RU2481614C2

RU2481614C2 - METHOD TO GENERATE ARGUMENTS OF ANALOG SIGNALS OF PARTIAL PRODUCTS [ni]&[mj]f(h)↓CD ARGUMENTS OF MULTIPLICAND ±[mj]f(2n) AND ARGUMENTS OF MULTIPLIER ±[ni]f(2n) - "ADDITIONAL CODE" IN PYRAMIDAL MULTIPLIER fΣ(↓CDΣ) FOR SUBSEQUENT LOGICAL DECODING f1(CD↓) AND GENERATION OF RESULTING SUM IN FORMAT ±[SΣ]f(2n) -"ADDITIONAL CODE" AND FUNCTIONAL STRUCTURE FOR ITS REALISATION (VERSIONS OF RUSSIAN LOGICS)

Info

Publication number: RU2481614C2
Application number: RU2011123171/08A
Authority: RU
Inventors: Лев Петрович Петренко
Original assignee: Лев Петрович Петренко
Priority date: 2011-06-08
Filing date: 2011-06-08
Publication date: 2013-05-10
Also published as: RU2011123171A

Abstract

FIELD: information technologies.

SUBSTANCE: invention may be used to build arithmetic devices for performance of arithmetic operations of multiplication of multiplicand arguments ^±[m_j]f(2ⁿ) and multiplier arguments ^±[n_i]f(2ⁿ) - "Additional code". In one of versions the structure is realised using logical elements CFU, OR-CFU.

EFFECT: increased efficiency of a process of transformation of arguments of partial products.

4 cl

Description

Текст описания приведен в факсимильном виде.

The text of the description is given in facsimile form.

Claims

1. The method of forming analog signals of the arguments of partial works [n_i] & [m_j] f (h)_{↓ CD} multiplier^±[n_i] f (2ⁿ) and many^±[m_j] f (2ⁿ) - “Additional code” in the pyramidal multiplier f_Σ(↓_CDΣ) for subsequent logical decryption f_one(CD ↓) and the formation of the resulting amount^±[S_Σ] f (2ⁿ) - “Additional code”, including activation of an ordered sequence of analog signals of partial products of the least significant digits^min[n_i] & [m_j] f (h)_{↓ CD}→^1,2[m_j-2h ^&]_{max ↓} and^one(m_j ^&)_min and activation of analog signals of partial products of medium discharges⁰[n_i] & [m_j] f (h)_{↓ CD}→^1,2(S_h ^&) groups “h” of the first and second levels and partial products of the highest orders of the highest orders^max[n_i] & [m_j] f (h)_{↓ CD}→^one(m_j ^&)_max and^1,2[m_j-2h ^&]_{min ↓} groups “h” of the first and second levels in accordance with the logical-dynamic process of converting the arguments of analog signals, which in the “logical information space” corresponds to a graphic-analytical expression of the form

Where^1,2[m_j-2h ^&]_{min ↓} - the structure of the arguments “Level 1” and “Level 2” in the group “h” with the specification of the deletion action (_{min ↓}) of the least significant argument, and in each “h” group, a simultaneous analysis is performed at a logical level as the activity of the arguments of the “Multiply” analog signals^h[m_j-1min] and^h[m_j-2min], and taking into account "h" correspond to structures of analog signals of multiplicable [m_{j-2h + 1}]_{min ↓} and [m_j-2h]_{min ↓}in which, depending on the “Level 1” and “Level 2” in the “h” group, one and two arguments of the analog signal of the lower digits are excluded^h(m_j)_min and^h(m_{j + 1})_min the corresponding group “h”, and the activity of the corresponding argument of the analog signal^one(n_i)^max first level and argument of the analog signal²(n_{i + 1})_maxsecond level conditionally “i” bits of the multiplier^±[n_i] f (2ⁿ) of the same group “h” and, when they are simultaneously active, activate the argument of analog signals^one(m_j ^&)_max senior level one and argument structure^1,2[m_j-2h ^&]_{min ↓} first and second levels of partial products of senior ranks^max[n_i] & [m_j] f (h)_{↓ CD}→^one(m_j ^&)_max and^1,2[m_j-2h ^&]_{min ↓}, while the arguments of the partial signal analog signals are the product of the middle digits⁰[n_i] & [m_j] f (h)_{↓ CD}→^1,2(S_h ^&) activate in accordance with the logical-dynamic process of converting analog arguments, which in the "logical information space" corresponds to a graphical analytical expression of the form

where in each “h” group a simultaneous analysis is performed at a logical level of activity as arguments of analog signals (n_i)_max and (m_j)_min conditionally “i” and “j” bits and arguments of analog signals (n_{i + 1})_max and (m_{j + 1})_min conditionally “i + 1” and “j + 1” bits of the same group “h” of the factor^±[n_i] f (2ⁿ) and many^±[m_j] f (2ⁿ) and activate the arguments of the analog signals of partial products of medium digits⁰[n_i] & [m_j] f (h)_{↓ CD}→^1,2(S_h ^&), characterized in that the activation of the arguments of the analog signals of the partial products of the lower digits^min[n_i] & [m_j] f (h)_{↓ CD}→^1,2[m_j-2h ^&]_{max ↓} and^one(m_j ^&)_minthe first and second levels are also performed in the “h” group in accordance with the logical-dynamic process of converting the arguments of analog signals, which in the “logical information space” corresponds to a graphic-analytical expression of the form

where also in each “h” group, simultaneous analysis at a logical level is performed as the activity of the structure of the arguments of the analog signals of the multiplicable^h[m_j-1max] and^h[m_j-2max], and taking into account "h" they correspond to the structures of the analogue signals of the arguments of the multiplicable [m_{j-2h + 1}]_{max ↓} and [m_j-2h]_{max ↓} with high-order arguments removed^h(m_j)_max and^h(m_j-1)_maxthe previous group “h”, and two consecutive arguments of analog signals^h(n_i)_min and^h(n_{i + 1})_minconditionally "i" factor bits^±[n_i] f (2ⁿ) of the same group “h” and activate the arguments of the analog signals of the partial products of the lower digits^min[n_i] & [m_j] f (h)_{↓ CD}→^1,2[m_j-2h ^&]_{max ↓} and^one(m_j ^&)_min, which include in the general structure of partial products of analog signals of medium discharges⁰[n_i] & [m_j] f (h)_{↓ CD} →^1,2(S_h ^&)and higher ranks^max[n_i] & [m_j] f (h)_{↓ CD}→^one(m_j ^&)_max and^1,2[m_j-2h ^&]_{min ↓} in accordance with the logical-dynamic process of converting the arguments of analog signals, which in the “logical information space” corresponds to a graphic-analytical expression of the form

2. The method of generating analog signals of the arguments of the partial products [n _i ] & [m _j ] f (h) _{↓ CD of the} multiplier ^± [n _i ] f (2 ⁿ ) and the multiplier ^± [m _j ] f (2 ⁿ ) - "Additional code ”in the pyramidal multiplier f _Σ (↓ _CD Σ) for subsequent logical decryption of f ₁ (CD ↓) and generating the resulting sum in the format ^± [S _Σ ] f (2 ⁿ ) -“ Additional code ”, which includes simultaneous analysis of the structure of arguments multiplier analog signals [n _{i-2h + 1} ] and [n _i-2h ] of the factor ^± [n _i ] f (2 ⁿ ), where “h” is the number of first and second levels in the structure of partial products of the highest digits ^max [n _i ] & [m _j ] f (h) _{↓ CD} → ¹ (m _j ^& ) _max and ^1.2 [m _j-2h ^& ] _{min ↓} and the corresponding arguments of the factors (m _{j + 1} ) _{kj + h-1} and (m _j ) _{kj + h-1 of the} multiplied ^± [m _j ] f (2 ⁿ ), and this analysis is performed by the functional linear structure of the first level f ₁ [& _{i-2h + 1} ] -I and the functional linear structure f ₂ [ & _i-2h ] -A of the second level with logical functions f ₁ ( ^h & _i ) -I and f ₂ ( ^h & _i ) -I conditionally “i” bits in accordance with mathematical models of the form

and in accordance with the graphoanalytic expression of the form

and form the argument of the analog signal ¹ (m _j ) _max senior bit and the arguments of the analog signal of the least significant bits ¹ [m _j-2h ] _{min ↓} first level and the arguments of the analog signals ² [m _j-2h ] _{min ↓} second level partial works with deleted ( _{min ↓} ) with the least significant arguments of the structure of the multiplicable ^± [m _j ] f (2 ⁿ ), and this includes the simultaneous analysis of the arguments (m _{j + 1} ) _{kj + h-1} , (n _i ) _{ki + h-1} and (m _j ) _{kj + h-1} , (n _{i + 1} ) _{ki + h-1} through the logical function f ₁ ( ^h &) - And and the logical function f ₂ ( ^h &) - And in accordance with mathematical models of the form

and in accordance with the graphoanalytic expression of the form

and form the arguments of the analog signals ¹ (S _h ^& ) and ² (S _h ^& ), respectively, of the first and second levels in the group “h” of partial products of the middle digits ⁰ [n _i ] & [m _j ] f (h) _{↓ CD} → ^{1 , 2} (S _h ^& ), characterized in that the simultaneous analysis of the activation of the arguments of the analog signals of the partial products of the least significant digits ^min [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 [m _j-2h ^& ] _{max ↓} and ¹ (m _j ^& ) _min groups of the first and second levels “h” execute the argument structures of the analog signals of the multiplied [m _{j-2h + 1} ] and [m _j-2h ] structures ^± [m _j ] f (2 ⁿ ) and the corresponding arguments of the factors (n _i ) _{kj + h-1} and (n _{i + 1} ) _{kj + h-1} structure ^{± ±} [n _i ] f (2 ⁿ ), and it is performed by means of the functional linear structure f ₃ [ ^h & _{j-2h + 1} ] -I and by the functional linear structure f ₄ [ ^h & _j-2h ] -I conditionally " j "bits in accordance with mathematical models of the form

and in accordance with the graphoanalytic expression of the form

and activate the argument of the analog signal ¹ (m _j ^& ) _min low order and the structure of the arguments ¹ [m _j-2h ^& ] _{max ↓ of the} first level and the structure of the arguments ² [m _j-2h ^& ] _{max ↓ of the} second level, respectively, while the functional structures partial products of the least significant digits ^min [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 [m _j-2h ^& ] _{max ↓} and ¹ (m _j ^& ) _{min of the} first and second levels of the “h” group with functional structures that activate the resulting arguments of the partial products of the highest digits ^max [n _i ] & [m _j ] f (h) _{↓ CD} → ¹ (m _j ^& ) _max and ^1.2 [m _j-2h ^& ] _{min ↓} and average bits ⁰ [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 (S _h ^& ) the first and second levels of the same group "h" in accordance with a mathematical model of the form

by means of which analog signals of the partial product arguments [n _i ] & [m _j ] f (h) _{↓ are generated CD} factors ^± [n _i ] f (2 ⁿ ) and ^± [m _j ] f (2 ⁿ ) - “Additional code "In the pyramidal multiplier f _Σ (↓ _CD Σ) for subsequent logical decryption of f ₁ (CD ↓) and the formation of the resulting sum in the format ^± [S _Σ ] f (2 ⁿ ) -" Additional code ".

3. The functional structure of the formation of analog signals of the arguments of the partial products [n _i ] & [m _j ] f (h) _{↓ CD of the} factor ^± [n _i ] f (2 ⁿ ) and the multiplicative ^± [m _j ] f (2 ⁿ ) - " Additional code ”in the pyramidal multiplier f _Σ (↓ _CD Σ) for subsequent logical decryption of f ₁ (CD ↓) and generation of the resulting sum in the format ^± [S _Σ ] f (2 ⁿ ) -“ Additional code ”, including the functional linear structure f ₁ [& _j-2h ] -I and the functional linear structure f ₂ [& _j-2h ] -I conditionally “j” digits, where “h” is the group of the first and second levels of partial works performed in according to the mathematical model of the form

in which the first functional relationships are the functional relationships of the structure for receiving the arguments of the multiplicable [m _{j-2h + 1} ] _{min ↓} and [m _j-2h ] _{min ↓ of the} multiplicand ^± [m _j ] f (2 ⁿ ), the second functional relationships are the input function by connections of the structure for receiving the argument (n _{i + 1} ) _{ki + h-1} conditionally “i + 1” of the discharge and the argument (n _i ) _{ki + h-1} conditionally “i” discharge of the factor ^± [n _i ] f (2 ⁿ ) , and the functional output connections forming the partial product argument ¹ (m _j ^& ) _max senior bit and the argument structure ¹ [m _j-2h ^& ] conditionally “j” bits of the first level and the argument structure ² [m _j-2h ^& ] conditionally “j” bits of the second level are the functional output links of the structure, including functional structures with logical functions f ₁ ( ^h &) - And and f ₂ ( ^h &) - And the middle bits, made in accordance with mathematical models of the form

in which the first functional relationships are functional relationships of the structure for receiving the argument (m _{j + 1} ) _{kj + h-1} conditionally “j + 1” of the discharge and the argument (m _j ) _{kj + h-1} conditionally “j” of the discharge of the multiplicable ^± [m _j ] f (2 ⁿ ), the second functional links are the functional input links of the structure for receiving the argument (n _i ) _{ki + h-1} conditionally “i” of the discharge and the argument (n _{i + 1} ) _{ki + h-1} conditionally “i + 1 "digit multiplier ^± [n _i] f (2 ^n), and the functional output connection forming the argument of the partial product bits medium ¹ (S _h ^&) and ² (S _h ^&) input connections are functional p Keturah and comprising linear functional structure f ₃ ^[h & _{j-2h + 1]} -And and f ₄ ^[h & _j-2h] -And conditionally «j» bits made in accordance with the analytical expressions of the form

in which the functional input links are the functional input links of the structure for receiving the argument structure [m _{j-2h + 1} ] _{max ↓} and [m _j-2h ] _{max ↓ of the} multiplied ^± [m _j ] f (2 ⁿ ) and for receiving the argument ( n _i ) _{ki + h-1} conditionally “i” of the discharge and argument (n _{i + 1} ) _{ki + h-1} conditionally “i + 1” of the discharge of the factor ^± [n _i ] f (2 ⁿ ), while the functional output connection linear functional structure f ₃ ^[h & _{j-2h + 1]} is a functional -And output coupling structure for forming argument ¹ LSB (m _j ^&) _min partial products, the second functional relationship, as is functional e output communication function f ₄ linear structure ^[h & _j-2h] -And output connections are functional structures characterized in that the functional output communication function f ₃ of linear structures ^[h & _{j-2h + 1]} -And and f ₄ [ ^h & _j-2h ] -and made in accordance with a mathematical model of the form

in which the second functional output links of the functional linear structure f ₃ [ ^h & _{j-2h + 1} ] -and designed to form partial products of ¹ [m _j-2h ^& ] _{max ↓} conditionally “j” bits of the first level in the group “h” and functional output links of the functional linear structure f ₄ [ ^h & _{j-2h + 1} ] -and designed to form partial products ² [m _j-2h ^& ] _{max ↓} conditionally “j” bits of the second level in the group “h” are functional output links patterns for activation of the partial products ¹ _{^{_{[m j-2h &] max}}} ↓ + ² _{^{_{[m j-2h &] max}}} ↓, and the medium which is formed analog signals arguments the partial products _{_{[n i] & [m j}} ] f (h) ↓ CD multiplier ^± [n _i] f (2 ⁿ⁾ and the multiplicand ^± [m _j] f (2 ⁿ⁾ - «Additional code" in the pyramidal multiplier f _Σ (↓ _CD Σ) for subsequent logical decryption of f ₁ (CD ↓) and the formation of the resulting sum in the format ^± [S _Σ ] f (2 ⁿ ) - “Additional code”.

4. The functional structure of the formation of analog signals of the arguments of the partial products [n _i ] & [m _j ] f (h) _{↓ CD of the} factor ^± [n _i ] f (2 ⁿ ) and the multiplicative ^± [m _j ] f (2 ⁿ ) - " Additional code ”in the pyramidal multiplier f _Σ (↓ _CD Σ) for subsequent logical decryption of f ₁ (CD ↓) and generating the resulting sum in the format ^± [S _Σ ] f (2 ⁿ ) -“ Additional code ”, characterized in that the functional the structure is made in the form of functional structures for activating the arguments of partial products of the first and second levels of the “Group of levels” “h” of higher ranks ^max [n _i ] & [m _j ] f (h) _{↓ CD} → ¹ (m _j ^& ) _max and ^1.2 [m _j-2h ^& ] _{min ↓} , medium digits ⁰ [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 (S _h ^& ) and the least significant bits ^min [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 [m _j-2h ^& ] _{max ↓} and ¹ ( m _j ^& ) _min , while in the functional structure of activating the arguments of the partial products of the “Level Group” “h” of the highest digits ^max [n _i ] & [m _j ] f (h) _{↓ CD} → ¹ (m _j ^& ) _max and ^{1 , 2} [m _j-2h ^& ] _{min ↓ the} functional set [ & _{i-2h + 1} ] ₁ and [ & _i-2h ] _{2 of the} logical functions f ₁ ( & _i ) -НЕ, logical functions f ₁ ( ^h & ) are introduced -HE and f ₂ ( ^h & ) -HE and the functional linear structure f ₁ [} ( & ) _i-2h ] -OR-NOT and f ₂ [} ( & ) _i-2h ] -OR-NOT, but functional connections made in accordance Twi with a mathematical model of the form

where [ & _{j-2h + 1} ] ₁ and [ & _j-2h ] ₂ is a functional set of logical functions f ₁ ( & _i ) -НЕ; ^h & ₁ and ^h & ₂ - analytical symbol of the logical function f ₁ ( & ) -НЕ and f ₂ ( & ) -НЕ; “H” - “Level Group” of the first and second in the pyramidal structure of the multiplier f _Σ (↓ _CD Σ);

- functional linear structure f ₁ [} ( & ) _j-2h ] OR NOT logical functions f ₁ (} & _j ) OR NOT conditionally “j” bits;

- functional linear structure f ₂ [} ( & ) _i-2h ] -OR-NOT;
and the logical functions f ₁ ( ^h } are introduced into the functional structure of activating the arguments of partial products of the “Level Group” “h” of the middle digits ⁰ [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 (S _h ^& ) & ) -OR-NOT and f ₂ ( ^h } & ) -OR-NOT, and the functional relationships are made in accordance with mathematical models of the form

Where

and

- the logical function f ₁ ( ^h } & ) - OR NOT and f ₂ ( ^h } & ) - OR NOT;
and into the functional structure of activating the arguments of the partial products of the “Level Group” “h” of the lower digits ^min [n _i ] & [m _j ] f (h) _{↓ CD} → ^1,2 [m _j-2h ^& ] _{max ↓} and ¹ (m _j ^& ) _min introduced the functional set ^h [ & _{j-2h + 1} ] ₃ and ^h [ & _j-2h ] ₄ logical functions f ₃ ( ^h & _j ) -НЕ and f ₄ ( ^h & _j ) -НЕ, logical functions f ₃ ( ^h & ) -HE and f ₄ ( ^h & ) -HE, as well as the functional linear structure f ₃ [ ^h } ( & ) _j-2h ] -OR-NOT and f ₄ [ ^h } ( & ) _{j- 2h} ] -OR-NOT conditionally “j” bits, and functional relationships are made in accordance with a mathematical model of the form

where ^h [ & _{j-2h + 1} ] ₃ and ^h [ & _j-2h ] ₄ is a functional set of logical functions f ₃ ( ^h & _j ) -HE and f ₄ ( ^h & _j ) -HE; ^h & ₃ and ^h & ₄ - analytical symbol of the logical function f ₃ ( ^h & ) -НЕ and f ₄ ( ^h & ) -НЕ;

- functional linear structure f ₃ [ ^h } ( & ) _j-2h ] -OR NON-logical functions f ₃ (} & _j ) -OR NOT conditionally “j” bits;

- functional linear structure of f ₄ [ ^h } ( & ) _j-2h ] -OR NON-logical functions f ₄ ( ^h } & _j ) -OR-NOT conditionally “j” digits.