i}_kactivate through functional structures of graphoanalytic expression of the form

 with input logic functions f₃₅(&) - And f₃₆(&)-AND;
wherein "^{± 0}Complex argument ”(^{± 0x0}S^{i + 1} _i)_k the inactivity of the arguments in the conditionally “k” “minimization zone” is activated by means of the functional structure of a graphoanalytic expression of the form

with input logic function f₅(}&)-OR NO;
and "^±Complex argument ”(^{± 11.0, ± 1, ± 0x0}S^{i + 1} _i)_ksimultaneous activity of positive and conditionally negative arguments in the conditionally “k” “minimization zone”, which correspond to the arithmetic axiom “+1” “- 1” → “^±0^one”And inactivity of the arguments in the conditionally“ k ”“ Minimization Zone ”are activated through the functional structure of a graphoanalytic expression of the form

with input logic functions f₃₇(&) - And, f₃₈(&) - And, f₃₉(&) - And, f₄₀(&) - And and the output logical function f₉(})-OR;
then they perform a simultaneous analysis of the active “Complex arguments” of the analog signals of the terms in the corresponding conditionally “k” “Minimization Zones” in accordance with the graphic-analytical expression of the form

and activate possible additional "Complex arguments":
    ▶ "⁺Comprehensive transfer argument ”⁺¹⁰((Yes⁺←⁺) S^{i + 1} _i)_k activate through functional structures of graphoanalytic expression of the form

with output logic f₁₀(})-OR;
    ▶ "^-Comprehensive transfer argument ”^-10((Yes^-←^-) S^{i + 1} _i)_k activate through functional structures of graphoanalytic expression of the form

with output logic f_eleven(})-OR;
    ▶ "⁺Comprehensive transfer argument ”⁺¹¹((Yes⁺←⁺) S^{i + 1} _i)_k activate through a combination of transformed positive arguments {⁺¹¹S^{i + 1} _i}_k graphoanalytic expression of the form

with output logic f₁₂(})-OR;
    ▶ "^-Comprehensive transfer argument ”^-eleven((Yes^-←^-) S^{i + 1} _i)_k activate through a set of transformed conditionally negative arguments {^-elevenS^{i + 1} _i}_kgraphoanalytic expression of the form

with output logic f₁₃(})-OR;
      ▶ "⁺Complex Argument ”((Not⁺←⁺) S^{i + 1} _i)_k activate through functional structures of graphoanalytic expression of the form

 with input logic functions f₆(} &) - OR NOT, f_fourteen(}) - OR and f₉(&) - AND NOT and with output logic f₄₁(&)-AND;
    ▶ "^-Complex Argument ”((Not^-←^-) S^{i + 1} _i)_k activate through functional structures of graphoanalytic expression of the form

 with input logic functions f₇(} &) - OR NOT, f_fifteen(}) - OR and f₁₀(&) - AND NOT and with output logic f₄₂(&)-AND;
     ▶ "⁺Complex transfer argument ”((Yes⁺←⁺) S^{i + 1} _i)_k without changing the level of the analog signal activate through the functional structures of graphoanalytic expression of the form

with output logic f₁₆(})-OR;
     ▶ "^-Complex transfer argument ”((Yes^-←^-) S^{i + 1} _i)_k without changing the level of the analog signal activate through the functional structures of graphoanalytic expression of the form

with output logic f₁₇(})-OR;
    ▶ "⁺Complex Argument ”((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of an analog signal is activated by means of functional structures of graphoanalytic expression of the form

with output logic f₄₃(&)-AND;
    ▶ "^-Complex Argument ”((Yes^-←^-) S^{i + 1} _i)_k with a changed level of an analog signal is activated by means of functional structures of graphoanalytic expression of the form

with output logic f₄₄(&)-AND;
    ▶ “Comprehensive Argument” (^{+ 01, -11, + 1x-1}S^{i + 1} _i)_kthrough functional structures of graphoanalytic expression of the form

with output logic f_eighteen(}) - OR and input logical functions f₅(}) - OR, f_one(} &) - OR NOT, f₂₁(&) - And, f_one(&) - NAND, f₂₇(&) - And, f₂₈(&) - And, f₃₃(&) - And and f₃₄(&)-AND;
    ▶ “Comprehensive Argument” (^{-01, + 11, -1x + 1}S^{i + 1} _i)_k through functional structures of graphoanalytic expression of the form

with output logic f₁₉(}) - OR and input logical functions f₆(}) - OR, f_four(} &) - OR NOT, f₂₄(&) - And, f₂(&) - NAND, f₂₇(&) - And, f₂₈(&) - And, f₃₅(&) - And and f₃₆(&)-AND;
then through the output functional structure of the "Positive channel of the adder" i "discharge" type

with common output logic f_one(}) - OR and in accordance with the graphic-analytical expression of the form

perform a simultaneous analysis of the active “Complex arguments” of the analogue terms in the corresponding conditionally “k” “Minimization Zones” and activate the positive resulting argument of the sum (⁺S_i)_k,
where ((Yes⁺←⁺) S^{i + 1} _i)_k-1 and ((Yes^-←^-) S^{i + 1} _i)_k-2  - “Complex arguments” conditionally “k-1” “Minimization zones” and conditionally “k-1” “Minimization zones” respectively;
and also through the output functional structure "Conditionally negative channel of the adder" i "discharge" type

with common output logic f₃(}) - OR and in accordance with the graphic-analytical expression of the form

perform simultaneous analysis of the active "Complex arguments" of the analogue terms in the corresponding conditionally "k" "Minimization Zones" and activate the resulting conditionally negative argument of the sum (^-S_i)_k, while using an additional output functional structure with the output logical function f₂(}) - OR "Positive channel of the adder" i + 1 "category" in accordance with the graphoanalytic expression of the form

and an additional output functional structure with output logical function f₂(}) - OR "Conditionally negative channel of the adder" i + 1 "category" in accordance with the graphoanalytic expression of the form

perform a simultaneous analysis of the active "Complex arguments" of the analog signals of the terms in the corresponding conditionally "k" "Minimization Zones" and activate the positive resulting argument of the resulting sum (⁺S_{i + 1})_k  and the conditionally negative argument of the resulting sum (^-S_{i + 1})_k conditionally "i + 1" discharge. 2. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, which include the output structure of logical functions implemented in accordance with with a mathematical model of the form

and with input logical functions f_one(&) - And - f₆(&) - And with input logic functions f_eleven(&) - And - f₁₆(&) - And, the functional output connections (=) of which are the functional input connections of the output logical function f_one(}) - OR and f₃(}) - OR to activate a positive sum argument (⁺S_i)_k conditionally "i" discharge and to activate a conditionally negative argument (^-S_i)_k conditionally “i” discharge, while “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones” also includes a functional input structure formed in accordance with a mathematical model of the form

and with output logical functions f₅(}) - OR and f₆(}) - OR, whose functional input links are functional input links for receiving positive analogue argument signals (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k  and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization”, to activate the positive “Complex argument” (⁺nVm_i)_kand conditionally negative "Complex argument" (^-nVm_i)_kmoreover, the "Positive channel of the adder" i "discharge" also includes functional input structures formed in accordance with the mathematical model of the form

with output logical functions f_one(} &) - OR NOT, f₃(} &) - OR NOT and f_one(&) - AND NOT, the functional input connections of which are the functional input connections of the adder for receiving positive analogue signals of arguments (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the “k” discharge of the “Minimization Zone” to activate the “Complex arguments” (^-Comp) s^{i + 1} _i)_k,⁺(^±Comp) s^{i + 1} _i)_k and the “Comprehensive Argument” (⁺n & m_i)_k with a changed level of the analog signal, while the "Positive channel of the adder" i "discharge" also includes the logical function f₂₁(&) - And, and the “Conditionally negative channel of the adder“ i ”category” also includes functional input structures formed in accordance with a mathematical model of the form

and with output logical functions f₂(} &) - OR NOT, f_four(} &) - OR NOT and f₂(&) - AND NOT, the functional input connections of which are the functional input connections of the adder for receiving positive analogue signals of arguments (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the “k” discharge of the “Minimization Zone” to activate the “Complex arguments” (⁺Comp) s^{i + 1} _i)_k,^-(^±Comp) s^{i + 1} _i)_k and the “Comprehensive Argument” (^-n & m_i)_k with a changed level of the analog signal, while the "Conditionally negative channel of the adder" i "discharge" also includes the logical function f₂₂(&) - And, characterized in that in conditionally “k” the “Zone of minimization” is introduced in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f₇(&) - And - f₁₀(&) - And, whose functional output connections are the functional input connections of the logical function f₂(}) - OR, which activates a positive resulting argument (⁺S_{i + 1})_k conditionally "i + 1" discharge in the "Positive channel of the adder" i + 1 "discharge", and an additional structure of logical functions with input logical functions f₁₇(&) - And - f_twenty(&) - And, whose functional output connections are the functional input connections of the logical function f_four(}) - OR, which activates a conditionally negative resulting argument (^-S_{i + 1})_k conditionally "i + 1" discharge in the "Conditionally negative channel of the adder" i + 1 "discharge", while in the system of input logic functions f_one(&) - And - f₁₀(&) - And the "Positive channel of the adder" i "discharge" and the "Positive channel of the adder" i + 1 "discharge", which are formed in accordance with the mathematical model of the form

with the input "Complex arguments", which are also included in the "Conditionally negative channel of the adder" i + 1 "and" i "category", as well as "Complex argument" (^{+ 01, -11, + 1x-1}S^{i + 1} _i)_k functional input structure, which is formed in accordance with the mathematical model of the form

and with output logic f_eighteen(}) - OR and input logical functions f₄₅(&) - And, f₄₆(&) - And, f₄₇(&) - And and f₄₈(&) - And, in which "⁺Complex argument ”(⁺⁰¹S^{i + 1} _i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₅(}) - OR, f_one(} &) - OR NOT and f_one(&) - AND NOT and output logic function f₂₁(&)-AND;
and to the system of input logical functions f_one(&) - And - f₁₀(&) - And “Conditionally negative channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i + 1 ”discharge”, which are formed in accordance with the mathematical model of the form

“Integrated arguments” are included, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as“ Complex argument ”(^{-01, + 11, -1x + 1}S^{i + 1} _i)_k functional input structure, which is formed in accordance with the mathematical model of the form

with output logic f₈(}) - OR and input logical functions f₂₂(&) - And, f₂₇(&) - And, f₂₈(&) - And and f_29th(&) - And, in which "^-Complex argument ”(^-01S^{i + 1} _i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₆(}) - OR, f₂(} &) - OR NOT and f₂(&) - AND NOT and output logic function f_thirty(&)-AND;
at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” category "formed by the following functional structures:
    ▶ "^±Complex argument ”(^{± 11.0, ± 1, ± 0x0}S^{i + 1} _i)_kis a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₃₁(&) - And, f₃₂(&) - And, f₃₃(&) - And, f₃₄(&) - And and the output logical function f₉(}) - OR, in which "^{± 0}Complex argument ”(^{± 0x0}S^{i + 1} _i)_k the inactivity of the arguments in the conditionally “k” “minimization zone” is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic function f₅(}&)-OR NO, "⁺Complex argument ”(⁺n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₅(&) - And, and^-Complex argument ”(^-n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₆(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹⁰((Yes⁺←⁺) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₀(}) - OR, in which "⁺Complex argument ”(⁺¹⁰S^{i + 1} _i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_eleven(}) - OR, f₃(} &) - OR NOT and f₃(&) - AND NOT and output logic function f₃₇(&) - And, and⁺Complex argument ”(⁺n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₈(&)-AND;
    ▶ "^-Comprehensive transfer argument ”^-10((Yes^-←^-) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

 with output logic f₁₂(}) - OR, in which "^-Complex argument ”(^-10S^{i + 1} _i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₁₃(}) - OR, f_four(} &) - OR NOT and f_four(&) - AND NOT and output logic function f₃₉(&) - And, and^-Complex argument ”(^-n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₄₀(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹¹((Yes⁺←⁺) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fourteen(})-OR;
    ▶ "^-Comprehensive transfer argument ”^-eleven((Yes^-←^-) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

 with output logic f_fifteen(})-OR;
      ▶ "⁺Complex Argument ”((Not⁺←⁺) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₆(} &) - OR NOT, f₁₆(}) - OR and f_one(&) - AND NOT and with output logic f₄₁(&) - And, in which "⁺Comprehensive Argument ”{⁺¹¹S^{i + 1} _i}_k    with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₅(&) - NAND and f₆(&) - AND NOT;
    ▶ "^-Complex Argument ”((Not^-←^-) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(} &) - OR NOT, f₁₇(}) - OR and f₂(&) - AND NOT and with output logic f₄₂(&) - And, in which "^-Complex argument ”(^-elevenS^{i + 1} _i)_k  with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(&) - NAND and f₈(&) - AND NOT;
     ▶ "⁺Complex transfer argument ”((Yes⁺←⁺) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_eighteen(})-OR;
     ▶ "^-Complex transfer argument ”((Yes^-←^-) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₁₉(})-OR;
    ▶ "⁺Complex Argument ”((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₄₃(&)-AND;
    ▶ "^-Complex Argument ”((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₄₄(&)-AND. 3. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analog signals of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, which include the output structure of logical functions implemented in accordance with with a mathematical model of the form

and with input logical functions f_one(&) - AND NOT - f₆(&) - NAND and with input logic functions f₁₃(&) - AND NOT - f_eighteen(&) - AND NOT, the functional output links (=) of which are the functional input links of the output logical function f_eleven(&) - NAND and f₂₃(&) - AND NOT to form a positive argument to the sum (⁺S_i)_k conditionally "i" discharge and to activate a conditionally negative argument (^-S_i)_k conditionally “i” discharge, while “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones” also includes a functional input structure formed in accordance with a mathematical model of the form

and with output logical functions f_one(}) - OR and f₂(}) - OR, whose functional input links are functional input links for receiving positive analogue argument signals (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k  and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization”, to activate the positive “Complex argument” (⁺nVm_i)_kand conditionally negative "Complex argument" (^-nVm_i)_kmoreover, the "Positive channel of the adder" i "discharge" also includes functional input structures formed in accordance with the mathematical model of the form

and with output logical functions f_one(} &) - OR NOT, f₃(} &) - OR NOT and f₂₅(&) - AND NOT, the functional input connections of which are the functional input connections of the adder for receiving positive analogue signals of arguments (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization” for the formation of a generalized “Complex argument” (^-Comp) s^{i + 1} _i)_k and⁺(^±Comp) s^{i + 1} _i)_k and the positive “Comprehensive Argument” (⁺n & m_i)_k with a changed level of the analog signal, while the "Positive channel of the adder" i "discharge" also includes the logical function f₂₆(&) - NAND and f₅(}&)-OR NO;
and the "Conditionally negative channel of the adder" i "discharge" also includes functional input structures formed in accordance with the mathematical model of the form

and with output logical functions f₂(} &) - OR NOT, f_four(} &) - OR NOT and f₂₇(&) - AND NOT, the functional input connections of which are the functional input connections of the adder for receiving positive analogue signals of arguments (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization” for the formation of a generalized “Complex argument” (⁺Comp) s^{i + 1} _i)_k and^-(^±Comp) s^{i + 1} _i)_k and conditionally negative "Complex argument" (^-n & m_i)_k with a changed level of the analog signal, while the "Conditionally negative channel of the adder" i "discharge" also includes the logical function f₂₈(&) - NAND and f₆(}&)-OR NO; characterized in that in conditionally “k” the “minimization zone” is introduced in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f₇(&) - AND NOT - f₁₀(&) - AND NOT, whose functional output links are the functional input links of the logical function f₁₂(&) - AND NOT, which activates a positive resulting argument (⁺S_{i + 1})_k conditionally "i + 1" discharge in the "Positive channel of the adder" i + 1 "discharge", and an additional structure of logical functions with input logical functions f₁₉(&) - AND NOT - f₂₂(&) - AND NOT, whose functional output links are the functional input links of the logical function f₂₄(&) - AND NOT, which activates a conditionally negative resulting argument (^-S_{i + 1})_k conditionally "i + 1" discharge in the "Conditionally negative channel of the adder" i + 1 "discharge", while in the system of input logic functions f_one(&) - AND NOT - f₁₀(&) - AND NOT the “Positive channel of the adder“ i ”discharge” and the “Positive channel of the adder“ i + 1 ”discharge”, implemented in accordance with the mathematical model of the form

with the input "Complex arguments", which are also included in the "Conditionally negative channel of the adder" i + 1 "and" i "category", as well as "Complex argument" (^{+ 01, -11, + 1x-1}S^{i + 1} _i)_k functional input structure, which is formed in accordance with the mathematical model of the form

and with output logic f₃(}) - OR and input logical functions f_one(&) - And, f₂(&) - And, f₃(&) - And and f_four(&) - And, in which "⁺Complex argument ”(⁺⁰¹S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_one(}) - OR, f_one(} &) - OR NOT and f₂₅(&) - AND NOT and output logic function f₅(&)-AND;
and to the system of input logical functions f_eleven(&) - AND NOT - f_twenty(&) - AND NOT “Conditionally negative channel of the adder" i "category" and "Conditionally negative channel of the adder" i + 1 category ", formed in accordance with the mathematical model of the form

with the input "Complex arguments", which are common arguments with the "Positive channel of the adder" i + 1 "and" i "category", as well as "Complex argument" (^{-01, + 11, -1x + 1}S^{i + 1} _i)_k functional input structure, which is formed in accordance with the mathematical model of the form

with output logic f_four(}) - OR and input logical functions f₆(&) - And, f₇(&) - And, f₈(&) - And and f₉(&) - And, in which "^-Complex argument ”(^-01S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₂(}) - OR, f₂(} &) - OR NOT and f₂₇(&) - AND NOT and output logic function f₁₀(&)-AND;
at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:
    ▶ "^±Complex argument ”(^{± 11.0, ± 1, ± 0x0}S^{i + 1} _i)_kis a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_eleven(&) - And, f₁₂(&) - And, f₁₃(&) - And, f_fourteen(&) - And and the output logical function f₅(}) - OR, in which "^{± 0}Complex argument ”(^{± 0x0}S^{i + 1} _i)_k the inactivity of the arguments in the conditionally “k” “minimization zone” is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic function f₅(}&)-OR NO, "⁺Complex argument ”(⁺n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fifteen(&) - And, and^-Complex argument ”(^-n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₆(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹⁰((Yes⁺←⁺) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₆(}) - OR, in which "⁺Complex argument ”(⁺¹⁰S^{i + 1} _i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(}) - OR, f₃(} &) - OR NOT and f₂₆(&) - AND NOT and output logic function f₁₇(&) - And, and⁺Complex argument ”(⁺n & m_i)_k   is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_eighteen(&)-AND;
    ▶ "^-Comprehensive transfer argument ”^-10((Yes^-←^-) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₈(}) - OR, in which "^-Complex argument ”(^-10S^{i + 1} _i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₉(}) - OR, f_four(} &) - OR NOT and f₂₈(&) - AND NOT and output logic function f₁₉(&) - And, and^-Complex argument ”(^-n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_twenty(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹¹((Yes⁺←⁺) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₀(})-OR;
    ▶ "^-Comprehensive transfer argument ”^-eleven((Yes^-←^-) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

 with output logic f_eleven(})-OR;
      ▶ "⁺Complex Argument ”((Not⁺←⁺) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₆(} &) - OR NOT, f₁₂(}) - OR and f_29th(&) - AND NOT and with output logic f₂₁(&) - And, in which "⁺Comprehensive Argument ”{⁺¹¹S^{i + 1} _i}_k    with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_thirty(&) - NAND and f₃₁(&) - AND NOT;
    ▶ "^-Complex Argument ”((Not^-←^-) S^{i + 1} _i)_k is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(} &) - OR NOT, f₁₃(}) - OR and f₃₂(&) - AND NOT and with output logic f₂₂(&) - And, in which "^-Complex argument ”(^-elevenS^{i + 1} _i)_k  with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₃₃(&) - NAND and f₃₄(&) - AND NOT;
     ▶ "⁺Complex transfer argument ”((Yes⁺←⁺) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fourteen(})-OR;
     ▶ "^-Complex transfer argument ”((Yes^-←^-) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fifteen(})-OR;
    ▶ "⁺Complex Argument ”((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₂₃(&)-AND;
    ▶ "^-Complex Argument ”((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₂₄(&)-AND. 4. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analogue signal of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, which include the output structure of logical functions implemented in accordance with with a mathematical model of the form

and with input logical functions f_one(}) - OR - f₆(}) - OR and with input logical functions f_eleven(}) - OR - f₁₆(}) - OR, the functional output links (=) of which are the functional input links of the output logical function f_one(&) - NAND and f₃(&) - AND NOT to form a positive argument to the sum (⁺S_i)_k conditionally "i" discharge and to activate a conditionally negative argument (^-S_i)_k conditionally “i” discharge, while “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones” also includes a functional input structure, which is formed in accordance with a mathematical model of the form

with output logic f₂₁(}) - OR, f₂₅(}) - OR and f₂₂(}) - OR, f₂₆(}) - OR, in which the functional input links are functional input links for receiving positive analogue argument signals (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k  and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization”, to form a positive “Complex argument” (⁺nVm_i)_kand conditionally negative "Complex argument" (^-nVm_i)_kmoreover, the "Positive channel of the adder" i "discharge" also includes functional input structures formed in accordance with the mathematical model of the form

with output logic f_one(} &) - OR NOT and f_one(&) - And, the functional input connections of which are the functional input connections of the adder for receiving positive analogue signals of arguments (⁺n_i)_k  and (⁺m_i)_k   conditionally “i” of the discharge “k” of the “Zone of minimization” to activate the generalized “Complex argument” (⁺Comp) s^{i + 1} _i)_k  and the positive “Comprehensive Argument” (⁺n & m_i)_k without changing the level of the analog signal, while the "Positive channel of the adder" i "discharge" also includes the logical function f₂₃(}) - OR, and the “Conditionally negative channel of the adder“ i ”category” also includes functional input structures formed in accordance with a mathematical model of the form

with output logical functions f₂(} &) - OR NOT and f₂(&) - And, the functional input connections of which are the functional input connections of the adder for receiving conditionally negative arguments of analog signals (^-n_i)_k and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization” for the formation of a generalized “Complex argument” (^-Comp) s^{i + 1} _i)_k  and conditionally negative "Complex argument" (^-n & m_i)_k without changing the level of the analog signal, while the "Conditionally negative channel of the adder" i "discharge" also includes the logical function f₂₄(}) - OR, characterized in that in conditionally “k” the “minimization zone” is entered in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f₇(}) - OR - f₁₀(}) - OR, whose functional output connections are the functional input connections of the logical function f₂(&) - AND NOT, which activates a positive resulting argument (⁺S_{i + 1})_k conditionally "i + 1" discharge in the "Positive channel of the adder" i + 1 "discharge", and an additional structure of logical functions with input logical functions f₁₇(}) - OR - f_twenty(}) - OR, whose functional output connections are the functional input connections of the logical function f_four(&) - AND NOT, which generates a conditionally negative resulting argument (^-S_{i + 1})_k conditionally "i + 1" discharge in the "Conditionally negative channel of the adder" i + 1 "discharge", while in the system of input logic functions f_one(}) - OR - f₁₀(}) - OR “Positive channel of the adder“ i ”discharge” and “Positive channel of the adder“ i + 1 ”discharge”, implemented in accordance with the mathematical model of the form

with the input "Complex arguments", which are also included in the "Conditionally negative channel of the adder" i + 1 "and" i "category", as well as "Complex argument" (^{+ 01, -11, + 1x-1}S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

and with output logic f₃(} &) - OR NOT and input logic functions f₃(&) - And, f_four(&) - And, f₅(&) - And and f₆(&) - And, in which "⁺Complex argument ”(⁺⁰¹S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₂₁(}) - OR, f_four(} &) - OR NOT and f_one(&) - AND NOT and output logic function f₇(&)-AND;
and to the system of input logical functions f_eleven(}) - OR - f_twenty(}) - OR “Conditionally negative channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i + 1 ”discharge”, formed in accordance with the mathematical model of the form

“Integrated arguments” are included, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as“ Complex argument ”(^{-01, + 11, -1x + 1}S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₅(} &) - OR NOT and input logic functions f₈(&) - And, f₉(&) - And, f₁₀(&) - And and f_eleven(&) - And, in which "^-Complex argument ”(^-01S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₂₂(}) - OR, f₆(} &) - OR NOT and f₂(&) - AND NOT and output logic function f₁₂(&)-AND;
at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:
    ▶ "^±Complex argument ”(^{± 11.0, ± 1, ± 0x0}S^{i + 1} _i)_kwith a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₁₃(&) - And, f_fourteen(&) - And, f_fifteen(&) - And, f₁₆(&) - And and the output logical function f₇(} &) - OR NOT, in which "^{± 0}Complex argument ”(^{± 0x0}S^{i + 1} _i)_k the inactivity of the arguments in the conditionally “k” “minimization zone” is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic function f₈(}&)-OR NO, "⁺Complex argument ”(⁺n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₇(&) - And, and^-Complex argument ”(^-n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_eighteen(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹⁰((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₉(} &) - OR NOT, in which "⁺Complex argument ”(⁺¹⁰S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₂₃(}) - OR, f_one(} &) - OR NOT and f₃(&) - AND NOT and output logic function f₁₉(&) - And, and⁺Complex argument ”(⁺n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_one(&)-AND;
    ▶ "^-Comprehensive transfer argument ”^-10((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₀(} &) - OR, in which "^-Complex argument ”(^-10S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₂₄(}) - OR, f₂(} &) - OR NOT and f_four(&) - AND NOT and output logic function f_twenty(&) - And, and^-Complex argument ”(^-n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₂(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹¹((Yes⁺←⁺) S^{i + 1} _i)_k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_eleven(}&)-OR NO;
    ▶ "^-Comprehensive transfer argument ”^-eleven((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₂(}&)-OR NO;
      ▶ "⁺Complex Argument ”((Not⁺←⁺) S^{i + 1} _i)_k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₁₃(} &) - OR NOT, f₂₅(}) - OR and f₆(&) - AND NOT and with output logic f₅(&) - AND NOT, in which "⁺Comprehensive Argument ”{⁺¹¹S^{i + 1} _i}_k    with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(&) - NAND and f₈(&) - AND NOT;
    ▶ "^-Complex Argument ”((Not^-←^-) S^{i + 1} _i)_k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_fourteen(} &) - OR NOT, f₂₆(}) - OR and f₁₀(&) - AND NOT and with output logic f₉(&) - AND NOT, in which "^-Complex argument ”(^-elevenS^{i + 1} _i)_k  with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_eleven(&) - NAND and f₁₂(&) - AND NOT;
     ▶ "⁺Complex transfer argument ”((Yes⁺←⁺) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fifteen(}&)-OR NO;
     ▶ "^-Complex transfer argument ”((Yes^-←^-) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₆(}&)-OR NO;
    ▶ "⁺Complex Argument ”((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₃(&) - AND NOT;
    ▶ "^-Complex Argument ”((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fourteen(&) - AND NOT. 5. The functional structure of the logical-dynamic process of converting conditionally minimized structures of the arguments of the analogue signal of the terms^±[n_i] f (+/-)_min and^±[m_i] f (+/-)_minin functional adder structure^±f_one(Σ_RU)_min without end-to-end transfer f_one(^±←) and ∆t_Σ → 5 ∙ f (&) - And five conditional logical functions f (&) - And, implemented using the procedure of simultaneous transformation of the arguments of the terms using arithmetic axioms of the ternary number system f_RU(+ 1,0, -1), including “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” “Minimization zones”, including the output structure of logical functions, which is implemented in accordance with with a mathematical model of the form

and with input logical functions f_one(} &) - OR NOT - f₆(} &) - OR NOT and with input logic functions f_eleven(} &) - OR NOT - f₁₆(} &) - OR NOT, whose functional output links (=) are the functional input links of the output logical function f_one(}) - OR and f₃(}) - OR to activate a positive sum argument (⁺S_i)_k conditionally "i" discharge and to activate a conditionally negative argument (^-S_i)_k conditionally “i” discharge, while “Positive channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i ”discharge” conditionally “k” of “Minimization zone” also includes a functional input structure formed in accordance with a mathematical model of the form

and with output logical functions f₅(}) - OR, f_fourteen(}) - OR and f₆(}) - OR, f_fifteen(}) - OR, in which the functional input links are functional input links for receiving positive analogue argument signals (⁺n_i)_k  and (⁺m_i)_k  and conditionally negative analogue argument signals (^-n_i)_k  and (^-m_i)_k conditionally “i” of the discharge “k” of the “Zone of minimization”, to activate the positive “Complex argument” (⁺nVm_i)_kand conditionally negative "Complex argument" (^-nVm_i)_kmoreover, the "Positive channel of the adder" i "discharge" also includes functional input structures formed in accordance with the mathematical model of the form

with output logical functions f₂₁(} &) - OR NOT and f_one(&) - And, in which the functional input links are the functional input links of the adder for receiving positive analogue argument signals (⁺n_i)_k  and (⁺m_i)_k    conditionally “i” of the discharge “k” of the “Zone of minimization” to activate the generalized “Complex argument” (⁺Comp) s^{i + 1} _i)_k   “Integrated Argument” (⁺n & m_i)_kwhile the "Positive channel of the adder" i "discharge" also includes the logical function f₂₅(} &) - OR-NOT, but the “Conditionally negative channel of the adder“ i ”category” also includes functional input structures formed in accordance with a mathematical model of the form

with output logical functions f_four(} &) - OR NOT and f₂(&) - And, the functional input connections of which are the functional input connections of the adder for receiving conditionally negative analogue argument signals (^-n_i)_k and (^-m_i)_k conditionally “i” of category “k” of “Minimization zones” for activating the generalized “Complex argument” (^-Comp) s^{i + 1} _i)_k and the “Comprehensive Argument” (^-n & m_i)_k, while the "Conditionally negative channel of the adder" i "discharge" also includes the logical function f₂₆(} &) - OR NOT, characterized in that in conditionally “k” the “Zone of minimization” is introduced in accordance with the analytical expression of the form

additional structure of logical functions with input logical functions f₇(} &) - OR NOT - f₁₀(} &) - OR NOT, whose functional output links are the functional input links of the logical function f₂(}) - OR and which activates a positive resulting argument (⁺S_{i + 1})_k conditionally "i + 1" discharge in the "Positive channel of the adder" i + 1 "discharge", and an additional structure of logical functions with input logical functions f₁₇(} &) - OR NOT - f_twenty(} &) - OR NOT, whose functional output links are the functional input links of the logical function f_four(}) - OR and which activates a conditionally negative resulting argument (^-S_{i + 1})_k conditionally "i + 1" discharge in the "Conditionally negative channel of the adder" i + 1 "discharge", while in the system of input logic functions f_one(} &) - OR NOT - f₁₀(} &) - OR NOT the “Positive channel of the adder“ i ”discharge” and the “Positive channel of the adder“ i + 1 ”discharge”, which are implemented in accordance with the mathematical model of the form

included "Complex arguments", which are also included in the "Conditionally negative channel of the adder" i + 1 "and" i "category", as well as included "Complex argument" (^{+ 01, -11, + 1x-1}S^{i + 1} _i)_k with a changed level of the analog signal and it is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₂₂(} &) - OR NOT and input logic functions f₃(&) - And, f_four(&) - And, f₅(&) - And and f₆(&) - And, in which "⁺Complex argument ”(⁺⁰¹S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₅(}) - OR, f₂₅(} &) - OR NOT and f_one(&) - AND NOT and output logic function f₇(&)-AND;
and to the system of input logical functions f_one(}) - OR - f₁₀(}) - OR “Conditionally negative channel of the adder“ i ”discharge” and “Conditionally negative channel of the adder“ i + 1 ”discharge”, formed in accordance with the mathematical model of the form

“Integrated arguments” are included, which are common arguments with the “Positive channel of the adder“ i + 1 ”and“ i ”bits, as well as“ Complex argument ”(^{-01, + 11, -1x + 1}S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₂₄(} &) - OR NOT and input logic functions f₈(&) - And, f₉(&) - And, f₁₀(&) - And and f_eleven(&) - And, in which "^-Complex argument ”(^-01S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₆(}) - OR, f₂₁(} &) - OR NOT and f₂(&) - AND NOT and output logic function f₁₂(&)-AND;
at the same time, “Complex arguments” in the output functional structures that are implemented in accordance with the mathematical model of the “Positive channel of the adder“ i + 1 ”and“ i ”of the discharge” and the mathematical model of the “Conditionally negative channel of the adder“ i + 1 ”and“ i ” discharge ", formed by the following functional structures:
    ▶ "^±Complex argument ”(^{± 11.0, ± 1, ± 0x0}S^{i + 1} _i)_kwith a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₁₃(&) - And, f_fourteen(&) - And, f_fifteen(&) - And, f₁₆(&) - And and the output logical function f₂₇(} &) - OR NOT, in which "⁺Complex argument ”(⁺n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₇(&) - And, "^-Complex argument ”(^-n & m_{i + 1})_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_eighteen(&) - And, and^{± 0}Complex argument ”(^{± 0x0}S^{i + 1} _i)_k the inactivity of the arguments in the conditionally “k” “minimization zone” is a transformed argument of the functional structure, which is formed in accordance with a mathematical model of the form

with input logic function f₂₈(}&)-OR NO;
    ▶ "⁺Comprehensive transfer argument ”⁺¹⁰((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_29th(} &) - OR NOT, in which "⁺Complex argument ”(⁺¹⁰S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(}) - OR, f₂₁(} &) - OR NOT and f₃(&) - AND NOT and output logic function f₁₉(&) - And, and⁺Complex argument ”(⁺n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_one(&)-AND;
    ▶ "^-Comprehensive transfer argument ”^-10((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_thirty(} &) - OR, in which "^-Complex argument ”(^-10S^{i + 1} _i)_k  without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₈(}) - OR, f₂₃(} &) - OR NOT and f_four(&) - AND NOT and output logic function f_twenty(&) - And, and^-Complex argument ”(^-n & m_i)_k  is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₂(&)-AND;
    ▶ "⁺Comprehensive transfer argument ”⁺¹¹((Yes⁺←⁺) S^{i + 1} _i)_k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₁(}&)-OR NO;
    ▶ "^-Comprehensive transfer argument ”^-eleven((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₂(}&)-OR NO;
      ▶ "⁺Complex Argument ”((Not⁺←⁺) S^{i + 1} _i)_k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₃₃(} &) - OR NOT, f_fourteen(}) - OR and f₆(&) - AND NOT and with output logic f₅(&) - AND NOT in which "⁺Comprehensive Argument ”{⁺¹¹S^{i + 1} _i}_k    with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₇(&) - NAND and f₈(&) - AND NOT;
    ▶ "^-Complex Argument ”((Not^-←^-) S^{i + 1} _i)_k with a change in the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f₃₄(} &) - OR NOT, f_fifteen(}) - OR and f₁₀(&) - AND NOT and with output logic f₉(&) - AND NOT, in which "^-Complex argument ”(^-elevenS^{i + 1} _i)_k  with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with input logic functions f_eleven(&) - NAND and f₁₂(&) - AND NOT;
     ▶ "⁺Complex transfer argument ”((Yes⁺←⁺) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₄(}&)-OR NO;
     ▶ "^-Complex transfer argument ”((Yes^-←^-) S^{i + 1} _i)_k without changing the level of the analog signal is a transformed argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₃₅(}&)-OR NO;
    ▶ "⁺Complex Argument ”((Yes⁺←⁺) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f₁₃(&) - AND NOT;
    ▶ "^-Complex Argument ”((Yes^-←^-) S^{i + 1} _i)_k with a changed level of the analog signal is a converted argument of the functional structure, which is formed in accordance with the mathematical model of the form

with output logic f_fourteen(&) - AND NOT.