RU2502184C1 - METHOD OF CONVERTING STRUCTURE OF ARGUMENTS OF ANALOGUE LOGIC VOLTAGES «-/+»[mj]f(+/-) - "COMPLEMENTARY CODE" TO POSITION-SIGN STRUCTURE OF MINIMISED ARGUMENTS OF LOGIC VOLTAGES ±[mj]f(+/-)min AND FUNCTIONAL STRUCTURE FOR REALISATION THEREOF (VERSIONS OF RUSSIAN LOGIC) - Google Patents

Abstract

FIELD: information technology.

SUBSTANCE: inventions can be used in designing arithmetic units and performing arithmetic procedures over input conditionally negative arguments of analogue signals and conversion thereof to a position-sign structure of arguments "complementary code" using the arithmetic axioms of a ternary number system for subsequent summation with other arguments of analogue signals of terms in a position format. In one version, the converter is realised using logic elements AND, OR.

EFFECT: wider dynamic range of converting arguments and faster operation when performing arithmetic conversions in a position-sign adder and multiplier.

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Description

   The invention relates to computer technology and can be used to build arithmetic devices, perform arithmetic procedures on input conditionally negative arguments of analog signals “-” [n _i] f (2ⁿ) and transforming them into a position-sign structure of arguments "±" [n _i] f (-1 \ + 1,0, ... + 1) "additional code" using arithmetic axioms of the ternary number system f (+ 1,0, -1) for the subsequent summation with other arguments of the analog signals of the terms in the positional format.

     A known method of converting positionally negative negative arguments of analog signals "-" [n _i] f (2ⁿ) into the position-sign structure of the arguments “±” [n _i] f (-1 \ + 1,0, ... + 1) “additional code” (see Zilker B.Ya., Orlov SA Organization of computers and systems. “Peter” 2004, p. 339, fig. . 7.13), in which the conversion of conditionally negative arguments of analog signals “-” [n _i] f (2ⁿ) are performed by a logical-dynamic process of the form

Where

- логическая функция f₁(↕})-ИСКЛЮЧАЮЩЕЕ ИЛИ;

- the logical function f ₁ (↕ } ) is an EXCLUSIVE OR;

- линейная последовательность логических функций f₁(↕})-ИСКЛЮЧАЮЩЕЕ ИЛИ;

- a linear sequence of logical functions f ₁ (↕ } ) -EXCLUSIVE OR;

- функциональная структура сумматора, в котором использованы только первая группа входных связей (= [S¹ _i]) и входная связь переноса (= (р₀)) первого разряда.

- the functional structure of the adder, in which only the first group of input links (= [S ¹ _i ]) and the input transfer link (= (p ₀ )) of the first category are used.

 From the analysis of the logical-dynamic process of converting positionally conditionally negative arguments of analog signals "-" [n _i] f (2ⁿ) into the position-sign structure of the arguments "±" [n _i] f (-1 \ + 1,0, ... + 1) the "additional code" implies that at the preliminary stage of the conversion, the active and inactive conditionally negative arguments of the analog signals are changed in level by the logical functions f_1-8(↕}) - EXCLUSIVE OR. Then perform logical summation with the argument argument "-n"By means of the functional structure of the adder f (Σ) and only after the end-to-end transfer f (←empl) is completed, the resulting position-sign structure of the arguments is formed the term "±" [n _i] f (-1 \ + 1,0, ... + 1), the so-called "additional code" (prototype).

The known prototype has technological capabilities, which consist in the fact that to solve the problem of performing arithmetic operations of summing and “subtracting” the positional arguments of the analog signals “+” [ m _i ] f (2 ⁿ ) and “-” [ n _i ] f (2 ⁿ ) with different signs, using the same functional structure of the adder f ( Σ ), the procedure for converting the conditionally negative information structure of the arguments of the term “-” [ n _i ] f (2 ⁿ ) into the position-sign structure of the arguments “±” [ n _i ] f ( -1 \ + 1,0, ... + 1) to minimize the number of conditionally negative arguments ENTOV.

    A disadvantage of the known technological solution is the low speed of the conversion of conditionally negative arguments of analog signals "-" [n _i] f (2ⁿ) into the position-sign structure of the arguments "±" [n _i] f (-1 \ + 1,0, ... + 1) is an “additional code”, since in addition to the functional structure f_one(↕}) - EXCLUSIVE OR, which includes 3 ∙ f (&) - AND consecutive conditional logic functions f (&) - AND, also includes two consecutive functional structures f₁₂(↕}) - EXCLUSIVE OR without taking into account the technological cycle of end-to-end transfer f (←empl). As a result, the speed of the converter will be

∆t → 3 ∙ f (&) - And → 3 ∙ f (&) - And → 3 ∙ f (&) - And → 9 ∙ f (&) - And

nine conditional logical functions f (&) - And, and it can be reduced by three times.

The technological result of the proposed invention is to shorten the technological cycle of forming the resulting position-sign structure of the arguments “- / +” [ m _j ] f (+/-) - “ Additional code ”.

The specified technological and technical result is achieved by the following method and functional structures.

Option 1. The method of converting the structure of the arguments of analog logical voltages "- / +" [m _j] f (+/-) - "Additional code»Into the position-sign structure of minimized arguments of analog logical voltages^±[m _j] f (+/-)_minusing arithmetic axioms of the ternary number system f (+ 1,0, -1) (Variant of Russian logic), while from the structure of positive arguments of analog logical voltages “- / +” [m _j] f (+/-) - "Additional code"Form sequential" minimization zones "in one of them include a conditionally negative argument of the sign dischargem _± → (^- m _j)_{k + 1}  and it is “k + 1” “Minimization Zone”, and the positive subsequent arguments conditionally “j + 1” and “j” of the least significant bits include sequentially in “k” - “k-7” the “Minimization Zone”, in which the logical analysis of the activity of positive arguments by means of functional parallel structures f_one(00) min and f₂(0,0) min pass-through activation of minimized arguments "0,0one0 "and" 0,one0,0 ”in conditionally“ j + 1 ”and“ j ”digits, and through functional parallel structures of through activation f_one(eleven) min and f₂(one,one) min activate inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” digits, and if the functional parallel structure f_one(00) min pass-through activation of minimized arguments "0,0one, 0 ”in conditionally“ j ”“ k ”“ Minimization zone ”simultaneously activate by means of inactive arguments conditionally“ j + 1 ”and“ j ”bits, as, for example, in“ k ”_one"Zone of minimization", and through its transformed argument (⁰⁰ m _j)_k activate as a positive argument the conditionally “j” discharge in the minimized argument structure^±[m _j] f (+/-) min, and activates through a functional structure with the output logical function f_one(&) - And conditionally negative signed argument^±(^- m _j)_{k + 1} in a minimized argument structure^±[m _j] f (+/-) min, while the process of activating minimized arguments is performed in accordance with the logical-dynamic process of the form

Where

- логическая функция f₁(&)-И

- logical function f ₁ (&) - AND

and the functional parallel structure f₂(0,0) min through activation of minimized arguments “0,one0,0 ”in conditionally“ j + 1 ”“ k ”“ Minimization zones ”are activated simultaneously by means of inactive arguments conditionally“ j + 1 ”and“ j ”of the discharge between“ Minimization zones ”and through its converted argument (^0,0 m _j)_kactivate a positive argument conditionally "j + 1" discharge of the minimized structure of arguments^±[m _j] f (+/-) min with the exception of "k" "Minimization zones" if the sign argument is activem _± → (^- m _j)_{k + 1}, the process of activating the resulting minimized arguments is performed in accordance with the logical-dynamic process of the form

then the functional parallel structure of the end-to-end activation f_one(eleven) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in the conditionally “j” bit are activated by means of two arguments, conditionally “j + 1” and “j”, which are active in the previous “Minimization zone” under the condition that the argument in the conditionally “j + 1” category is also active, and through its resulting argument (^eleven m _j)_k activate a conditionally negative argument in the conditionally “j” category “Zone minimization”, while performing logical differentiation⁺d / dn positive arguments in the adjusted structure^±[m _j] f (+/-)_one  and form a conditionally negative argument in the minimized structure^±[m _j] f (+/-) min corresponding to the local conditionally negative hyphenation -f_one(⁺↓_-)_{d / dn}provided that in the previous “Minimization Zone” the argument is active (^0,0 m _j)_k functional structure f_one(00) min, and perform the formation of a positive local transfer argument + f_one(⁺←⁺)_{d / dn} in the next “minimization zone”, if the argument of the sign discharge is not active in itm _± → (^- m _j)_{k + 1}, the process of activating the resulting minimized arguments is performed in accordance with the logical-dynamic process of the form

and the functional parallel structure of end-to-end activation f_one(one,one) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in the conditionally “j + 1” category are activated by two arguments, conditionally “j + 1” and “j”, which are active between the “minimization zones” at provided that the argument in the conditionally “j” bit of the “Minimization Zone” is also active, and by means of its resulting argument (^1,1 m _j)_k activate conditionally negative argument conditionally "j + 1" discharge in the "minimization zone", while performing logical differentiation⁺d / dn positive arguments in the adjusted structure^±[m _j] f (+/-)_one with the formation of a conditionally negative argument in a minimized argument structure^±[m _j] f (+/-) min corresponding to the local conditionally negative hyphenation -f₂(⁺↓_-)_{d / dn}provided that in the previous “Minimization Zone” the argument is active (^0,0 m _j)_k functional structure f_one(0,0) min, and with the formation of a positive local transfer argument + f₂(⁺←⁺)_{d / dn} in the next “minimization zone”, if the argument of the sign discharge is not active in itm _± → (^- m _j)_{k + 1}, the process of activating the resulting minimized arguments is performed in accordance with the logical-dynamic process of the form

Option 2 Functional parallel structure f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and “j” bits “k” of the “Minimization Zone”, while the structures conditionally “j + 1” and “j” of the bits forming the positive minimized arguments ^min (+ m _j ) _{k + 1} and ^min (+ m _j ) _k are made according to the functional equivalent structure and each of them includes logical functions f ₁ (&) - And, f ₂ (&) - And, f ₃ (&) - And, f ₄ (&) - And, f ₅ (&) - And, f ₆ (&) - And, f ₇ (&) - And, f ₈ (&) - And, f ₉ (&) - And, f ₁₀ (&) - And, f ₂₁₁ (&) - And, f ₁ ( } ) -OR and f ₂ ( } ) -OR, while the functional relationships are made in accordance with mathematical models of the form

Where

и

- логическая функция f₁(})-ИЛИ и f₁(&)-И условно «j+1» разряда;

and

- logical function f ₁ ( } ) -OR and f ₁ (&) - And conditionally "j + 1"category;

- логическая функция f₁(})-ИЛИ и f₁(&)-И условно «j» разряда.

- logical function f ₁ ( } ) -OR and f ₁ (&) - And conditionally "j" discharge.

Option 3 Functional parallel structure of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” digits “k »“ Minimization zones ”, while the structures conditionally“ j + 1 ”and“ j ”bits are made according to the functional equivalent structure, forming conditionally negative minimized arguments ^min (- m _j ) _{k + 1} and ^min (- m _j ) _k , and each of them includes the logical functions f ₁ (&) - And, f ₂ (&) - And, f ₃ (&) - And, f ₄ (&) - And, f ₅ (&) - And, f ₆ (& ) -I, f ₇ (&) - And, f ₈ (&) - And, f ₉ (&) - And, f ₁₀ (&) - And, f ₁ ( } ) -OR and f ₂ ( } ) - OR, while functional relationships are made in correspondence with mathematical models of the form

Option 4 Functional parallel structure f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and “j” bits “k” of the “Minimization Zone”, while the structures conditionally “j + 1” and “j” of the bits forming the positive minimized arguments ^min (+ m _j ) _{k + 1} and ^min (+ m _j ) _k are made according to the functional equivalent structure and each of them includes the logical functions f ₁ (&) - AND, f ₂ (&) - And, f ₁ ( & ) -AND-NOT, f ₂ ( & ) -AND-NOT, f ₃ ( & ) - AND NOT, f ₄ ( & ) -AND NOT, f ₅ ( & ) -AND NOT, f ₆ ( & ) -AND NOT, f ₇ ( & ) -AND NOT, f ₈ ( & ) - AND NOT, f ₉ ( & ) -AND NOT, f ₁₀ ( & ) -AND NOT and f ₁₁ ( & ) -AND NOT, while the function The connections are made in accordance with mathematical models of the form

Where

- логическая функция f₁(&)-И-НЕ условно «j+1» разряда;

- logical function f ₁ ( & ) -and NOT conditionally "j + 1"discharge;

- логическая функция f₁(&)-И-НЕ условно «j» разряда.

- logical function f ₁ ( & ) -and NOT conditionally "j" discharge.

Option 5 Functional parallel structure of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” digits “k »“ Minimization zones ”, while the structures conditionally“ j + 1 ”and“ j ”bits are made according to the functional equivalent structure, forming conditionally negative minimized arguments ^min (- m _j ) _{k + 1} and ^min (- m _j ) _k , and each of them includes the logical functions f ₁ (&) - And, f ₂ (&) - And, f ₁ ( & ) -I-NOT, f ₂ ( & ) -I-NOT, f ₃ ( & ) -I- NOT, f ₄ ( & ) -AND-NOT, f ₅ ( & ) -AND-NOT, f ₆ ( & ) -AND-NOT, f ₇ ( & ) -AND-NOT, f ₈ ( & ) -AND- NOT, f ₉ ( & ) -AND NOT and f ₁₀ ( & ) -AND NOT, while the func ionic bonds are made in accordance with mathematical models of the form

Option 6 Functional parallel structure f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and “j” bits “k” of the “Minimization Zone”, while the structures conditionally “j + 1” and “j” of the bits forming the positive minimized arguments ^min (+ m _j ) _{k + 1} and ^min (+ m _j ) _k are made according to the functional equivalent structure and each of them includes the logical functions f ₁ ( & ) -AND-NOT, f ₂ ( & ) -AND NOT, f ₁ ( } ) -OR, f ₁ ( } & ) -ORNAND, f ₂ ( } & ) -OR- NOT, f ₃ ( } & ) -OR- NOT, f ₄ ( } & ) -OR- NOT, f ₅ ( } & ) -OR- NOT, f ₆ ( } & ) -OR- NOT, f ₇ (} &) -or-NO, f ₈ (} &) -or-NO, f ₉ (} &) -and AND-NO element ₁₀ and f (} &) -or-NO, wherein the functional connections are made in accordance with mathematical models of the form

Where

- логическая функция f₁(}& )-ИЛИ-НЕ условно «j+1» разряда;

- logical function f ₁ ( } & ) - OR NOT conditionally "j + 1"discharge;

- логическая функция f₁(}& )-ИЛИ-НЕ условно «j» разряда.

- logical function f ₁ ( } & ) - OR NOT conditionally “j” discharge.

Option 7 . Functional parallel structure of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” digits “k »“ Minimization zones ”, while the structures conditionally“ j + 1 ”and“ j ”bits are made according to the functional equivalent structure, forming conditionally negative minimized arguments ^min (- m _j ) _{k + 1} and ^min (- m _j ) _k , and each of them includes logical functions, logical functions f ₁ ( & ) -AND-NOT, f ₂ ( & ) -AND NOT, f ₁ ( } ) -OR, f ₁ ( } & ) -ORNAND, f ₂ ( } & ) -OR- NOT, f ₃ ( } & ) -OR- NOT, f ₄ ( } & ) -OR- NOT, f ₅ ( } & ) -OR- NOT, f ₆ ( } & ) -OR- NOT f ₇ ( } & ) -OR- NOT, f ₈ ( } & ) -OR- NOT, f ₉ ( } & ) -OR- NOT and f ₁₀ ( } & ) -OR- NOT, while the functional relationships are made in accordance with mathematical models of the form

     The essence of the logical-dynamic process of converting the structure of the arguments of analog logical voltages "- / +" [m _j] f (+/-) - "Additional code»Into the position-sign structure of minimized arguments of analog logical voltages^±[m _j] f (+/-)_minusing arithmetic axioms of the ternary number system f (+ 1,0, -1) will be explained during its synthesis.

Synthesis of a mathematical model of the argument structure transformation procedure  "- / +" [m _j] f (+/-) - "Additional code"into a minimized position-sign structure of arguments ^±[m _j] f (+/-)_min)  If we analyze at a formalized level the positional structure of the positive active arguments of the terms “+” [m _j] f (2ⁿ) as an expression (1)

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

then by the level of the analog signal, with the exception of the argument argument “+” and “-” they are equivalent. Therefore, the performance of any arithmetic operations on the arguments of the terms “+” [ n _i ] f (2 ⁿ ) and “-” [ m _j ] 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 symbols “+” 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 _j ] 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 procedure can be correctly arithmetically implemented only 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 of 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 + m _{j of} local transfer + f ( ⁺ ← ⁺ ) _{d / dn} active an 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 - m _{j of} 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 number 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 graphoanalytic expression (7)

in which inactive arguments after the first active conditionally negative argument in the original structure “-” [ m _j ] 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 _j ] 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 logical differentiation procedure ^- d / dn conditionally negative arguments in the structure, which is performed in accordance with the graph-analytical expression (8).

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 conditionally negative argument - m _j local transfer -f ( ^- ← ^- ) _{d / dn} 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 positive argument + m _{j of} 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 wrapping 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. It should be noted that the “ Additional Code ” can be generated not only for the structure of conditionally negative arguments, but also for the structure of positive arguments. For example, if logical zeros are activated in accordance with the arithmetic axiom “± 0” → “+ 1 / -1” in expression (3) and the logical-dynamic process of transforming the arguments is written as a graph-analytical expression (10)

the position-sign structure “+/-” [ m _j ] f (+/-) will be formed. And this argument structure “+/-” [ m _j ] f (+/-) can be minimized by the number of active arguments, and for this in expression (11)

perform the logical differentiation procedure ^- d / dn conditionally negative arguments, but only consecutive active arguments.

From the analysis of the results obtained, it follows that any structure of position-sign arguments, including its not so good version, the so-called “ Additional code ” can be minimized by the number of active arguments in the structure, which will allow to form the functional structures of the adders f ( Σ ) _min and multipliers f _Σ ( Σ ) _min with a maximally reduced technological cycle Δ t _{Σ of the} formation of the resulting minimized sum of position-sign arguments ^± [ S _i ] f (+/-) _min . For example, if for the position-sign structure of the arguments “ Additional Code ” (12)

form a parallel-serial multiplication procedure f _Σ ( Σ ) for a specific positional structure of the arguments of the factors ⁺ [ m _j ] f (2 ⁿ ) and ⁺ [ n _j ] f (2 ⁿ ) → “+” “11111111” f (2 ⁿ ) in the form of graphoanalytic expression (13)

and for the position-sign structure of the arguments (14)

form a procedure for parallel-sequential multiplication f _Σ ( Σ ) for a specific positional structure of the arguments of the factors ^± [ m _j ] f (+/-) and ^± [ n _j ] f (+/-) → "+""10101010" f (2 ⁿ ) in the form of expression (15),

and for the minimized position-sign structure of arguments (16)

to formulate the procedure of parallel-sequential multiplication f _Σ ( Σ ) in the form of graphoanalytic expression (17),

where f (CD) is the functional structure of the encoder of partial works;

and compare with the positional structure of the multiplier (13), then the position-sign structures of the arguments of the factors ^± [ m _j ] f (+/-) min and ^± [ n _j ] f (+/-) min can significantly increase the speed of the logical-dynamic process conversion of arguments in the multiplier. And for this it is necessary to minimize the position-sign structures of the arguments of the factors ^± [ m _j ] f (+/-) and ^± [ n _j ] f (+/-), which in their structure include successive positive and conditionally negative arguments. And if we apply to such structures, for example, to position-sign factors ^± [ m _j ] f (+/-) and ^± [ n _j ] f (+/-) → “10101010” f (2 ⁿ ) the inverse arithmetic axiom “+ 2 "" - 1 "→" +1 "and write such a process in the form of a logical-dynamic expression (18),

then the procedure for the formation of pyramidally located partial works (18) can be formed in the form of a graphic-analytical expression (19),

in which the feature is the first level of summation of partial works. And it can be done by combining each two of their levels through the logical functions f _1-4 ( } ) -OR, which, on the one hand, will lead to the replacement of adders in the first level of summation of partial products by linear logical functions f _1-4 ( } )-OR. On the other hand, it leads to a significant decrease in the technological cycle Δ t _{Σ of the} logical-dynamic process of multiplying the minimized structures of the arguments of the factors ^± [ m _j ] f (+/-) min and ^± [ n _j ] f (+/-) min. It should be noted that the so-called “ Additional code ” “- / +” [ m _i ] f (+/-) or one of the possible options for the position-sign structure of arguments ^± [ m _j ] f (+/-), with on the one hand, it does not allow minimizing the functional structure of the multiplier f _Σ ( Σ ) and significantly reducing the technological cycle Δ t _Σ it in comparison with the minimized structures of the arguments of the factors ^± [ m _j ] f (+/-) min and ^± [ n _j ] f ( +/-) min. On the other hand, when performing the procedure of multiplying the arguments of the factors in “ Additional Codes ” with different signs “- / +” [ m _j ] f (+/-) and “+/-” [ m _i ] f (+/-) in addition to the functional structure of the multiplier f _Σ ( Σ ) requires a functional additional structure for analyzing and activating the “+” or “-” sign of the resulting argument structure, when, as when multiplying the minimized structures of the arguments of the factors ^± [ m _j ] f (+/-) min and ^± [ n _j ] f (+/-) min such an additional procedure is excluded. For example, if we formulate the procedure for multiplying the minimized structures of the arguments of the factors ^± [ m _j ] f (+/-) min → “-” “10101010” f (2 ⁿ ) and ^± [ n _j ] f (+/-) min → “+ "" 10101010 "f (2 ⁿ ) with different signs in the form of a graphic-analytical expression (20),

then the minimized structure of the resulting sum ⁺ [ S _j ] f (+/-) min → “-” “111000011100100” f (2 ⁿ ) is positionally significant because its structure carries information about the sign. In this regard, the question arises of how the procedures for converting positive and conditionally negative intermediate sums of partial products in graph-analytic expression (19), which has a positive structure of partial product arguments, and in graph-analytic expression (20), which have a conditionally negative structure of partial product arguments, differ significantly. And for this it makes sense to form two logical-dynamic processes of converting arguments in the functional structures of adders f ₁ ( Σ ) - f ₃ ( Σ ), in which the minimization procedure is performed only taking into account the arithmetic axioms of the ternary number system f (+ 1,0, - fifteen). It should be noted that the logical differentiation procedure ⁺ d / dn of positive arguments and conditionally negative arguments ^- d / dn is a multiple use of arithmetic axioms (5). Indeed, if we formulate the procedure for transforming partial products in the adder f ₂ ( Σ ) of the graphoanalytic expression (19), writing it as a logical-dynamic process (21),

then after converting the arguments of the second intermediate sum ⁺ [ S ² _j ] f (&) - And in accordance with the arithmetic axiom “+1” → “+2” “- 1” in the structure of the intermediate sum ⁺ [ S _j ] f (+ / -) ₀ a sequence of active positive arguments is formed, and even after its logical differentiation ⁺ d / dn, the resulting position-sign sum ^± [ S _j ] f ₁ (+/-) min has a minimized structure of active arguments.

Similar transformations in the adder f ₁ ( Σ ), which we write in the form of a logical-dynamic expression (22),

in which, after logical differentiation ⁺ d / dn of the intermediate sum ⁺ [ S _j ] f (+/-) _{0, the} resulting position-sign sum ^± [ S _j ] f ₂ (+/-) min has a minimized structure of active arguments. And after combining in the output adder f ₃ ( Σ ) the preliminary sums ^± [ S _j ] f (+/-) ₁ and ^± [ S _j ] f ₁ (+/-) ₂ (23)

and performing argument transformations in accordance with the inverse arithmetic axioms “+ 1 / -1” → “± 0” and “-2” “+ 1” → “-1” and logical differentiation ⁺ d ₁ / dn of a continuous sequence of positive arguments will be formed the resulting position-sign sum ^± [ S _j ] f ₁ (+/-) min, which has a minimized structure of active arguments. It should be especially noted that the resulting resulting minimized position-sign sum ^± [ S _j ] f ₁ (+/-) min can be used as the correct structure of the term or factor. But if it becomes necessary to transform conditionally negative arguments ⁺ [ S _j ] f (+/-) min into the structure of positive arguments ⁺ [ S _j ] f (2 ⁿ ), then this procedure is performed using the arithmetic axiom “-1” → “- 2 "" + 1 "in the expression (24),

but it is equivalent, in essence, to the end-to-end transfer f (← program), which increases the technological cycle Δ t _{Σ of the} formation of the resulting sum.

Further, if we formulate the procedure for transforming partial products in the adder f ₂ ( Σ ) of the graphoanalytic expression (20), writing it as a logical-dynamic process (25),

then after converting the arguments of the second intermediate sum ^- [ S ² _j ] f (&) - And in accordance with the arithmetic axiom “-1” → “-2” “+ 1” in the structure of the subtotal ^- [ S _j ] f (+ / -) ₀ a sequence of active conditionally negative arguments is formed, and even after its logical differentiation ^- d / dn, the resulting position-sign sum ^± [ S _j ] f ₁ (+/-) min has a minimized structure of active arguments.

Similar transformations in the adder f ₁ ( Σ ), which we write in the form of a logical-dynamic expression (26),

in which, after logical differentiation ^- d / dn of conditionally negative arguments in the structure ^- [ S _j ] f (+/-) _{0 the} resulting position-sign sum ^± [ S _j ] f ₂ (+/-) min also has a minimized structure of active arguments. And after combining in the output adder f ₃ ( Σ ) the resulting sums ^± [ S _j ] f (+/-) ₁ and ^± [ S _j ] f ₁ (+/-) ₂ (27)

and also performing argument conversions in accordance with the inverse arithmetic axioms “+ 1 / -1” → “± 0” and “+2” “- 1” → “+1” and logical differentiation ^- d ₁ / dn of a continuous sequence of conditionally negative arguments the resulting position-sign sum ^± [ S _j ] f ₁ (+/-) min will be generated, which also has a minimized structure of active arguments. It should be especially noted that the resulting resulting minimized position-sign sum ^± [ S _j ] f ₁ (+/-) min can be used as the correct structure of the term or factor. But if it becomes necessary to transform conditionally negative arguments ⁺ [ S _j ] f (+/-) min into the structure of positive arguments ⁺ [ S _j ] f (2 ⁿ ), then this procedure is performed using the same arithmetic axiom “-1” → "-2""+1" in the expression (28),

but it is also essentially equivalent to the end-to-end transfer f (← program), which increases the technological cycle Δ t _{Σ of the} formation of the resulting sum “- / +” [ m _j ] f (+/-).

From the comparative analysis in expression (28) of the minimized structure of the arguments ^± [ S _j ] f (+/-) min and the non-minimized structure “- / +” [ m _j ] f (+/-) “Additional code” it follows that the minimized structure arguments ^± [ S _j ] f (+/-) min has a significant quality, which consists in the fact that, on the one hand, a continuous sequence of positive arguments “111 ... 1” is presented in it with previously introduced end-to-end hyphenation in the form of conditionally negative arguments in the structure "+ 100 ... -1". On the other hand, the active arguments in the structure ^± [ S _j ] f (+/-) min alternate through at least one inactive discharge, which completely excludes the end-to-end transfer procedure f (←) in the functional structures of the adders f ( Σ ) min and multipliers f _Σ ( Σ ) min. It should be especially noted that when some arithmetic operations (calculations) are continuously performed, there is no need to convert the minimized structure of intermediate arguments ^± [ S _j ] f (+/-) min to the structure of arguments “- / +” [ m _j ] f (+/-) “Additional code”, since the technological cycle ^± Δ t _{Σ of the} functional structures of position-sign adders f ( Σ ) min is four times less than the technological cycle ⁺ Δ t _{Σ of} positional adders f ( Σ ) ⁺ , in which only the structure of conditionally negative arguments of the terms in expression (12) has t referred to as the “ Additional Code ”. Therefore, it makes sense to conduct an additional analysis of the appropriateness of the further use in the functional structures of adders and multipliers of the non-minimized structure “- / +” [ m _j ] f (+/-) “Additional Code”, and for this we will form a graphic-analytical expression (29).

From the analysis of graphoanalytic expression (29) it follows that if in the positional structure of conditionally negative arguments “-” [ m _j ] f (2 ⁿ ) there are structures “-” [ m _j ] f (+/-) _min in which the active arguments alternate with inactive arguments, and when summing up such arguments, end-to-end transfer f (←tar) is not formed, and in the position-sign structure “- / +” [ m _j ] f (+/-) “Additional code” of conditionally negative arguments they are completely are absent. It should be noted that in the structure of positive arguments “- / +” [ m _j ] f (+/-) there are also separate structures, and they can form through in the adder f ( Σ ) ⁺ and the multiplier f _Σ ( Σ ) transfer f (←empl), therefore, it is necessary to form a different number system that minimizes the end-to-end transfer f (←empl) to the local transfer f (←), which are limited by the next digit. And there is such a possibility if, for example, we apply the arithmetic axioms of the ternary numeral system f (+ 1,0, -1) (5) to non-minimized structures in the graph-analytical expression (29), which include the inverse arithmetic axioms (30).

But before minimizing the structure “- / +” [ m _j ] f (+/-) “Additional Code” (29) it should be noted that its conditionally negative block as a position-sign category is written with incorrectly located sign arguments that should be adjusted using the inverse arithmetic axiom “-2” “+ 1” → “-1” and in accordance with the graphic-analytical expression (31)

and written as informational arguments in non-minimized position-sign structures of the conditionally negative block “- / +” [ m _j ] f (+/-) in expression (32).

As a result of the transformations performed in the conditionally negative block “- / +” [ m _j ] f (+/-), the conditionally negative information sign argument is included in the information structure of the arguments of terms and factors, which are only partially minimized. Since if the procedure for minimizing the corrected structures “- / +” [ m _j ] f (+/-) ₁ “Additional code” (32) is written in the form of a graphic-analytical expression (33),

then its minimized expression (34) can be written,

in which in which all active positive and conditionally negative arguments in the position-sign expressions ^± [ m _j ] f (+/-) ⁺ min and ^± [ m _j ] f (+/-) ^- min are positionally located, at least through inactive discharge. It should be noted that, on the one hand, the logic of converting positive arguments in both the position-sign block “- / +” [ m _j ] f (+/-) ₁ and the position block “+” [ m _j ] f (2 ⁿ ) essentially boils down to the procedure of logical differentiation ⁺ d / dn of a positive sequence of arguments and application of the inverse arithmetic axiom “-2” “+ 1” → “-1”. As a result, in minimized expression (34), both its conditionally negative block ^± [ m _j ] f (+/-) ^- min and the positive block ^± [ m _j ] f (+/-) ⁺ min have active arguments in their sequences alternate, at least through one inactive discharge, which, when summed, leads to the formation of only local transfers f (←). It should be noted that minimized structures ^± [ m _j ] f (+/-) ⁺ min and ^± [ m _j ] f (+/-) ^- min of expression (34) can also be formed directly from previously not transformed structures “- / + "[ M _j ] f (+/-) &" + "[ m _j ] f (2 ⁿ )" Additional code "using the same procedures.

Indeed, if the procedure for minimizing the structures “- / +” [ m _j ] f (+/-) “Additional code” is written in the form of a graphic-analytical expression (35),

then its minimized expression (36) can be written,

in which all active positive and conditionally negative arguments in position-sign expressions ^± [ m _j ] f (+/-) ⁺ min and ^± [ m _j ] f (+/-) ^- min are positionally located, at least through an inactive discharge . It should be noted that during the formation of a minimized block of conditionally negative arguments ^± [ m _j ] f (+/-) ^- min in the structure of the argument with the information content “ –5 ”, both in expression (33) and in expression (35 ) the procedure for activating inactive logical zero arguments “± 0” → “+ 1 / -1” was performed and only after this activation was the logical differentiation procedure ⁺ d / dn of a positive sequence of arguments implemented.

From a comparative analysis of the “ Numbering system “ - / + ”[ m _j ] f (+/-) - Additional code ” (35) and the “ Minimum numbering system ^± [ m _j ] f (+/-) min” (36) it follows that in the minimized argument structures ^± [ m _j ] f (+/-) ^- min and ^± [ m _j ] f (+/-) ⁺ min there is no additional sign discharge, and this circumstance allows us to significantly increase the dynamic range in technological processes of systems control, in which the "digital" form of information in the form of position-sign arguments must be converted into an analog form of information in the form of continuously th analog voltage signal ^± U ( ⁺ [ m _j ]). And this increase in the dynamic range of the analog voltage signal ^± U ( ⁺ [ m _j ]) can be realized using the existing functional structures f ₁ (DAC) of the digital-to-analog conversion of positional arguments. Moreover, the expansion of the dynamic range of variation of analog signals includes both its increase in the positive level of the analog voltage ⁺ U _DAC ( ⁺ [ m _j ]) and the increase in the negative level of the analog voltage ^- U _DAC ( ⁺ [ m _j ]). Since if we write the functional structure of the digital-to-analog converter f ₁ (DAC) with input information arguments m _± & ⁺ [ m _j ] and the converted argument ^± U of the _DAC (t), in the form of an analytical expression (37),

then the senior argumentm _±  argument structures (38) "Number systems"- / +" [m _j] f (+/-) -Additional code"Performs the function of discrete shift"0"←m _±→ "one"In the graph-analytical expression (39) of the resulting analogue argument^± U _DAC(t) the functional structure of the digital-to-analog converter f_one(DAC) (37) either in the range of arguments "+" [m _j] f (2ⁿ) positive levels of the analog signal⁺ U _DAC(t) form _±→ "0", Or in the range of conditionally negative arguments" - / + "[m _j] f (+/-) negative analog signal levels^- U _DAC(⁺[m _j]) whenm _±→ "one". And this procedure in a formalized arithmetic space, for example, for an argument with informational content “-one"(40) and" +7»(41)

can be written in the form of graphoanalytic expression (42).

It should be noted that the formalized arithmetic space is not an abstract, but a very specific sequence of information arguments, and its basis, as in the Rene-Descartes coordinate system (1596 - 1650), is two orthogonal sets ^± [ n _j ] and ^± [ m _j ], which form four functional areas of combinational arguments. And we will write this formalized arithmetic space in the form of a graphic-analytical expression (45),

in which the information arguments of two orthogonal sets ^± [ n _j ] and ^± [ m _j ] delimit the entire arithmetic space into the region of positive combinational arguments ⁺ [ n _j & m _j ] and the region of conditionally negative combinational arguments ^- [ n _j & m _j ]. It should be noted that the combination arguments ⁺ [ n _j & m _j ] and ^- [ n _j & m _j ] are the informational resulting value of the vector sum in turn belonging to two orthogonal sets ^± [ n _j ] and ^± [ m _j ] and their equivalent arguments are positioned in such a way that they coincide with equivalent informational arguments, including two orthogonal sets, and form common equipotential levels. The situation is similar in the other two position-sign areas ^± [ n _j & m _j ] ₁ and ^± [ n _j & m _j ] ₂ , but they have a common equipotential level “ 0 ” for the entire arithmetic space, which delimits the entire arithmetic space (45) to the positive region “+” and the conditionally negative region “-”, which can be written as a formalized graphoanalytic expression (43).

Returning to the analysis of the logical-dynamic process in the functional structure of the digital-to-analogue conversion of the expression f ₁ (DAC) (42), it has a feature in the form of a positive input argument ⁺ U _op with an information level, for example, for specific examples (40) and (41) equal to "+ 8 ", and the argument of the sign discharge m _± from the logical function f ₁ ( & ) -НЕ, which is also equivalent to the information level "+ 8 ". It should be noted that the structure of the input arguments ⁺ [ m _j ] is equivalent to the maximum information content “+ 4 + 2 + 1 ” → “+ 7 ” and this information content in the arithmetic space (43) has a vector structure in the form of successively orthogonal weight vectors in its positive area is “+”, which have two options. Since each of the following terms of the vectors in the information content “+ 4 + 2 + 1 ” → “+ 7 ” functionally belong to the equally probable orthogonal sets ⁺ [ n _j ], ^- [ n _j ] → ^± [ n _j ] and ⁺ [ m _j ] , ^- [ n _j ] → ^± [ m _j ] or ^± [ m _j ] and ^± [ n _j ], the vector summation procedure in arithmetic space is performed by combining the end of the previous information vector with the beginning of the next information vector at an equipotential level, which is positionally aligned with equivalent levels of orthogonal sets ^± [ n _j ] and ^± [ m _j ]. As a result of only such a procedure of summing vector arguments “+ 4 + 2 + 1 ”, the end of the last one is positionally positioned at the equipotential level “+ 7 ”, which corresponds to their resulting informational sum, provided that the next vector that corresponds to the equipotential level is “± 0 ", An example of the expression (41).

An example of expression (40) has a similar vector structure in arithmetic space (43), with the exception of a conditionally negative argument with information content “ –8 ”, the beginning of which is also aligned with the end of the vector structure “+ 4 + 2 + 1 ” and its end also combined with the equivalent level “- 1 ” of orthogonal sets ^± [ n _j ] and ^± [ m _j ], but in position-sign areas “+/-”, since the so-called “subtraction” procedure has been performed. It should be specially noted that the direction of vectors in the arithmetic space must correspond to the direction of positive vector sets ⁺ [ n _j ], ⁺ [ m _j ] and the direction of conditionally negative vector sets ^- [ n _j ], ^- [ m _j ] orthogonal sets ^± [ m _j ] and ^± [ n _j ], and they, in contrast to the generally accepted representation in a formalized arithmetic space, have a mutually opposite direction. Since in this situation it is not the conditional sign that is important, but the magnitude of the information content, and the fact that the argument has either positive properties or conditionally negative properties, it does not affect the direction of increasing its information content, the direction of the vector indicates the direction of increasing its information value. And if we write down the logical-dynamic process of forming the structure of the arguments “- 1 ” of expression (40) in the “ Additional Code ” in the form of a graphic-analytical expression (45),

in which, before logical differentiation ^- d / dn of conditionally negative arguments of the positional structure ^- [ n _j ] f (2 ⁿ ), all inactive arguments “0” → “+ 1 / -1” are activated after the first active argument in the low order, then after execution logical differentiation procedures ^- d / dn in the low order, a positive additional argument is activated, and a conditionally negative argument is activated in the high order and, unlike the sign “-” in the structure ^- [ n _j ] f (2 ⁿ ), it is already an information argument - 8 ". And on the one hand, in the arithmetic space (43) the vector of the information argument “- 8 ” is located coplanarly to one of the orthogonal sets ^± [ m _j ] or ^± [ n _j ] and its orientation corresponds to the orientation of the vector conditionally negative sets ^- [ n _j ], ^- [ m _j ]. On the other hand, in the arithmetic space (43), the end of the information argument “- 8 ” of expression (45) is aligned with the equipotential level “ –1 ”, and its beginning is positionally located in the positive region “+” of the formalized space and is a logical continuation of the vector structure as the positive argument "+ 1 " _{d / dn of} the logical differentiation procedure ^- d / dn, and the positive arguments "+ 4 " _{± 1} and "+ 2 " _{± 1 of the} procedure for activating inactive arguments "0" → "+ 1 / -1" of the expression (45). It should be noted that a significant complication of the minimized structure of the arguments, which corresponds to the argument with the minimized information content “ -1 ” in this situation, is directly related to the “desire” to perform all arithmetic operations of summation and multiplication, including the transition of arguments from one form of information (positional or analog) to another form of information (analog or positional) only in the positive area “+” of arithmetic space (43). But this “desire” is incorrect, since the arithmetic space (43) is not limited only to the positive area “+”, but includes the conditionally negative area “-” and two position-sign areas “+/-” ₁ and “+/-” ₂ and only their combination is a formalized arithmetic space. And in this formalized arithmetic space (43) by means of the sign argument m _± and the logical function f ₁ ( & ) -НЕ in the high order of the functional structure f ₁ (DAC) (42), the output argument of the ionized current ⁺ I _k f ( m _± & ⁺ [ m _j ]), the value of which, or rather the positional position of the vector structure of the arguments ⁺ [ m _j ] → “+ 4 + 2 + 1 ” in the arithmetic space (43) essentially depends on the sign argument m _± with a changed analog level signal. If the argument of the sign digit is active m _± → “ 1 ”, then the beginning of the vector structure of arguments ⁺ [ m _j ] → “+ 4 + 2 + 1 ” is located at the equipotential level “ 0 ”, and its end is at the equipotential level “+ 7 ", But if the argument of the signed digit is inactive m _± →" 0 ", then the beginning of the vector structure of the arguments ⁺ [ m _j ] →" + 4 + 2 + 1 "is shifted to the conditionally negative level" -8 ", as a result of such a shift its end is located at the equipotential level “- 1 ”, which is fully consistent with the information content ozitsionno-sign structure of conditionally negative argument ^± [ m _j ] → "- 8 + 4 + 2 + 1 " → "- 1 ". And such a shift is performed by the functional structure of the operational amplifier f ₁ (OA) (44), in which the logical-dynamic process of converting the input argument of the reference voltage ⁺ U _op consists in the fact that it is converted into the argument of the ionized current field ^- I _n f ( U _op ), which, on the one hand, corresponds to the information argument “- 8 ”. On the other hand, the argument of the ionized current field ^- I _n f ( U _op ) of the operational amplifier f ₁ (ОУ) (44) corresponds to the information content of the sign argument argument m _± , and it is included as a vector in the vector structure of the argument of ionized current ⁺ I _k f ( m _± & ⁺ [ m _j ]) of the functional structure f ₁ (DAC). And if you write a mathematical model of digital-to-analog conversion (46),

then at the inverting input of the output operational amplifier f ₂ (op-amp) the active argument of the ionized current field ^- I _n f ( U _op ) of the operational amplifier f ₁ (op-amp) compensates for the active argument of the sign m _± → " 1 " of the vector structure ↓ ⁺ I _k f ( m _± & ⁺ [ m _j ]). As a result, the beginning of the vector structure of arguments ⁺ [ m _j ] → “+ 4 + 2 + 1 ” coincides with the equipotential level “ 0 ”, and its end coincides with the equipotential level “+ 7 ” in arithmetic space (43) and the transformed argument ^± U _{The DAC} f ([ m _j ]) of the operational amplifier f ₂ (op-amp) will also have an information content of “+ 7 ”. And if in the vector structure ↓ ⁺ I _k f ( m _± & ⁺ [ m _j ]) the argument of the sign m _± → “ 0 ” is not active, then the input argument ^is I _n f ( ⁺ U _op ) of the functional structure of the operational amplifier f ₂ ( OU) (46) in the arithmetic space (43) performs the displacement of the beginning of the vector structure of arguments ⁺ [ m _j ] → “+ 4 + 2 + 1 ” and combines it with the equipotential level “ –8 ”, as a result, its end coincides with the equipotential level “- 1 ” and the transformed argument ^± U _DAC f ([ m _j ]) of the operational amplifier f ₂ (op amp) will also have the information content “- 1 ”. Moreover, from the analysis of the functional structure of the digital-to-analog converter f ₁ (DAC), it follows that its bit capacity is reduced by one senior bit, since it performs the function of discrete displacement of the resulting vector structure of the arguments of the ionized current ↓ ⁺ I _k f ( m _± & ⁺ [ m _j ] ) And if we write down a conditionally negative area from the “ Number system “ - / + ”[ m _j ] f (+/-) - Additional code ” (38) and the same area of the “ Minimized number system ^± [ m _j ] f (+/-) min "in the form of graphoanalytic expression (47),

then from his analysis it follows that when switching from the “ Numbering system “ - / + ”[ m _j ] f (+/-) - Additional code ” (38), in which the high-order argument m _± performs the sign function of the converted analog signal ^± U _DAC ( m _j ) of the functional structure of the digital-to-analog converter f ₁ (DAC), to “ Minimum number system ^± [ m _j ] f (+/-) min”, on the one hand, will increase the dynamic range of the resulting voltage argument ^± U _DAC f ([ m _j ]) in the functional structure f ₁ (DAC) by “32%”. On the other hand, if the functional structure of the digital-to-analog conversion (46) is written as an analytical expression (48),

in which the functional non-inverting coupling (+) of the output operational amplifier f ₁ (OA) includes a functional additional resistor structure f (R ₁ ) and a functional additional structure of a digital-to-analog converter f ₂ (DAC), then the voltage argument ^± U _{j of the} sampling step in the output argument voltage ^± U _DAC f ( ^± [ m _j ] min) of the operational amplifier f ₁ (op amp) will be reduced by half. Since if we write the graphoanalytic expression (49),

then to maximize the use of the information interval "Minimized number system ^±[m _j] f (+/-) min »expressions (47) initial reference voltage⁺ U _opshould be increased by⁺ΔU _op → "32%"⁺ U _op. Wherein if we return to the analysis of the analytical expression (46) and, in particular, to the analysis of the functional structure of the digital-to-analog converter f_one(DAC) (50)

and logical-dynamic process (39) of the formation of the transformed argument^± U _DAC(⁺[m _j]), then its senior rank is not used as intended as the senior additional rank argument information structure⁺[m _j]. Resulting sampling step⁺ U _j in digital to analog converter f_one(DAC) (50) is determined by the bit capacity reduced by the most significant digit, and the most significant bit performs the function of discrete displacement of the vector structure of the arguments⁺ I _kf ( m _±&⁺[m _j]). And in the analytical expression (48) as in the functional structure f_one(DAC) and in the functional structure f₂(DAC) sampling step⁺ U _j is formed taking into account their full capacity, including senior bit, which leads to a decrease in the sampling step⁺ U _j/ 2  in graphoanalytic expression (49) twice. And if we take into account the additional dynamic range of minimized structures of the arguments of expression (47), then for them the discretization step⁺ U _j/ 2  additionally reduced by "32%". Moreover, if we write for a specific implementation of the minimized structure of arguments⁺[m _j] f (+/-)_min→ "+" "111000011100100" f (2ⁿ) the logical-dynamic process of simultaneous transformation of its conditionally negative sequence of arguments in the functional structure f_one(DAC) and a positive sequence of arguments in the functional structure f₂(DAC) in the form of a graphic-analytical expression (51),

then a feature in it is the procedure for transforming the structure of its conditionally negative arguments^-[m _j] f (+/-) min. And this feature is that at the first stage of transformation as a positive structure of arguments⁺[m _j] f (+/-) min in f_one(DAC) and conditionally negative arguments^-[m _j] f (+/-) min in f₂(DAC) the converted vector information sum “+33028"And" +4128»A positive sign. And if on the non-inverting functional connection (+) of the adder f (Σ) operational amplifier f_one(ОУ) vector information sum "+33028"Argument of the ionized current field⁺ I _onef (⁺[m _j]) f₂(DAC) does not change the resulting sign, then on the inverting (-) functional connection of the adder f (Σ) operational amplifier f_one(ОУ) information amount “+4128"Your⁺ I _onef (⁺[m _j]) f₂(DAC) changes the resulting sign and becomes conditionally negative "-4128". As a result, the resulting converted stress argument^± U _DACf (^±[m _j] min) operational amplifier f_one(DU) will correspond to the information amount “+33028"&" -4128"→" +28900»Of expression (52), and analytical expression (52) is a mathematical model of the logical-dynamic process of transforming minimized argument structures^±[m _j] f (+/-)_min with both positive informational content and conditionally negative informational content. Because ifminimized number system ^±[m _j] f (+/-)_min write as expression (52),

both its positive region of argument structures ⁺ [ m _j ] f ₂ (+/-) _min and the conditionally negative region of argument structures ^- [ m _j ] f ₁ (+/-) _min include various combinations of both positive arguments and conditionally negative arguments, unlike the “ Numbering system “ - / + ”[ m _j ] f (+/-) - Additional code ” (38), in which only the entire conditionally negative region of argument structures “- / +” [ m _j ] f (+/-) includes the conditionally negative argument of the sign digit m _± . And to reduce the sampling step ⁺ U _{j, the} functional structure of the digital-to-analog conversion (46) can be written either in the form of an analytical expression (54),

Where

- функциональная структура с аналого-цифровой логической функцией f(&)-И, реализующей процедуру активизации входного аргумента ионизированного тока ^- I _nf(⁺ U _оп);

- functional structure with an analog-to-digital logic function f (&) - And, which implements the procedure for activating the input argument of the ionized current ^- I _n f ( ⁺ U _op );

in which, on the one hand, a functional structure with resistor functions f (R_one) and f (R₂) dividing the input analog voltage argument⁺ U _op two to feed into a functional analogue connection (→) f_one(DAC) analog voltage argument⁺ U _op/ 2. On the other hand, a functional structure has been introduced with an analog logical function f (&) - And, which, with an active argument of the signm _±  allows you to perform the procedure of discrete displacement of the vector structure⁺ I _kf (⁺[m _j]) f_one(DAC) with a minimized sampling step from the conditionally negative region of the arithmetic space (43) to its positive region.

Or in the form of an analytical expression (55),

the feature of which is the argument of the sign m _± and the logic of activating the resulting argument ^± U _DAC f ( ^± [ m _j ]) of the operational amplifier f ₁ (OA), and this feature is that the information content vector of the positive vector structure of the transformed argument ⁺ I _k f ( ⁺ [ m _j ]) f ₁ (DAC), when it is an argument in the positive region of the arithmetic space (43), in this situation, the system of the analog logical function f (&) - And the sign argument m _± is not active. As a result, the information content of the transformed argument ^± U _DAC f ( ^± [ m _j ]) of the operational amplifier f ₁ (OA) completely repeats the information content of the ionized field of the current argument ⁺ I _k f ( ⁺ [ m _j ]) f ₁ (DAC), but as soon as the argument of the sign m _{± is} activated, then on the output connection of the analog logic function f (&) - And the argument of the reference voltage ⁺ U _op is activated and goes to the inverting functional connection (-) of the operational amplifier f ₁ (ОУ), which is in the arithmetic space ( 43) leads to a discrete displacement of the vector structure ry ⁺ I _k f ( ⁺ [ m _j ]) into the domain of conditionally negative arguments, but does not lead to an additional “32%” decrease in the sampling step of the transformed voltage argument ^± U _DAC f ( ^± [ m _j ]), which is formed in the functional structure digital-to-analog conversion (54) and (55), in contrast to the functional structure (51).

Based on the results obtained, we can conclude that the “ Numbering System “ - / + ”[ m _j ] f (+/-) - Additional Code ” (38) as a non-minimized position-sign number system cannot realize the potential capabilities of the “ Minimized number system ^± [ m _j ] f (+/-) min ”(53) both during digital-to-analog conversion and when performing arithmetic operations of summation and multiplication. It should be especially noted that in the logical-dynamic process of converting the minimized arguments of the terms ⁺ [ n _j ] f (+/-) _min and ⁺ [ m _j ] f (+/-) _min in the adder ± f ( Σ ) _min , as well as in the logical-dynamic process of converting positional sign arguments of the terms “- / +” [ m _j ] f (+/-) - “ Additional code ”, it does not depend on their sign information content. For example, if we write down the logical-dynamic process of converting arguments in the adder ± f ( Σ ) _min for specific minimized structures of the positive term ⁺ [ n _j ] f (+/-) _min → “0100110010110011” f (2 ⁿ ) and the conditionally negative term ^- [ m _j ] f (+/-) _min → “0111000101110100” f (2ⁿ) in the position system f (2 ⁿ ) in the form of a logical expression with the economic concept of “Loan” (56)

 and with the use of arithmetic axioms (5) in the form of a graphic-analytical expression (57),

then after converting the second intermediate sum ^± [ S ² _j ] f (&) - And in accordance with the arithmetic axioms “+1” → “+2” “–1” and “-1” → “-2” “+ 1” the combined structure of the first and second intermediate sums is formed ^± [ S ¹ _j ] f ( } ) -OR & ^± [ S ² _j ] f (&) - AND, in which it is necessary to perform only local transformations of the arguments. And these local transformations of non-minimized arguments are also performed using the logical differentiation procedure ^- d / dn and the inverse arithmetic axioms “-2” “+ 1” → “-1” and “+ 1 / -1” → “± 0”. It should be noted that, given the multivariance of the argument structures of the terms ^± [ n _j ] f (+/-) _min and ^± [ m _j ] f (+/-) _min , the situation in the adder ± f ( Σ ) _min is possible when the combined structure of the first and second intermediate sums ^± [ S ¹ _j ] f ( } ) -OR & ^± [ S ² _j ] f (&) - And it will be formed completely equivalent to the structure of the arguments “- / +” [ m _j ] f (+ / -) - “ Additional code ”. And such a situation is always formed when the structure of minimized arguments of the terms ^± [ n _j ] f (+/-) _min and ^± [ m _j ] f (+/-) _min has either all positive active arguments, or when only the high-order argument is conditionally negative. For example, if we write down the logical-dynamic process of transforming arguments in the adder ± f ( Σ ) _min for specific minimized structures of the positive term ⁺ [ n _j ] f (+/-) _min → “+” “0100010100010010” f (2 ⁿ ) and conditionally the negative term ^- [ m _j ] f (+/-) _min → "-""111010110110110" f (2 ⁿ ) in the form of a graphic-analytical expression (58),

then the combined structure of the first and second subtotals^±[S ^one _j] f (})-OR&^±[S ² _j] f (&) - And with the exception of the active logical zero, “+ 1 / -1” → “± 0” is formed completely equivalent to the structure of the arguments “- / +” [m _j] f (+/-) - "Additional code". Therefore, it makes sense to form a functional structure of the logical-dynamic process of converting the arguments of the structure “- / +” [m _j] f (+/-) - "Additional code»Into a minimized position-sign structure^±[m _j] f (+/-)_min, for example, for its subsequent use in parallel-serial multipliers ± f_Σ(Σ) to significantly reduce its technological cycle Δt _Σ and increase the dynamic range of the information content of the arguments in "Minimized number system ^±[m _j] f (+/-) min. " And for this, we write the structure of the arguments “- / +” [m _j] f₂(+/-) - “Additional code"And its equivalent minimized structure^±[m _j] f_one(+/-) min in the form of a graphoanalytic expression (59)

where f ₁ ( 11 ) min and f ₂ ( 1 , 1 ) min are functional structures that activate the inactive logical zero argument “± 0” → “+ 1 / -1”, which are activated when there are two sequentially active arguments in the positive structure located in the "minimization zone" and between the "minimization zones", respectively;

and the structure “- / +” [ m _j ] f ₂ (+/-) - “ Additional code ” and the equivalent minimized structure ^± [ m _j ] f ₂ (+/-) min in the form of graph-analytical expression (60),

where f ₁ ( 00 ) min and f ₂ ( 0 , 0 ) min are functional structures that activate the minimized structures of the arguments “ 01 ” and “ 10 ” in the conditionally “k” “Minimization Zone”, which are activated if there is a “- / + "[ M _j ] f ₂ (+/-) -" Additional code "of two sequentially inactive arguments positionally located in the" Minimization Zone "and between the" Minimization Zones ", respectively;

in which the logical-dynamic process of transforming the active positive minimized argument f ₁ (0 1 , 0) min conditionally “j” the discharge and the active positive minimized argument f ₁ (0 1 , 0) min conditionally “j + 1” the discharge is significantly different. And this difference for each of the minimized arguments f ₁ (0 1 , 0) min is directly related to the activity or inactivity of the converted argument or the functional structure f ₁ ( 11 ) min or f ₁ ( 00 ) min, activated in the “Minimization Zone”, or functional structures f ₂ ( 1 , 1 ) min and f ₂ ( 0 , 0 ) min, activated between the "minimization zones". Moreover, from the analysis of graphoanalytic expressions (59) and (60) it follows that, on the one hand, the transformed arguments of the functional structures f ₁ ( 11 ) min, f ₂ ( 1 , 1 ) min and f ₁ ( 00 ) min, f ₂ ( 0 , 0 ) min implements different procedures. And if the transformed arguments of the functional structures f ₁ ( 11 ) min and f ₂ ( 1 , 1 ) min in expression (59) perform the function of pass-through activation of inactive arguments in the structure f ₁ (0, 1 , 0, 1 ) in accordance with the arithmetic axiom “± 0” → “+ 1 / -1”, then the transformed arguments of the functional structures f ₁ ( 00 ) min and f ₂ ( 0 , 0 ) min in the expression (60) perform the function of activating the minimized arguments f ₁ (0 1 , 0 ) min and f ₂ ( 1 0,0) min in the resulting structure of minimized arguments ^± [ m _j ] f (+/-) min, but have a common feature. And this feature consists essentially in the activation of the minimized argument in the resulting argument structure ^± [ m _j ] f (+/-) min. For example, if we introduce the activation vectors of functional structures f ₁ ( 11 ) min and f ₁ ( 00 ) min into a concrete implementation of the argument structure “- / +” [ m _j ] f (+/-) - “ Additional code ” and write it in the form of graphoanalytic expression (61),

then from his analysis it follows that the introduced vectors indicate the argument m _j conditionally “j” of the discharge in each “Minimization Zone”, which should be activated. And if the activation vector of the functional structure f ₁ ( 00 ) min activates an active positive argument in the “Minimization Zone”, then the activation vector of the functional structure f ₁ ( 00 ) min also indirectly activates the ^{± ±} m _j ] f (+ / -) min is an inactive conditionally negative argument of the same conditionally “j” of the discharge “Minimization Zones”.

A similar situation is formed when the activation vectors of functional structures f ₂ ( 1 , 1 ) min and f ₂ ( 0 , 0 ) min are introduced into a concrete implementation of the argument structure “- / +” [ m _j ] f (+/-) - “ Additional code ”in graphoanalytic expression (62),

in which the introduced activation vectors also indicate the argument m _{j + 1} conditionally “j + 1” of the discharge in each “Minimization Zone”, which should be activated. And in this argument structure “- / +” [ m _j ] f (+/-), the resulting argument of the functional structures f ₂ ( 1 , 1 ) min and f ₂ ( 0 , 0 ) min is activated, which is formed between the “minimization zones” and functionally refers only to the argument m _{j + 1 of the} conditionally “j + 1” discharge in each “Minimization Zone” both when activating positive minimized arguments and activating conditionally negative minimized arguments in the resulting structure ^± [ m _j ] f (+ / -) min. It should be noted that the implementation of the logical differentiation procedure ⁺ d / dn in expression (62), which directly relates to the formation of the local transfer argument + f ( ⁺ ← ⁺ ) _{d / dn} , is specific. Since the procedure of logical differentiation ⁺ d / dn of positive arguments with conditionally negative information content and with positive information content can be written in the form of graphoanalytic expressions (63) and (64),

where ^1,1 ( ^{± 1} m _{j + 1} ) _k is the resulting argument of the conditionally “j + 1” discharge of the functional structure f ₂ ( 1 , 1 ) min “k” of the “Minimization Zone” formed as a result of activation of an inactive logical zero “± 0 ”→“ + 1 / -1 ”in the“ Zone of minimization ”; ( ^- m _j ) _{k + 1} - argument of the sign digit in the structure of positive arguments “- / +” [ m _j ] f (+/-) - “ Additional code ”.

     Feature invocation argument^{d / dn}(m _{j + 1})_k conditionally “j + 1” discharge in “k” “minimization zone” is the activation of a conditionally negative argument^{d / dn}(-m _{j + 1})_k in expression (63), if active in the system of the logical function f_one(&) - And a conditionally negative signed argument (^- m _j)_{k + 1}“K + 1” “Minimization zones” and the resulting argument^1,1(^{± 1} m _{j + 1})_k activation of inactive logical zero arguments “± 0” → “+ 1 / -1” of the functional structure f₂(one,one) min “k” “Minimization zones”. It should be noted that the conditionally negative argument^{d / dn}(-m _{j + 1})_k  logical function f_one(&) - And in expression (63) it is activated only when the positive structure of the arguments has conditionally negative information content. But if the positive structure is “- / +” [m _j] f (+/-) - "Additional code»Corresponds to the positive information content, as in expression (64), then the logical differentiation procedure⁺d / dn in the “k” “minimization zone” is realized by the logical function f₂(&) - And with an input argument^1,1(^{± 1} m _{j + 1})_k activation of inactive logical zero arguments “± 0” → “+ 1 / -1” and an input signed argument (^- m _j)_{k + 1} with a changed analog signal level. And such an indirect logic of activating the positive argument of the logical differentiation procedure⁺d / dn directly refers only to the penultimate information category “k” of the “Minimization Zone” in the structure of the arguments “- / +” [m _j] f (+/-) - "Additional code". Since activating a positive argument^{d / dn}(+m _{j + 1})_k conditionally "j + 1" category and argument^{d / dn}(+m _j)_k conditionally “j” of discharge in “k” “Zone of minimization” of local transfer + f_one(⁺←⁺)_{d / dn}logical differentiation procedures⁺d / dn in the previous lower digits is realized in accordance with the analytical expression (65) and (66),

where ¹¹ ( ^{± 1} m _j ) _k is the resulting argument of conditionally “j” of the discharge of the functional structure f ₁ ( 11 ) min “k” of the “Minimization Zone” formed as a result of activation of the inactive logical zero “± 0” → “+ 1 / - 1 "in the" Zone of minimization "; ⁰⁰ ( m _j ) _k is the resulting argument “j” of the discharge of the functional structure f ₁ ( 00 ) min “k” “Minimization zones”; ^0,0 ( m _{j + 1} ) _{k + 1} - the resulting argument of the conditionally “j + 1” discharge of the functional structure f ₁ ( 1 , 1 ) min “k + 1” “Minimization zones”.

    From the analysis of graphoanalytic expressions (65) and (66) it follows that the logical functions f_one(&) - And and f₂(&) - And correctly activate as a positive argument^{d / dn}(+m _j)_k  conditionally "j" discharge, and a positive argument^{d / dn}(+m _{j + 1})_k conditionally “j + 1” discharge in “k” “Minimization Zone”, which are equivalent to the local transfer arguments + f_one(⁺←⁺)_{d / dn} and + f₂(⁺←⁺)_{d / dn}  logical differentiation procedures⁺d / dn. Since in the system of the logical function f_one(&) - And at the same time the argument is active^eleven(^{± 1} m _j)_kfunctional structure f_one(eleven) min through activation of inactive logical zero “± 0” → “+ 1 / -1” and argument⁰⁰(m _j)_k  functional structure f_one(00) min activation of the minimized argument structure f_one(0one, 0) min and f₂(one0,0) min. And in the system of the logical function f₂(&) - And at the same time the argument is active^1,1(^{± 1} m _{j + 1})_k functional structure f₂(one,one) min through activation of inactive logical zero “± 0” → “+ 1 / -1” and argument^0,0(m _{j + 1})_{k + 1}conditionally "j + 1" discharge of the functional structure f₂(0,0) min end-to-end activation “k + 1” of the “Zone of minimization”. And if we form graphoanalytic expressions with functional structures (67) and (68),

then they with the output logical function f ₁ (&) - And and f ₂ (&) - And correctly activate both the conditionally negative argument ^{d / dn} (- m _j ) _k conditionally “j” of the discharge and the conditionally negative argument ^{d / dn} (- m _{j + 1} ) _k conditionally “j + 1” discharges in “k” “Minimization Zone”, which are arguments of local transfer + f ₁ ( ⁺ ← ⁺ ) _{d / dn} and + f ₂ ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure ⁺ d / dn. And if you write graphoanalytic expressions (69) and (70),

then additionally introduced into the system of the logical function f ₁ ( } ) -OR and f ₂ ( } ) -OR functional structures with the output logical function f ₂ (&) - And conditionally “j” discharge and with the output logical function f ₄ (&) -And conditionally “j + 1” bits correctly activate both conditionally negative argument ^{± 1} (- m _j ) _k and minimized conditionally negative argument ^min (- m _j ) _k conditionally “j” bits in expression (69), and conditionally negative argument ^{± 1} (- m _{j + 1} ) _k-1 “k-1” “Minimization zones” and minimized conditionally negative argument ^min (- m _{j + 1} ) _k conditionally “j + 1” bits in the expression (70) “k” “Minimization zones”. Since in the system of the logical function f ₂ (&) - And the argument ( m _{j + 1} ) _{k is} conditionally “j + 1” of the discharge and the argument ( m _j ) _{k is} conditionally “j” of the discharge with a changed level of the analog signal, which are a condition activation of the resulting argument ¹¹ ( ^{± 1} m _j ) _k-1 “k-1” “Minimization zones” of the functional structure f ₁ ( 11 ) min activation of inactive arguments of logical zero “± 0” → “+ 1 / -1”. And in the logical function system f ₄ (&) - And at the same time, the argument with the changed level of the analog signal ( m _{j + 1} ) _k conditionally “j + 1” of the discharge “k” “Minimization zones” and the argument ( m _j ) _{k + 1} are active conditionally “j” of the discharge “k + 1” “Minimization zones”, which are also a condition for activating the resulting argument ^1.1 ( ^{± 1} m _{j + 1} ) _{k of the} functional structure f ₂ ( 1 _, 1 ) min activation of inactive arguments of logical zero “ ± 0 "→" + 1 / -1 ". It should be noted that functional structures with output logical functions f ₂ (&) - And and f ₄ (&) - And in analytical expressions (69) and (70) are essentially analytical expressions of the functional structure of activation f ₁ ( 11 ) min conditionally “j” of the discharge and the functional structure f ₂ ( 1 , 1 ) min conditionally “j + 1” of the discharge, which can be written in the form of graphic-analytical expressions (71) and (72),

which are functional structures of sequential activation of inactive logical zero arguments “± 0” → “+ 1 / -1” while minimizing the structure of arguments “- / +” [ m _j ] f (+/-) - “ Additional code ”. Since in the system of logical functions f ₂ (&) - And and f ₄ (&) - And both analytical expressions (69) and (70) include two arguments “Conditions of activation”, and in the system of analytical expressions (71) and (72 ) also included the same two arguments, “Conditions of activation”. And if we take into account that the main quality of any functional structure of argument conversion is its minimized technological cycle Δ t _Σ , and it is minimized in the functional parallel structure of activation f ₁ ( 11 ) min conditionally “j” of the discharge and the functional structure f ₂ ( 1 , 1 ) min conditionally "j + 1" category. Therefore, the analytical expressions (71) and (72) for the conditionally “j” discharge and “j + 1” discharge can be written in the form of analytical expressions (73) and (74),

in which the systems of logical functions f ₂ (&) - And and f ₃ (&) - And, essentially, include the converted arguments ¹¹ ( ^{± 1} m _j ) _k-1 and ^1,1 ( ^{± 1} m _{j + 1} ) _{k -1} “k-1” “Minimization zones”, which are the “Prerequisite” for activation and converted arguments ¹⁰ ( m _j ) _k and ^1,0 ( m _j ) _k “Activation condition” for activation of inactive logical zero arguments “± 0” → “+ 1 / -1” in “k” “minimization zone”. It should be noted that the converted arguments are ¹¹ ( ^{± 1} m _j ) _k-1 and ^1.1 ( ^{± 1} m _{j + 1} ) _k-1 "k-1""Minimizationzones" and the converted arguments ¹⁰ ( m _j ) _k and ^1,0 ( m _j ) _k “k” “Minimization zones” are formed by the logical functions f (&) - And, therefore, we write the analytical expressions (73) and (74) in the form of functional structures (75) and (76) .

And if we write the functional parallel activation structure f ₁ ( 11 ) min conditionally “j” of the discharge and f ₂ ( 1 , 1 ) min conditionally “j + 1” of the discharge for the next “k” “Minimization Zone”, we write in the form of analytical expressions (77 ) and (78),

then to activate the resulting minimized conditionally negative argument^min(-m _{j + 1})_k and^min(-m _{j + 1})_k in this “k” of the “Minimization Zone” it is enough to introduce a functional additional structure with an output logical function f_four(&) - And and f₈(&) - And into the system of the output logical function f_one(}) -OR and f₂(}) -OR with the corresponding argument ↓^eleven(^{± 1} m _j)_k-2 and ↓^1,1(^{± 1} m _{j + 1})_k-2 “Prerequisite” for activation of “k-2” “Minimization zones” and for only one converted argument ↓¹⁰(m _j)_k-1   and ↓^1,0(m _{j + 1})_k-1   “K-1” “Minimization zones” and one transformed argument ↓¹⁰(m _j)_k   and ↓^1,0(m _{j + 1})_k   “K” “Minimization zones” that correspond to the “Activation condition”. It should be noted that the logical functions f₃(&) - And and f₇(&) - And in the analytical expressions (77) and (79) activate the transformed argument^eleven(-m _j)_k  and^1,1(-m _{j + 1})_k  output logic f_one(}) -OR and f₂(}) -OR only when the argument is active^eleven(^{± 1} m _j)_k-1 and^1,1(^{± 1} m _{j + 1})_k-1 “Prerequisite” in "k-1" "minimization zone", and the transformed argument of logical functions by the function f_four(&) - And and f₈(&) - And activates them only when simultaneously active as a transformed argument ↓¹⁰(m _j)_k-1  and^1,0(m _{j + 1})_k-1“K-1” “minimization zone” and the converted argument¹⁰(m _j)_k  and^1,0(m _{j + 1})_k "K" "Zone of minimization." Since in the structure of arguments "- / +" [m _j] f (+/-) - "Additional code”Both the“ Activation Condition ”and the“ Necessary Condition ”are equally probable in any of the previous“ Minimization Zones ”. And if for the next “k” of the “Minimization Zone” a functional parallel activation structure f_one(eleven) min conditionally “j” of the discharge and f₂(one,one) min conditionally “j + 1” of the discharge is written in the form of analytical expressions (79) and (80),

then to activate the resulting minimized conditionally negative argument ^min (- m _{j + 1} ) _k and ^min (- m _{j + 1} ) _k in this “k” of the “Minimization Zone” it is also sufficient to introduce a functional additional structure with the output logical function f ₅ (& ) -And and f ₁₀ (&) - AND into the system of the output logical function f ₁ ( } ) -OR and f ₂ ( } ) -OR with only one “Additional argument” ↓ ¹⁰ ( m _j ) _k-2 and ↓ ^{1 , 0} ( m _{j + 1} ) _k-2 “k-2” “Minimization zones”. Moreover, in the system, the logical function f ₅ (&) - And and f ₁₀ (&) - And “Necessary condition" is the argument ↓ ¹¹ ( ^{± 1} m _j ) _k-3 and ↓ ^1,1 ( ^{± 1} m _{j + 1} ) _k-3 “k-3” “Minimization zones”, and it follows that for the 8-bit structure of the arguments “- / +” [ m _j ] f (+/-) - “ Additional code ” into the functional parallel structure of activating both f ₁ ( 11 ) min conditionally “j” discharges and f ₂ ( 1 , 1 ) min conditionally “j + 1” discharges, only three logical functions f (&) - And are introduced, by means of which a correct minimized argument will be generated ^min (- m _{j + 1} ) _k and ^min (- m _{j + 1} ) _k . And with the next additional “Minimization Zone” a functional additional structure with the output logical function f (&) - And with one additional argument should be introduced. And if the 16-bit structure of the arguments “- / +” [ m _j ] f (+/-) - “ Additional code ” is minimized, then into the functional parallel structure of activation both f ₁ ( 11 ) min is conditionally “j” of the discharge, and f ₂ ( 1 , 1 ) min conditionally “j + 1” bits in its system of output logic function f ₁ ( } ) -OR and f ₂ ( } ) -OR additionally it is necessary to include four logical functions f (&) - And and their the total number, taking into account the logical differentiation procedure ⁺ d / dn, will correspond to 6 logical functions f (&) - And. Moreover, the technological cycle Δ t _{Σ of} activating the resulting minimized conditionally negative arguments ^min (- m _{j + 1} ) _k and ^min (- m _{j + 1} ) _k in analytical expressions (79) and (80) will correspond to

four conditional logical functions f (&) - And. And if we take into account that the functional activation structures f ₁ ( 11 ) min conditionally “j” of the discharge and f ₂ ( 1 , 1 ) min conditionally “j + 1” of the discharge are essentially equivalent to the end-to-end transfer f (←) in the positional adder f ( Σ ), for example, in the 16-bit adder f ( Σ ) _{16, the} number of consecutive logic elements is

eighteen conditional logical functions f (&) - And, and in the end-to-end transfer f (←ready) _{32 of the} 32-bit adder f ( Σ ) _{32, the} number of consecutive logical elements is

thirty conditional logical functions f (&) - And. And if we take into account that the functional activation structures f ₁ ( 11 ) min conditionally “j” of the discharge and f ₂ ( 1 , 1 ) min conditionally “j + 1” of the discharge also enter the functional structure of the adder ± f ( Σ ) _min , which implements the procedure of summing the minimized arguments of the terms “+” [ n _i ] f (+/-) _min and “+” [ m _i ] f (+/-) _min , then the minimized technological cycle Δ t _{Σ of} these functional structures justifies the need to switch from positionally -sign structure of arguments “- / +” [ m _j ] f (+/-) - “ Additional code ” to its minimized structure ^± [ m _j ] f (+/-) min. It should be especially noted that the need to switch from the number system “- / +” [ m _j ] f (+/-) - “ Additional code ” to its minimized system ^± [ m _j ] f (+/-) min is not only is associated with a significant reduction in the technological cycle of the functional structures of adders ± f ( Σ ) _min and multipliers ± f _Σ ( Σ ) _min , but also with the ability to form a different quality. And this quality of the structure of arguments of the number system ^± [ m _j ] f (+/-) min during digital-to-analog conversion in the functional structure f ₁ (DAC) allows us to form the resulting output voltage argument ^± U _DAC f ( ^± [ m _j ] min) with the sampling step ^± U _j f (+/-) min, two times smaller than the similar voltage argument ^± U _j f (+/-), which forms the structure of arguments of the number system “- / +” [ m _j ] f (+ / -) - " Additional code ." And such a decrease in the sampling step ^± U _j f (+/-) min will significantly reduce the error in the control of technological processes, but its real decrease is even less by “+ 32%”, since “The minimized number system ^± [ m _j ] f (+ / -) min ”has increased information content by“ + 32% ”with the same bit structure of the arguments. And this increased information content by “+ 32%” is directly related to the fact that if in the “ Numbering System “ - / + ”[ m _j ] f (+/-) - Additional Code ”, the argument of the highest order m _± fulfills essentially , only a conditionally negative sign (-) function, then in the " Minimized number system ^± [ m _j ] f (+/-) min" argument ^± m _{jmax of the} highest order not only fulfills the sign function and is either a positive argument or a conditionally negative argument , but also allows you to increase the number of additional information combinations in argum structures ents as in its conditionally negative region (81),

and in its positive region (82).

And this increase in information content by “+ 32%” of the “ Minimized number system ^± [ m _j ] f (+/-) min” allows you to significantly expand the arithmetic capabilities of the functional structures of the adders ± f ( Σ ) _min and multipliers ± f _Σ ( Σ ) _min with this number system.

Returning to the synthesis of a mathematical model of a functional parallel activation structure f ₁ ( 11 ) min conditionally “j” discharge and f ₂ ( 1 , 1 ) min conditionally “j + 1” discharge taking into account the logic of formation of additional functional structures in expressions (79) and ( 80), we write it, for example, for “k” → “8” “Minimization zones”, which include the 16-bit structure of the arguments “- / +” [ m _j ] f (+/-) - “ Additional code ” in the form analytical expressions (83) and (84),

which also correctly activate the resulting minimized conditionally negative arguments ^min (- m _j ) _k and ^min (- m _{j + 1} ) _k in the “k” “Minimization Zone”, but in the graph-analytical expression the argument structure (85) has a peculiarity in the implementation of the logical differentiation ⁺ d / dn positive argument structure. And this feature is peculiar to the argument structures “- / +” [ m _j ] f (+/-) - “ Additional code ” with sequentially active arguments in which inactive logical zeros “± 0” → “+ 1 / -1” activate the functional structures f ₁ ( 11 ) min and f ₂ ( 1 , 1 ) min in any of their alternations. Since if we write the graphoanalytic expression (86)

then its minimized argument structure “- / +” [ m _j ] f (+/-) includes a sequence of active arguments in which inactive logical zero arguments “± 0” → “+ 1 / -1” activate a conditionally negative argument, but in this situation, by means of functional structures of the same name f _1.1 ( 11 ) min and f _1.2 ( 11 ) min. In this case, the procedure of logical differentiation ⁺ d / dn of the positive structure of the arguments both in expression (85) and in expression (85) and in expression (86) is performed one for the whole sequence of active arguments, only if such a sequence of active arguments in the structure “- / + "[ M _j ] f (+/-) -" Additional code "is not interrupted by at least two inactive arguments" 00 ". And if the positive sequence of active arguments in the structure “- / +” [ m _j ] f (+/-) - “ Additional code ” is interrupted by two inactive arguments “ 00 ”, for example, in the graph-analytical expression (87),

in which the “Necessary condition” of activation is positionally located in the “Zone of minimization” both in the functional structures of activation f _1.1 ( 11 ) min and f _1.2 ( 11 ) min, and in the functional structure f ₁ ( 00 ) min, activating the minimized arguments “0 1 , 0 ”, then the logical differentiation procedure is functionally divided into ⁺ d ₁ / dn and ⁺ d ₂ / dn. And only in such a situation can a conditionally negative argument be activated in the resulting structure ^- m _j local transfer -f ₁ ( ⁺ ↓ _- ) _{d / dn} and -f ₁ ( ⁺ ↓ _- ) _{d / dn} .

A similar result of activating the conditionally negative local transfer argument -f ₁ ( ⁺ ↓ _- ) _{d / dn} and -f ₁ ( ⁺ ↓ _- ) _{d / dn by} the logical differentiation procedure ⁺ d ₁ / dn and ⁺ d ₂ / dn can be obtained if write down graphoanalytic expression (88),

in which the “Necessary condition” of activation is positionally located between the “Minimization zones” both in the functional structures of activation f _2.1 ( 1 , 1 ) min and f _2.2 ( 1 , 1 ) min, and in the functional structure f ₂ ( 0 , 0 ) min activating the minimized arguments "0, 1 0".

Based on the results obtained, it follows that the conditionally negative argument ^{d / dn} (- m _j ) _{k is} conditionally “j” of the discharge and the conditionally negative argument ^{d / dn} (- m _{j + 1} ) _{k is} conditionally “j + 1” of the local transfer discharge -f ₁ ( ⁺ ↓ _- ) _{d / dn} and -f ₁ ( ⁺ ↓ _- ) _{d / dn} can be activated by means of the logical functions f ₁ (&) - And and f ₂ (&) - And functional structures (89) and (90 ),

in which there is a feature. And this feature is that when activating the local transfer -f₂(⁺↓_-)_{d / dn} in the system of the logical function f_one(&) - And expressions (89) must be active not only two consecutive arguments (m _{j + 1})_k  and (m _j)_k   conditionally “k” of the “Minimization Zone”, but the converted argument is also active⁰⁰(m _{j + 1})_k-1  functional structure f_one(00) min, in which the “Activation condition" ",00, "Belongs to" k-1 "" Zone of minimization ". The same logic applies when activating local transfer -f_one(⁺↓_-)_{d / dn} in the system of the logical function f₂(&) - And expressions (90), but in this situation in the system it should be active as two consecutive arguments (m _{j + 1})_k  and (m _j)_{k + 1}positionally located between the "minimization zones", and the converted argument is active^0,0(m _{j + 1})_k-1  functional structure f_one(00) min, in which also the “Activation condition” “0,0"Positionally located between the" minimization zones ". It should be noted that minimizing the structure of positive and conditionally negative arguments "- / +" [m _j] f (+/-) - "Additional code”Is no different except for its conditionally negative argument argument, which is positionally located in the“ k + 1 ”“ Minimization Zone ”in the graph-analytical expression (91), and it is functionally incomplete, since it does not include the“ j + 1 ”digit. But if the procedure for summing conditionally negative arguments is “- / +” [m _j] f (+/-) - "Additional code", eg, "-"[n _j] f (+/-)_min → "0010111011011010" f (2ⁿ) and "-" [m _j] f (+/-) → "0001000100100011" f (2ⁿ) write in the form of graphoanalytic expression (91),

in which the so-called “Overflow” is performed, then the argument structure of the resulting sum “- / +” [ S _j ] f (+/-) ₁ should include the conditional “j + 1” bit in the “k + 1” “Minimization zone”. Since the activation process of the local process is -f ₁ (← 11) and + f ₁ (← 11) in the graph-analytical expression (91) of both the conditionally negative argument in “k + 1” “Minimization Zone” and the positive argument in “k-5 »“ The minimization zone ”in the conditionally“ i ”bit of the positional adder f ( Σ ) is realized by means of a functional input structure (92),

in which the logical function f ₁ ( & ) - NOT in the system of the output logical function f ₂ (&) - AND excludes the activation of the resulting argument of the first intermediate sum S ¹ _j f ( } ) -OR logical function f ₁ ( } ) -OR and the transformed argument + S ³ _j in the analyzed category. Therefore, the sign digit in “k + 1” “Minimization zone” of the structure “- / +” [ m _j ] f (+/-) ₁ - “ Additional code ” in expression (91) has two positions “j + 1” _{k + 1} and “j” _{k + 1} in the “k + 1” “Minimization Zone”, in which, to eliminate “Overflows,” essentially the procedure of minimizing the structure of arguments is performed in accordance with the inverse arithmetic axiom “-2” “+ 1” → "-one". And this minimization procedure at the arithmetically correct level can be written in the form of a graphoanalytic expression (93),

from which it follows that the “Numbering system“ - / + ”[ m _j ] f (+/-) -“ An additional code ”taking into account“ k + 1 ”of the“ Minimization Zone ”, for example, to perform the summation procedure at a formalized level can be written as a graph-analytical expression (94).

Because, if the process of converting the arguments of the terms “- / +” [m _j] f (+/-) - "Additional code»With conditionally negative information content in the functional structure of the adder f (Σ), eg,^-[n _j] f (+/-) → "0010111011011010" f (2ⁿ) and^-[m _j] f (+/-) → "0011010110101011" f (2ⁿ) write in the form of graphoanalytic expression (95),

then the sign conditionally negative argument ^is ( m _{j + 1} ) _{k + 1} “k + 1” “Minimization zones”, the so-called “Overflow”, in a formalized record is positionally located in the conditionally “j + 1” category and cannot be at the arithmetic level to be minimized. Moreover, conditionally “j + 1” bit “k + 1” “Minimization zones” is not used as an information bit And if the same transformation is written using minimized conditionally negative arguments of the terms ^± [ n _i ] f (+/-) _min → "0010111011011010" f (2 ⁿ ) and ^± [ m _i ] f (+/-) _min → "0011010110101011" f (2 ⁿ ) in the form of a graphic-analytical expression (96),

then in this situation conditionally “j” bit “k + 1” “Minimization zones” is not used as an information bit, since its inactivity is a necessary “Minimization condition”. But if you write down the structure with the maximum possible information content in the “ Number System “ - / + ”[ m _j ] f (+/-) - Additional Code ” and the “ Minimized Number System ^± [ m _j ] f (+/-) min” for conditionally negative arguments in the form of expression (97)

  and for positive arguments in the form of expression (98)

then from their analysis it follows that the information range of the " Minimum number system ^± [ m _j ] f (+/-) min" is " 2.6 times" higher than the information range of the Number system "- / +" [ m _j ] f ( +/-) - Additional code ”, and this is only one of its advantages, which will allow you to further expand the arithmetic information capabilities of the functional structures of the adders ± f ( Σ ) _min and the multipliers ± f _Σ ( Σ ) _min with this number system.

Returning to the analysis of activating the local transfer f ( ⁺ ← ⁺ ) _{d / dn of} the logical differentiation procedure ⁺ d / dn of the positive argument structure “- / +” [ m _j ] f (+/-) - “ Additional code ”, we write the graphoanalytic expression ( 99)

in which a positive argument is activated^{d / dn}(+m _j)_k local transfer f_one(⁺←⁺)_{d / dn} in conditionally “k” “minimization zone” by means of the logical function f_one(&) - And, and as the “Activation conditions” are the converted argument ↓^eleven(m _{j + 1})_k-1 functional structure f_one(eleven) min "k-1" "Minimization zones" and the converted argument ↓⁰⁰(m _{j + 1})_k functional structure f_one(00) min "k" "Zone of minimization." A functional structure f_one(00) min in “k” “Minimization zone” is activated only when in the system of logical function f₂(&) - And at the same time its two input arguments are active ( m _{j + 1})_k and ( m _j)_k with a changed analog signal level.

    A similar structure of functions in the graph-analytical expression (100)

when activating a positive argument^{d / dn}(+m _{j + 1})_k local transfer f₂(⁺←⁺)_{d / dn} in the conditionally “k” “minimization zone”, but in this situation, on the one hand, its activity forms a logical function f_one(&) - And, in the system of which the argument must be active^1,1(m _{j + 1})_k-1functional structure of activation f₂(1,1) min of inactive logical zero arguments “± 0” → “+ 1 / -1” of conditional “k-1” “Minimization zones” and the converted argument^0,0(m _{j + 1})_k functional structure f₂(0,0) min activation of minimized arguments "0,one0,0 ". A converted argument^0,0(m _{j + 1})_k  directly forms the logical function f₂(&) - And, in the system of which should be active as an argument ( m _{j + 1})_k  "K" of the "minimization zone", and the argument ( m _j)_{k + 1}  “K + 1” “Minimization zones” with changed analog signal levels. In this case, it should be noted a feature when activating a sign dischargem _± arguments "- / +" [m _j] f (+/-) - "Additional code"Which is an argument^±(-m _j)_{k + 1} conditionally “j” of the discharge “k + 1” “Minimization zones” in the graphic-analytical expression (101)

and it is activated by the logical function f ₁ (&) - And with the active argument ⁰⁰ ( m _j ) _{k of the} functional structure f ₁ ( 00 ) min activating the minimized arguments “0, 1 0,0” and the active argument ( ^- m _j ) _{k + 1} sign digit. But if the converted argument of the functional structure f ₂ ( 1 , 1 ) min is active, as in expression (102)

then the sign digit m _± changes the positional position in the " Minimized number system ^± [ m _j ] f (+/-) min" and is activated as a conditionally negative argument (- m _{j + 1} ) _k in the "k""Minimizationzone" by of the logical function f ₁ (&) - And, and for this it is necessary that the converted argument ^1,1 ( m _{j + 1} ) _{k of the} functional structure f ₂ ( 1 , 1 ) min and the conditionally negative argument ^± (- m _j ) _{k + 1} sign digit of the argument structure “- / +” [ m _j ] f (+/-) - “ Additional code ”. Moreover, the positive local transfer argument f ( ⁺ ← ⁺ ) _{d / dn is} not activated in the “k + 1” “Minimization Zone”, since with the conditionally negative argument ^± (- m _j ) _{k + 1,} it forms an active logical zero “+1 / -1 "→" ± 0 ".

Further, to form the functional structure of activating local transport f ( ⁺ ↓ _- ) _{d / dn of} the logical differentiation procedure ⁺ d / dn, we write the graphoanalytic expression (103),

in which the conditionally negative argument ^{d / dn} (- m _j ) _k conditionally “k” “Minimization zones” in “k-3” “Minimization zone” is activated by the logical function f ₂ (&) - And provided that in its system at the same time, both the arguments ( m _j ) _k and ( m _{j + 1} ) _k conditionally “k” of the “Minimization Zone” are active, as well as the argument ↓ ⁰⁰ ( m _j ) _{k-1 of the} logical function f ₃ (&) - And, and she in this situation, it enters into the functional structure f ₁ ( 00 ) min through the activation of the minimized arguments “0,0 1 , 0” of the arguments “- / +” [ m _j ] f (+/-). At the same time, a feature of graphoanalytic expression (103) is the process of minimizing the structure of the arguments of the sign discharge m _± in the structure “- / +” [ m _j ] f (+/-) - “ Additional code ”, which is the argument ( m _j ) _{k + 1} conditionally “j” of the discharge “k + 1” “Minimization zones”. And this minimization of the structure of the arguments is performed in the system of the logical function f ₁ (&) - And using the inverse arithmetic axiom “-2” “+ 1” → “-1”, but under the condition that in “k-1” the “Zone of minimization "The resulting argument ↓ ^0,0 ( m _{j + 1} ) _k-1 through activation of the functional structure f ₁ ( 0 , 0 ) min of the minimized arguments" 0,0 1 , 0 "is active.

A similar situation is formed in the structure of the arguments “- / +” [ m _j ] f (+/-) - “ Additional code ” (104),

in which the functional structure f ₁ ( 0 , 0 ) min through activating the minimized arguments “0, 1 0,0” and its converted argument in all the least significant bits of the minimized structure ^± [ m _j ] f (+/-) min activates the positive argument, but in “k” “Minimization Zone” “An additional condition for the“ k ”zone” ^± ( m _j ) _{k + 1} excludes such activation of the resulting minimized argument ^min ( ⁺ m _{j + 1} ) _k as in functional structures (105) junior “Zones of minimization”, and in the functional structure (106) “k” of “Zones of minimization”. It should be noted that if the functional structure (106) with the output logical function f ₄ (&) - And in the "k""MinimizationZone" is one, then the functional structure (105) with the output logical function f ₁ (&) - And in this zone it is represented as a group of functional structures of the “Activation Conditions” with decreasing indices of the “Minimization Zones”, which we write in the form of analytical expressions (107) and (108).

And after combining through the output logical function f ₁ ( } ) -OR of analytical expressions (107) and (108) with analytical expression (106), the mathematical model “k” of “Minimization zones” (109) can be written

which is the functional structure f ₁ ( 0 , 0 ) min through activation of the minimized arguments “0, 1 0,0” of the structure “- / +” [ m _j ] f (+/-) - “ Additional code ” conditionally “j + 1 "Discharge for" k "" Zone of minimization. " It should be noted that the feature of the mathematical model “k” of the “Minimization Zone” (109) is the mandatory presence in the system of logical functions f ₁ (&) - And - f ₇ (&) - And the sign argument ^± ( m _j ) _{k + 1} and this is due to the fact that only in the “k” “Minimization Zone” while minimizing the structure of the arguments “- / +” [ m _j ] f (+/-) - “ Additional code ” does such a need arise. And in the remaining lower digits, the logical functions f ₁ (&) - And - f ₇ (&) - And of the functional structure f ₁ ( 0 , 0 ) min of the through activation of the minimized arguments "0,0 1 , 0" should not include the sign argument ^± ( m _j ) _{k + 1} ; therefore, it can be written in the form of the analytical expression (110).

     From the analysis of the analytical expression (110) it follows that the functional input structures with the output logical function f_one(&) - And - f₈(&) - And include the converted argument ↓^0,0(m _{j + 1})_k-1 - ↓^0,0(m _{j + 1})_k-8A “prerequisite” for end-to-end activation of minimized arguments “0,one0,0 "in the structure "- / +" [m _j] f (+/-) and the converted arguments ↓^0.1(m _{j + 1})_k- ↓^0.1(m _{j + 1})_k-7 "Conditions of activation", which with each subsequent minor rank only increase by one argument of this category. From the analysis of the structure of functions (110) it also follows that the technological cycle Δt parallel conversion of input arguments corresponds

Δt  → f ( & ) → f₉(&) → f₇(&) → f_one(}) → 4 ∙ f (&) - AND

four conditional logical functions f (&) - And for a 16-functional bit structure f ₁ ( 0 , 0 ) min through activation of the minimized arguments “0, 1 0,0” of the structure “- / +” [ m _j ] f (+ / -) - “ Additional code ” conditionally “j + 1” of category “k” “Minimization zones”.

If we take into account that the sequence of inactive arguments in the structure “- / +” [ m _j ] f (+/-) - “ Additional code ” is equally probable between the “Minimization Zones” and the “Minimization Zone”, we therefore form a mathematical model for functional structure f ₁ ( 00 ) min through activation of minimized arguments “0,0 1 , 0” for conditionally “j” of discharge “k” “Minimization zones”, and for this we write the graphoanalytic expression (111)

From a comparative analysis of the analytical expressions (104) and (111) it follows that the functional structures f ₁ ( 00 ) min of the through activation of the minimized arguments “0,0 1 , 0” for the conditionally “j” discharge “k” of the “Minimization Zone” (112 ) and (113) with the exception of the input and converted arguments, are completely analogous to the functional structures f ₁ ( 0 , 0 ) min of the pass-through activation of the minimized arguments “0, 1 0,0” with the exception of the signed argument ^± ( m _j ) _{k + 1} “k + 1 "" Zone of minimization ", which in this situation does not change its positional position in minimizing the actual argument structure ^± [ m _j ] f (+/-) min. ” And the functional structure (112) with the output logical function f ₁ (&) - And is also presented as a group of functional structures of the “Activation Conditions” with decreasing indices of the “Minimization Zones”, which we write in the form of analytical expressions (114) and (115).

And after combining through the output logical function f ₁ ( } ) -OR of analytical expressions (113) and (114) with analytical expression (112), a mathematical model of the functional structure f ₁ ( 00 ) min of through activation of minimized arguments “0,0 1 , 0 "" k "" Minimization zones "(115).

It should be noted that the system of logical functions f ₁ (&) - And - f ₈ (&) - And in expression (115) does not include the sign argument ^± ( m _j ) _{k + 1} "k + 1""Minimizationzones" , since if we write the graphoanalytic expression (116),

then only the minimized argument ^min (+ m _j ) _{k of the} functional structure f ₁ ( 00 ) min through the activation of the minimized arguments “0,0 1 , 0” “k” of the “Minimization Zone” in the analytical expression (117) with the output logical function f ₁ (&) - And activates the signed argument ( ^- m _j ) _{k + 1 of the} structure “- / +” [ m _j ] f (+/-) - “ Additional code ”. Since the functional structure f ₁ ( 0 , 0 ) min of the end-to-end activation of minimized arguments “0, 1 0,0” “k” “Minimization zones” (118)

and the functional structure of activation f ₁ ( 1 , 1 ) min of inactive arguments of logical zero “± 0” → “+ 1 / -1” in the conditionally “j + 1” category of expression (119),

and also the functional structure of activation f ₁ ( 11 ) min of inactive arguments of logical zero “± 0” → “+ 1 / -1” in the conditionally “j” category of expression (120)

when forming the minimized structure of the arguments ^± [ m _j ] f (+/-) min do not activate the signed argument ( ^- m _j ) _{k + 1} in the “k + 1” “Minimization Zone”, but indirectly perform this procedure in “k” “Zone of minimization”, therefore, no functional additional structures are required, and this is due to the fact that all transformations are performed using arithmetic axioms of the ternary number system f (+ 1,0, -1) (5). It should be noted that to activate the local transfer argument + f ₁ ( ⁺ ← ⁺ ) _{d / dn} and + f ₂ ( ⁺ ← ⁺ ) _{d / dn} in the “k + 1” “Minimization Zone” there is also no need for functional additional structures, since their converted arguments with a conditionally negative argument ( ^- m _j ) _{k + 1} form an active logical zero “+ 1 / -1” → “± 0”, which is excluded from the minimized argument structure ^± [ m _j ] f (+ / -) min. But for the rest of the “Minimization Zones”, if we write the graphoanalytic expression (121)

the argument ^{d / dn} ( ⁺ m _{j + 1} ) _k in the conditionally “j + 1” bit of local transfer + f ₁ ( ⁺ ← ⁺ ) _{d / dn} and the argument ^{d / dn} ( ⁺ m _j ) _k in the conditionally “j” bit local transfer + f ₂ ( ⁺ ← ⁺ ) _{d / dn is} activated by means of the functional structure (122) with the output logical function f ₁ (&) - And and the functional structure (123) with the output logical function f ₂ (&) - And, respectively. In this case, the feature in the activation of the positive arguments ^{d / dn} ( ⁺ m _{j + 1} ) _k and ^{d / dn} ( ⁺ m _j ) _k are the input arguments of the logical functions f ₁ (&) - And and f ₂ (&) - And, which are the resulting arguments ^min ( ^1,1 m _{j + 1} ) _k-1 and ^min ( ¹¹ m _j ) _k-1 functional structures of activation f ₁ ( 11 ) min and f ₂ ( 1 , 1 ) min inactive arguments of logical zero "± 0 ”→“ + 1 / -1 ”“ k-1 ”“ Minimization zones ”and with arguments ^min ( ^0,0 m _{j + 1} ) _k and ^min ( ⁰⁰ m _j ) _{k of} functional structures f ₁ ( 00 ) min and f ₂ (0, 0) min activation minimized argument "0,0 1, 0" and "0, 1 0,0» is «k» «minimize Zone", and only allows them Activity orrektno form positive arguments local translations + f ₁ ⁽⁺ ← ⁺⁾ _{d / dn} + f ₂ and _{^{(+ ← +) d / dn}} . It should be especially noted that if the arguments ^min ( ^1,1 m _{j + 1} ) _k-1 and ^min ( ¹¹ m _j ) _{k-1 of the} logical functions f ₁ (&) - And and f ₂ (&) - And should being the resulting arguments of the functional activation structures f ₁ ( 11 ) min and f ₂ ( 1 , 1 ) min, then the input arguments are ^0,0 ( m _{j + 1} ) _k and ⁰⁰ ( m _j ) _k in expressions (122) and (123 ) are an intermediate argument of the functional structure f ₁ ( 00 ) min and f ₂ ( 0 , 0 ) min. Therefore, graphoanalytic expression (121) can be written in the form of expression (124),

Where

- логическая функция f₁(&)-И условно «j+1» разряда «k» «Зоны минимизации»;

- logical function f ₁ (&) - And conditionally “j + 1” of the discharge “k” “Minimization zones”;

- логическая функция f₁(&)-И условно «j» разряда «k» «Зоны минимизации»;

- logical function f ₁ (&) - And conditionally “j” of the discharge “k” “Minimization zones”;

in which the input arguments ( m _{j + 1})_k and ( m _j)_{k + 1} logical function f_one(&) - And are equivalent to an intermediate argument^0,0(m _{j + 1})_k functional structure (110) of the logical function f₁₀(&) - And, and the input arguments ( m _j)_kand ( m _{j + 1})_k logical function f₂(&) - And are equivalent to an intermediate argument⁰⁰(m _j)_k  functional structure (115) of the logical function f₁₀(&)-AND. But if we consider that the technological cycle Δt  functional structures (125) and (126) depends on the technological cycle of argument formation^min(^1,1 m _{j + 1})_kand^min(^eleven m _j)_k-1, then the minimized functional structure of the formation of the resulting arguments^{d / dn}(⁺ m _{j + 1})_kand^{d / dn}(⁺ m _j)_k local transfer + f_one(⁺←⁺)_{d / dn}  and + f₂(⁺←⁺)_{d / dn} logical differentiation procedures⁺d_one/ dn and⁺d₂/ dn are analytic expressions (122) and (123), since in the system of logical functions f_one(&) - And and f₂(&) - And the number of input arguments is minimized. And if we consider that in the mathematical model of functional structures f_one(00) min (115) and f₂(0,0) min (110) activation of minimized arguments "0,0one0 "and" 0,one0,0 ”there is no functional structure of the“ Necessary condition ”“ k ”of the“ Minimization zone ”, then we write the analytical expressions (122) and (123) taking into account this functional structure in the form of the structure of functions (127) and (128) in the graph-analytical expression ( 129).

A feature of the analytical expressions (127) and (128) is that the argument ^0,0 ( m _{j + 1} ) _k ↑ and ^0,0 ( m _j ) _k ↑ of the functional structure with the output logical function f ₂ (&) - And not only activates through the logical function f ₁ (&) - And in the “k” “Minimization Zone” the positive argument ^{d / dn} ( ⁺ m _j ) _k and ^{d / dn} ( ⁺ m _{j + 1} ) _k the logical differentiation procedure ⁺ d ₁ / dn and ⁺ d ₂ / dn, but it is also an input argument in the functional structures (110) and (115), which in this situation should be written in the form of analytical expressions (129) and (130).

And only in analytical expressions (129) and (130), the “Necessary condition” in the mathematical model is conditionally “j + 1” and “j” of the “k” bits of the “Minimization Zone” is presented in full, because if we write the graphoanalytic expression (131) ,

Where

- логическая функция f₁(})-ИЛИ и f₂(})-ИЛИ условно «j+1» разряда;

- logical function f ₁ ( } ) -OR and f ₂ ( } ) -OR conditionally "j + 1"category;

- логическая функция f₁(})-ИЛИ и f₂(})-ИЛИ условно «j» разряда;

- logical function f ₁ ( } ) -OR and f ₂ ( } ) -OR conditionally "j"discharge;

then the transformed argument ^{d / dn} ( ⁺ m _j can be introduced into the system of the logical function f ₁ ( } ) -OR conditionally “j + 1” bits (132) and conditionally “j” bits (133) “k” “Minimization zones” ₊₁ ) _k and ^{d / dn} ( ⁺ m _j ) _{k of} the logical differentiation procedure ⁺ d ₂ / dn and ⁺ d ₁ / dn of the analytical expressions (127) and (128), which conditionally in the adjusted expressions (132) and (133) “J + 1” and “j” digits form the logical function f ₁₁ (&) - AND. It should be noted that they activate the logical function f ₁₁ (&) - And in the conditionally “j + 1” category of expression (132) the converted argument is ^0.0 ( m _{j + 1} ) _k ↑ “Necessary condition” of the logical function f ₁₀ ( &) - AND and the transformed argument ( ^1,1 m _{j + 1} ) _{k of the} logical function f ₂ ( } ) -OR, in the system of which at least one of the intermediate arguments ₁ ( ^1,1 m _{j + 1} ) _k must be active - ₇ ( ^1,1 m _{j + 1} ) _k functional structure of activation f ₂ ( 1 , 1 ) min inactive arguments of logical zero “± 0” → “+ 1 / -1” “k” “Minimization zones” of expression (84) . And if we write expression (84) and expression (83) for the structure of arguments (134) and (135) in the form of functional structures (136) and (137) conditionally “j + 1” and “j” bits,

then from their analysis it follows that they are completely equivalent to the functional structures (132) and (133) of the conditionally “j + 1” and “j” discharges, with the exception of input arguments. The feature of functional structures (136) and (137) is a functional structure with an output logical function f ₁ (&) - And, since the index of its input arguments is reduced by one “Minimization zone” and corresponds to “k-7” “Minimization zone” . Since in this situation active positive arguments are analyzed, they can be active either in “k-7” “Minimization Zone” or between “k-6” and “k-7” “Minimization Zones”. It should be noted that in “k-7” “Minimization Zone” functional structures (136) and (137) with the output logical function f ₉ (&) - And only conditionally negative argument of the logical differentiation procedure ⁺ d ₂ / dn can be formed and ⁺ d ₁ / dn, which corresponds to the local carry -f ₁ ( ⁺ ↓ _- ) _{d / dn} and -f ₁ ( ⁺ ↓ _- ) _{d / dn} . Since, if we return to the analysis of analytical expressions (89) and (90) and write them in the form of a graphoanalytic expression (138),

then the conditionally negative argument ^{d / dn} (- m _j ) _k and ^{d / dn} (- m _{j + 1} ) _k can be activated by means of functional structures (139) and (140) with the output logical function f ₁ (&) - And, in which the input arguments ( m _{j + 1} ) _k , ( m _j ) _k and ( m _{j + 1} ) _k , ( m _j ) _{k + 1 are} equivalent to the converted argument ¹¹ ( m _{j + 1} ) _k ↑ and ^1,1 ( m _{j + 1} ) _k ↑ “Conditions of activation” of the functional structure with the output logical function f ₉ (&) - And expressions (136) and (137). Therefore, the adjusted functional structures (136) and (137) are conditionally “j + 1” and “j” of the discharge, taking into account the logical differentiation procedure ⁺ d ₁ / dn and ⁺ d ₂ / dn (139) and (140), can be written as analytic expressions (141) and (142).

From the analysis of the process of activating conditionally negative arguments for the formation of the “ Minimized argument structure ^± [ m _j ] f (+/-) min” in expression (143) and (144) of the procedure for transforming the argument structure “- / +” [ m _j ] f (+ / -) - “ Additional code ” implies that functional structures conditionally “j + 1” in expression (141) and conditionally “j” bits in expression (142) correctly activate in conditionally “k” ₁ and “k” ₂ “Zones minimization ”minimized conditionally negative argument ^min (- m _{j + 1} ) _k and ^min (- m _j ) _{k of} the logical differentiation procedure ⁺ d ₁ / dn and ⁺ d ₂ / dn. Since in the logical function system f ₁₀ (&) - AND of expressions (141) and (142), the converted argument of the logical function f ₂ ( } ) -OR is active at the same time, which in this situation is the argument of the “Necessary condition”, and the converted argument ^{1, 1} ( m _{j + 1} ) _k ↑ and ¹¹ ( m _{j + 1} ) _k ↑ of the logical function f ₈ (&) - And in this situation it is the argument “Activation conditions”. It should be noted that analytical expressions (141) and (142) as functional structures that activate the minimized conditionally negative argument ^min (- m _{j + 1} ) _k and ^min (- m _j ) _k are not functionally complete analytical expressions of the mathematical model the logical-dynamic process of converting the argument structure "- / +" [ m _j ] f (+/-) - " Additional code " to " Minimized argument structure ^± [ m _j ] f (+/-) min". Since the sign argument m _± is not only an informational conditionally negative argument (- m _j ) _{k + 1} “j” of the discharge in the “k + 1” “minimization zone”, for example, in the analytical expression (145),

but also by the information argument (- m _{j + 1} ) _{k of the} “j + 1” category in the “k” of the “Minimization Zone”, for example, in the graph-analytical expression (146).

Therefore, it is necessary to introduce an argument to prohibit (- m _j ) _{k + 1} "j" the discharge of the sign "k + 1""Minimizationzones" to activate the minimized positive argument ^min (+ m _{j + 1} ) _k "j + 1" the discharge into the functional structure f ₁ ( 0 , 0 ) min (132) activation of minimized arguments “0, 1 0,0”, but only in its analytical expression “k” “Minimization zones”, which, taking into account the fact that in the structure of arguments “- / + _{»[m j] f (+/-} ) -« additional code "in the actual implementation of this sign bit has no positional status, write it by introducing additional znakovo index of (±) in the argument _± (m _{j) k + 1 9} logical function f (k) - and conditionally «j + 1" analytical expression discharge (147).

As a result, all logical functions f ₁ (&) - AND - f ₁₀ (&) - AND systems of the output logical function f ₁ ( } ) -OR in the functional structure “k” of “Minimization zones” are correctly inactive, including the logical function f ₁₁ (&) - And, which forms a positive argument ^{d / dn} ( ⁺ m _{j + 1} ) _{k of} the logical differentiation procedure ⁺ d / dn. It should be noted that both the analytical expression (147) and the analytical expression (148) clarified the positional position of the logical function f ₂ ( } ) -OR, which forms the transformed argument ( ^0,0 m _{j + 1} ) _k ↑ and ( ⁰⁰ m _j ) _k ↑ in accordance with the input argument system. And such a change in positional position, on the one hand, is due to the fact that the logical function f ₂ ( } ) -OR in analytical expressions (147) and (148), as well as in analytical expressions (141) and (142), which we write in the form of adjusted analytical expressions (149) and (150)

functionally belongs to them. On the other hand, by means of the transformed argument ↓ ( ⁰⁰ m _j ) _{k of the} logical function f ₂ ( } ) -OR expressions (148) activate a conditionally negative argument in the analytical expression (151),

which, in essence, is an addition to the mathematical model of conditionally “j” category of expression (150).

Structural-functional synthesis of mathematical models of the logical-dynamic process of converting the argument structure “- / +” [ m _j ] f (+/-) - “ Additional code ” into a minimized structure ^± [ m _j ] f (+/-) min with alternation active and inactive arguments in its sequence with other logical functions .

Since mathematical models of functional parallel structures f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min pass-through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and "J" bits "k""Zoneminimization" (147) and (148),

as well as a mathematical model of activating the sign discharge of the argument structure “- / +” [ m _j ] f (+/-) - “ Additional code ” (151)

and mathematical models of functional parallel structures of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” bits "k""Zoneminimization" (149) and (150),

were formed correctly, therefore they are the first version of the functional structure of the converter

we write their logical-dynamic process of converting arguments using logical functions of another basis. And if we take into account that the analytical expressions (147), (148), (149) and (150) are completely equivalent in the structure of logical functions, therefore, the structural-functional transformation of logical functions is possible, for example, only in the analytical expression (147) and form the functional Converter structures “- / +” [ m _j ] f (+/-) ”→ ^± [ m _j ] f (+/-) min of the second option.

Option 2 We replace the functional input links in the expression (147) in the logical function f ₁ ( } ) -OR and f ₂ ( } ) -OR with the logical functions of double changing the level of the analog signal f ₁ ( & ₁ = & ₂ ) and write the vector graphic-analytical expression (151).

The indicated transfers of logical functions f ₂ ( & ) -НЕ performed through expression (151) through the logical function system f ₁ ( } ) -OR and f ₂ ( } ) -OR result in changing their logical properties to the properties of the logical function f (&) -I, and after combining them with the transferred logical function f ₂ ( & ) -НЕ they change their logical properties to the properties in the transformed expression (152) of the logical functions f ₁₀ ( & ) -I-NOT and f ₁₁ ( & ) -И -NOT.

Then, performing the transfer in the expression (151) of the logical functions f ₁ ( & ) -НЕ through the converted arguments of the logical functions f ₁ (&) - And - f ₈ (&) - And and f ₁₁ (&) - And, they change the level analog signal, and after combining the logical functions f ₁ ( & ) -НЕ with the logical functions f ₁ (&) - And - f ₈ (&) - And and f ₁₁ (&) - And they change their logical properties to the properties of logical functions f ₁ ( & ) -I-NOT - f ₉ ( & ) -I-NOT in expression (152).

 After the transformation, analytical expressions (148), (149) and (150) have a similar functional structure, which we write in the form of functional structures (153), (154) and (155).

    Since the analytical expressions (152) - (155) are synthesized by the formalized method, then to check the correctness of their logical-dynamic process of converting arguments, we will form vector structures for activating the logical functions (156) and (157).

From the analysis of the graph-analytical expression (156) it follows that the minimized positive arguments ^min (+ m _{j + 1} ) _k and ^min (+ m _j ) _{k are} activated correctly, since in the system of the logical function f ₆ ( & ) -I-NOT, which in “K” ₃ “Minimization zone” is the last one and both the converted argument ↓ ^0,0 ( m _{j + 1} ) _k-3 and ↓ ⁰⁰ ( m _j ) _k-3 “Activation conditions” and all arguments ⁰ are active in it ^{, 1} ( m _{j + 1} ) _k , ^0,1 ( m _{j + 1} ) _k-1 , ^0,1 ( m _{j + 1} ) _k-2 and ⁰¹ ( m _j ) _k , ⁰¹ ( m _j ) _{k- 1} , ⁰¹ ( m _j ) _{k-2 of the} “Prerequisite” of not activating (logical function f ₆ ( & ) -AND-NOT) the transformed argument ₆ ( ⁺ m _{j + 1} ) _k and ₆ ( ⁺ m _j ) _{k of} this fun ktsii. And it is precisely this inactivity of argument ₆ ( ⁺ m _{j + 1} ) _k and ₆ ( ⁺ m _j ) _{k of the} logical function f ₆ ( & ) -I-NOT activates the output logical function f ₁₀ ( & ) -I-NOT and its minimized positive argument ^min (+ m _{j + 1} ) _k and ^min (+ m _j ) _k .

From the analysis of graphoanalytic expression (157) it follows that minimized conditionally negative arguments ^min (- m _{j + 1} ) _k and ^min (- m _j ) _{k are} activated correctly, since in the system of the logical function f ₆ ( & ) -I-NOT, which in “k” _{4, the} “minimization zone” is the last one and the converted argument ↓ ^1,1 ( m _{j + 1} ) _k-3 and ↓ ¹¹ ( m _j ) _k-3 “activation conditions” and all arguments are active in it ^1,0 ( m _{j + 1} ) _k , ^1,0 ( m _{j + 1} ) _k-1 , ^1,0 ( m _{j + 1} ) _k-2 and ¹⁰ ( m _j ) _k , ⁰¹ ( m _j ) _{k -1} , ¹⁰ ( m _j ) _{k-2 of the} “Necessary condition” of non-activation (logical function (f ₆ ( & ) -AND) of the transformed argument ₆ ( ^- m _{j + 1} ) _k and ₆ ( ^- m _j ) _k This function. And it is precisely this inactivity of argument ₆ ( ^- m _{j + 1} ) _k and ₆ ( ^- m _j ) _{k of the} logical function f ₆ ( & ) -I-NOT activates the output logic function f ₉ ( & ) -I-NOT and its minimized positive argument ^min (- m _{j + 1} ) _k and ^min (- m _j ) _k .

Option 3 Since the logical functions f ₁ ( & = & ) of double changing the level of the analogue signal of the arguments are equivalent to the functional connection f ₁ (=), therefore, we will correct their replacement in expression (151) and form the vector structure of the transfer of logical functions f ₁ ( & ) -НЕ and f ₁ ( & ) -НЕ, writing it in the form of a graphoanalytic expression (158).

When performing the transfer of the logical function f ₁ ( & ) -НЕ through the system of the logical function f ₁ (&) - AND - f ₉ (&) - And it changes its logical properties to the properties of the logical function f ( } ) -OR, and combining it with the transferred logical function f ₁ ( & ) -НЕ leads to a change in its logical properties to the properties of the logical function f ₁ ( } & ) -OR-NOT - f ₉ ( } & ) -OR-NOT in the adjusted expression (159). And further transfer in the expression (158) of the logical function f ₁ ( & ) -НЕ through the input arguments of the logical functions f ₁ (&) - And - f ₉ (&) - And leads to a change in their levels of the analog signal in the corrected expression (159) . Moreover, in the expression (158), the logical function f ₁ ( & ) -НЕ is combined with the logical function f ₁₀ (&) - And and f ₁₁ (&) - And, which leads to a change in its logical properties to the properties of the logical function f ₁ ( & ) -I-NOT and f ₂ ( & ) -I-NOT, and perform the union of the logical function f ₂ ( } ) -OR or the logical function f ₃ ( & ) -НЕ to change its logical properties to the properties of the logical function f ₁₀ ( } & ) -OR-NOT and the level of its converted argument ( ^0,0 m _{j + 1} ) _k ↑. Since after transferring the logical function f ₉ (&) - AND the logical function f ₁ ( & ) -НЕ in the system through the input argument ↓ ( ^1,1 m _{j + 1} ) _k , its analog signal level changes, and this argument forms a similar structure in analytical expressions (149) and (150), which in turn include the transformed argument ( ^0,0 m _{j + 1} ) _k ↑ and ( ⁰⁰ m _j ) _k ↑. After the transformation, the analytical expression (148) also has a functional similar structure, which forms the minimized positive argument of the conditionally “j” discharge in the “k” “Minimization Zone”, which can be written as the functional structure (159) and (160).

  After the transformation, analytical expressions (149) and (150) have a similar functional structure, which we write in the form of functional structures (161) and (162).

From the analysis of analytical expressions (159) - (162) it follows that the technological cycle Δ t of the parallel conversion of input arguments corresponds to

Δt  → f ( & ) → f_one(&) → f_one(} & ) → f₁₀(} & ) → f₈(} & ) → f_one(}) → 6 ∙ f (&) - AND

six conditional logical functions f (&) - And for the 16-bit structure of the converter “- / +” [ m _j ] f (+/-) ”→ ^± [ m _j ] f (+/-) min.

    Since the analytical expressions (159) - (162) are synthesized by the formalized method, then to check the correctness of their logical-dynamic process of converting arguments, we form vector structures for activating the logical functions (163) and (164).

From the analysis of the graph-analytical expression (163) it follows that the minimized positive arguments ^min (+ m _{j + 1} ) _k and ^min (+ m _j ) _{k are} activated correctly, since in the system of the logical function f ₆ ( } & ) -OR-NOT, which in “k” _{3 the} “Minimization zone” is the last one and in it are not active as the transformed argument ↓ ^0,0 ( m _{j + 1} ) _k-3 and ↓ ⁰⁰ ( m _j ) _k-3 with a changed analog signal level “Activation conditions ", And all other arguments ^0.1 ( m _{j + 1} ) _k , ^0.1 ( m _{j + 1} ) _k-1 , ^0.1 ( m _{j + 1} ) _k-2 and ⁰¹ ( m _j ) _k , ⁰¹ ( m _j ) _k-1 , ⁰¹ ( m _j ) _k-2 also with a changed level of the analog signal "activation" (logical function f ₆ ( } & ) -ORNOR) of the converted argument ₆ ( ⁺ m _{j + 1} ) _k and ₆ ( ⁺ m _j ) _k without changing the level of the analog signal of this function. And it is precisely this activity of the argument ₆ ( ⁺ m _{j + 1} ) _k and ₆ ( ⁺ m _j ) _{k of the} logical function f ₆ ( } & ) -OR NOT activates the output logic function f ₁ ( } ) -OR and its minimized positive argument ^min (+ m _{j + 1} ) _k and ^min (+ m _j ) _k .

From the analysis of graphoanalytic expression (164) it follows that minimized conditionally negative arguments ^min (- m _{j + 1} ) _k and ^min (- m _j ) _{k are} activated correctly, since in the logical function system f ₅ ( } & ) -OR-NOT, which is the last in “k” ₄ “Minimization Zone” and is not active in it, as the converted argument ↓ ^1,1 ( m _{j + 1} ) _k-3 and ↓ ¹¹ ( m _j ) _k-3 with a changed analog signal level “ Conditions of activation ”, as well as all other arguments ^1,0 ( m _{j + 1} ) _k , ^1,0 ( m _{j + 1} ) _k-1 , ^1,0 ( m _{j + 1} ) _k-2 and ¹⁰ ( m _j ) _k, ⁰¹ (m _{j) k-1,} ¹⁰ (m _{j) k-2} with an altered level of "Requisite analog signal words "no activation (logical function (f ₆ (} &) -or-HE) transformed argument ₆ ^(- m _{j + 1) k,} and ₆ ^(- m _{j) k} without changing the level of the analog signal of this function and it is this inactivity. argument ₆ ( ^- m _{j + 1} ) _k and ₆ ( ^- m _j ) _{k of the} logical function f ₆ ( } & ) -OR NOR activates the output logic function f ₁ ( } ) -OR and its minimized positive argument ^min (- m _{j + 1} ) _k and ^min (- m _j ) _k .

    Using the method and functional structure of the argument converter of the position-sign structure of the arguments “- / +" [m _j] f (+/-) - "Additional code" at "Minimized structure ”arguments ^±[m _j] f (+/-) min ”will significantly expand the dynamic range of the conversion of arguments and increase the speed when performing arithmetic transformations in the position-sign adder ± f (Σ)_minand multiplier ± f_Σ(Σ)_min.

Claims (7)

1. The method of converting the structure of the arguments of the analog logical voltages "- / +" [m _j] f (+/-) - "Additional code»Into the position-sign structure of minimized arguments of analog logical voltages^±[m _j] f (+/-)_minusing arithmetic axioms of the ternary number system f (+ 1,0, -1) (Variant of Russian logic), characterized in that from the structure of the positive arguments of the analog logical voltages "- / +" [m _j] f (+/-) - "Additional code"Form sequential" minimization zones ", one of them includes a conditionally negative argument of the sign dischargem _± → (^- m _j)_{k + 1,}  and it is “k + 1” “Minimization Zone”, and the positive subsequent arguments conditionally “j + 1” and “j” of the least significant bits include sequentially in “k” - “k-7” the “Minimization Zone”, in which the logical analysis of the activity of positive arguments by means of functional parallel structures f_one(00) min and f₂(0,0) min pass-through activation of minimized arguments "0,0one0 "and" 0,one0,0 ”in conditionally“ j + 1 ”and“ j ”digits, and through functional parallel structures of through activation f_one(eleven) min and f₂(one,one) min activate inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” digits, and if the functional parallel structure f_one(00) min pass-through activation of minimized arguments "0,0one, 0 ”in conditionally“ j ”“ k ”“ Minimization zone ”are activated simultaneously by means of inactive arguments conditionally“ j + 1 ”and“ j ”of the discharge, as, for example, in“ k ”_one"Zone of minimization", and through its transformed argument (⁰⁰ m _j)_k activate as a positive argument the conditionally “j” discharge in the minimized argument structure^±[m _j] f (+/-) min, and activates through a functional structure with the output logical function f_one(&) - And conditionally negative signed argument^±(^- m _j)_{k + 1} in a minimized argument structure^±[m _j] f (+/-) min, while the process of activating minimized arguments is performed in accordance with the logical-dynamic process of the form

Where

is a logical function f_one(&)-AND
and the functional parallel structure f₂(0,0) min through activation of minimized arguments “0,one0,0 ”in conditionally“ j + 1 ”“ k ”“ Minimization zones ”are activated simultaneously by means of inactive arguments conditionally“ j + 1 ”and“ j ”of the discharge between“ Minimization zones ”and through its converted argument (^0,0 m _j)_kactivate a positive argument conditionally "j + 1" discharge of the minimized structure of arguments^±[m _j] f (+/-) min with the exception of "k" "Minimization zones" if the sign argument is activem _± → (^- m _j)_{k + 1}, while the process of activating the resulting minimized arguments is performed in accordance with the logical-dynamic process of the form

then the functional parallel structure of the end-to-end activation f_one(eleven) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in the conditionally “j” bit are activated by means of two arguments conditionally “j + 1” and “j” of the bit, which are active in the previous “Minimization zone” under the condition that the argument in the conditionally “j + 1” category is also active, and through its resulting argument (^eleven m _j)_k activate a conditionally negative argument in the conditionally “j” category “Zone minimization”, while performing logical differentiation⁺d / dn positive arguments in the adjusted structure^±[m _j] f (+/-)_one  and form a conditionally negative argument in the minimized structure^±[m _j] f (+/-) min corresponding to the local conditionally negative hyphenation -f_one(⁺↓_-)_{d / dn} provided that in the previous “Minimization Zone” the argument is active (^0,0 m _j)_k functional structure f_one(00) min, and perform the formation of a positive local transfer argument + f_one(⁺←⁺)_{d / dn} in the next “minimization zone”, if the argument of the sign discharge is not active in itm _± → (^- m _j)_{k + 1}, while the process of activating the resulting minimized arguments is performed in accordance with the logical-dynamic process of the form

and the functional parallel structure of end-to-end activation f_one(one,one) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in the conditionally “j + 1” category are activated by two arguments, conditionally “j + 1” and “j”, which are active between the “minimization zones” at provided that the argument in the conditionally “j” category of the “Minimization Zone” is also active by means of its resulting argument (^1,1 m _j)_k activate conditionally negative argument conditionally "j + 1" discharge in the "minimization zone", while performing logical differentiation⁺d / dn positive arguments in the adjusted structure^±[m _j] f (+/-)_one with the formation of a conditionally negative argument in a minimized argument structure^±[m _j] f (+/-) min corresponding to the local conditionally negative hyphenation -f₂(⁺↓_-)_{d / dn}provided that in the previous “Minimization Zone” the argument is active (^0,0 m _j)_k functional structure f_one(0,0) min, and with the formation of a positive local transfer argument + f₂(⁺←⁺)_{d / dn} in the next “minimization zone”, if the argument of the sign discharge is not active in itm _± → (^- m _j)_{k + 1}, while the process of activating the resulting minimized arguments is performed in accordance with the logical-dynamic process of the form

2. Functional parallel structure f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and “ j "bits" k "" Minimization zones ", characterized in that the structures are conditionally" j + 1 "and" j "bits forming positive minimized arguments ^min (+ m _j ) _{k + 1} and ^min (+ m _j ) _k , are executed according to a functional equivalent structure and each of them includes logical functions f ₁ (&) - And, f ₂ (&) - And, f ₃ (&) - And, f ₄ (&) - And, f ₅ (&) - And, f ₆ (&) - And, f ₇ (&) - And, f ₈ (&) - And, f ₉ (&) - And, f ₁₀ (&) - And, f ₂₁₁ (&) - And, f ₁ (}) f ₂ -or and (}) -or, wherein the functional relationship is formed in accordance with the mathematical models of the form

Where

and

- logical function f ₁ ( } ) -OR and f ₁ (&) - And conditionally "j + 1"category;

and

- logical function f ₁ ( } ) -OR and f ₁ (&) - And conditionally "j" discharge. 3. Functional parallel structure of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” bits “K” “Minimization zones”, characterized in that the structures of conditionally “j + 1” and “j” bits are made according to a functional equivalent structure, forming conditionally negative minimized arguments ^min (- m _j ) _{k + 1} and ^min (- m _j ) _k and each of them includes logical functions f ₁ (&) - And, f ₂ (&) - And, f ₃ (&) - And, f ₄ (&) - And, f ₅ (&) - And, f ₆ (&) - And, f ₇ (&) - And, f ₈ (&) - And, f ₉ (&) - And, f ₁₀ (&) - And, f ₁ ( } ) -OR and f ₂ ( }) -or, wherein the functional linkages in fully in accordance with the mathematical models of the form

4. Functional parallel structure f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and “ j "bits" k "" Minimization zones ", characterized in that the structure is conditionally" j + 1 "and" j "bits forming positive minimized arguments ^min (+ m _j ) _{k + 1} and ^min (+ m _j ) _k , are executed according to a functional equivalent structure and each of them includes the logical functions f ₁ (&) - AND, f ₂ (&) - AND, f ₁ ( & ) -I-NOT, f ₂ ( & ) -I-NOT, f ₃ ( & ) -AND-NOT, f ₄ ( & ) -AND NOT, f ₅ ( & ) -AND NOT, f ₆ ( & ) -AND NOT, f ₇ ( & ) -AND NOT, f ₈ ( & ) -I-NOT, f ₉ ( & ) -I-NOT, f ₁₀ ( & ) -I-NOT and f ₁₁ ( & ) -NI, for functional relationships are made in accordance with mathematical models of the form

Where

- logical function f ₁ ( & ) -and NOT conditionally "j + 1"discharge;

- logical function f ₁ ( & ) -and NOT conditionally "j" discharge. 5. Functional parallel structure of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” bits “K” “Minimization zones”, characterized in that the structures of conditionally “j + 1” and “j” bits are made according to a functional equivalent structure, forming conditionally negative minimized arguments ^min (- m _j ) _{k + 1} and ^min (- m _j ) _k , and each of them includes the logical functions f ₁ (&) - AND, f ₂ (&) - И, f ₁ ( & ) -AND-NOT, f ₂ ( & ) -AND-NOT, f ₃ ( & ) -AND-NOT, f ₄ ( & ) -AND NOT, f ₅ ( & ) -AND NOT, f ₆ ( & ) -AND NOT, f ₇ ( & ) -AND NOT, f ₈ ( & ) -AND NOT, f ₉ ( & ) -AND NOT and f ₁₀ ( & ) -AND NOT, while functional relationships are made in accordance with mathematical models of the form

6. Functional parallel structure f ₂ ( 0 , 0 ) min and f ₁ ( 00 ) min through activation of the minimized arguments “0, 1 0.0” and “0.0 1 , 0” into conditionally “j + 1” and “ j "bits" k "" Minimization zones ", characterized in that the structure is conditionally" j + 1 "and" j "bits forming positive minimized arguments ^min (+ m _j ) _{k + 1} and ^min (+ m _j ) _k , are executed according to a functional equivalent structure and each of them includes the logical functions f ₁ ( & ) -AND-NOT, f ₂ ( & ) -AND-NOT, f ₁ ( } ) -OR, f ₁ ( } & ) -OR , f ₂ ( } & ) - OR NOT, f ₃ ( } & ) - OR NOT, f ₄ ( } & ) - OR NOT, f ₅ ( } & ) - OR NOT, f ₆ ( } & ) -or-NO, f ₇ (} &) -or-NO, f ₈ (&}) - LEE NOR f ₉ (} &) -or-NO and f ₁₀ (} &) -or-NO, wherein the functional connections are made in accordance with mathematical models of the form

Where

- logical function f ₁ ( } & ) - OR NOT conditionally "j + 1"discharge;

- logical function f ₁ ( } & ) - OR NOT conditionally “j” discharge. 7. Functional parallel structure of end-to-end activation f ₂ ( 1 , 1 ) min and f ₁ ( 11 ) min of inactive logical zero arguments “± 0” → “+ 1 / -1” in conditionally “j + 1” and “j” bits “K” “Minimization zones”, characterized in that the structures of conditionally “j + 1” and “j” bits are made according to a functional equivalent structure, forming conditionally negative minimized arguments ^min (- m _j ) _{k + 1} and ^min (- m _j ) _k , and each of them includes logical functions, logical functions f ₁ ( & ) -AND-NOT, f ₂ ( & ) -AND-NOT, f ₁ ( } ) -OR, f ₁ ( } & ) -OR-NOT , f ₂ ( } & ) - OR NOT, f ₃ ( } & ) - OR NOT, f ₄ ( } & ) - OR NOT, f ₅ ( } & ) - OR NOT, f ₆ ( } & ) - OR NOT, f ₇ ( } & ) - OR NOT, f ₈ ( } & ) - OR NOT, f ₉ ( } & ) - OR NOT and f ₁₀ ( } & ) -OR-NOT, while the functional relationships are made in accordance with mathematical models of the form