RU2591009C1 - Method and device for arrangement of groups of numbers in homogeneous units of digital register - Google Patents

Abstract

FIELD: computer engineering.

SUBSTANCE: invention relates to special digital computer systems, can be used in communication systems and control of complex objects, is intended for compact arrangement in digital register groups numbers or data presented in modular formats. Device comprises input register, comparator unit, data transmission units, subtractor, output register.

EFFECT: reduced information redundancy of digital register, which increases efficiency of distribution of data, efficiency of operation, technological effectiveness of circuit design of homogeneous block register.

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Description

The invention relates to the field of specialized digital computing technology for parallel processing of digital information, can be used in communication systems and control complex objects, is intended for placement in blocks of a digital register of groups of numbers or data presented in modular formats.

There is a method of representing numbers in a modular number system in the form of an ordered set of modulo residues, in which base modules (simple or coprime integers) are used in the modular number system and the smallest non-negative modulo residues. The vector of the modular code of a number with components (α ₁ ..., α _i , ... α _n ) contains residues by the modules {p _l , ... p _i , ... p _j , ... p _n }. The indices (1, ... i, ..., n) specify the numbers of residues for the base modules of the modular system and the corresponding binary blocks (independent groups of bits) of the digital block modular register, designed to place the residues for the base modules. For a unique representation of a number in a modular system by modulo residues, it is necessary to fulfill the simplicity (mutual simplicity) condition for the bases i ≠ j ∀i, j = 1 ÷ n (p _i , p _j ) = 1. The mutually simple foundations of the modular number system in the general case are not powers of two. Only one of the bases can be a power of two. The deductions for different modules vary within different limits, the boundaries of which are not multiples of the powers of two. The numerical values of the residues modulo are integers ranging from zero to the value of the module, reduced by one. For these reasons, in binary heterogeneous blocks of the digital modular register, it is impossible to redundantly place the deductions in the blocks of the digital register, because not all possible binary combinations are used to represent residues; information redundancy appears. The heterogeneity of the blocks of the digital modular register is understood to mean their different lengths expressed in elementary (binary) cells for placing bits of the numerical value of the residue modulo in the binary code. With the maximum equal block lengths, information redundancy increases all the more and it is impossible to use all possible binary combinations in a digital block [Akushsky I.Ya., Yuditsky DI Machine arithmetic in residual classes. - M .: Owls. Radio, 1968. - 326 p.]. Redundancy in blocks reduces the efficiency of using digital register equipment.

The known method is used in devices "Device for dividing the number in the modular code" (RF patents No. 2231822, No. 2237274), "Device for monitoring computers" (RF patent No. 2458384), "Device for determining the sign of the modular number" (RF patent No. 2503995 ) containing digital inhomogeneous block registers intended for functional transformation, storage, shift, processing, placement of residues of the modular code.

A patent search did not find digit group conversion devices specifically designed for placement in homogeneous blocks of a digital register.

The closest taken as a prototype can be considered “Modulo arithmetic device” according to RF patent No. 2157560, containing an input heterogeneous block modular register for selecting modular code residues, over which functional transformations are performed in blocks of encoders, code converters, multiplication and division, and others blocks, and the result of the transformations is recorded in the output heterogeneous block modular register.

The disadvantage of this method, devices based on it and a prototype containing heterogeneous block registers for placing the numerical values of the residues of the modular code are:

- informational redundancy of blocks, because not all possible combinations of characters are used to place numerical values of residues in register blocks;

- the presence of heterogeneous blocks with different bit depths, with information redundancy, which reduces the interchangeability of blocks, and maintainability of the digital register of the computing system;

- increasing the complexity of the development and implementation of the chip modular register of heterogeneous blocks of various lengths.

A common feature of the known and claimed methods, as well as devices based on it, is the presence of digital block modular registers.

The technical result of the method and device for placing data and the numerical values of the residues modulo in homogeneous blocks of the digital register is that the method implements, and the technical device allows:

- increase the efficiency of use of the equipment of the blocks, reduce or completely eliminate the redundancy of the register for the placement of digital data, use all possible combinations of characters in the unit cells of the blocks to represent residues modulo;

- to increase maintainability and reliability of the digital register of the computing system, to obtain interchangeability of blocks;

- reduce the complexity of the development of homogeneous blocks of the chip modular register.

The inventive method is intended to implement the following tasks.

To place a number in the input block modular register of the modular code in the form of a set of residues for m≥2 base modules of the modular system, m-blocks are necessary. To reduce redundancy, all blocks have a different length specified by an integer n _i ≥] log ₂ p _i [, where i = 1, ... m indicates the block number, i.e. contain a different number of binary unit cells designed to store the binary components of the residues modulo.

A redundant representation of the residues of the modular code is not possible in heterogeneous binary blocks of the m-modular digital register for the following reason. The various numerical values of the residues modulo α _i not multiple of an integer power of two should be placed in a binary block with the length n =] log ₂ (maxα _i ) [, where the brackets denote the integer, the least part of the number. When placing, redundancy of equipment arises to represent the numerical values of the residues modulo in the binary blocks of the digital register, because to place the deductions, not all possible binary combinations are used in blocks of a digital register of length n. The redundancy in the block is measured by a rational number δ _i > 0: δ _i =] log ₂ (maxα _i ) [- log ₂ (maxα _i ) or δ _i =] log ₂ (p _i -1) [- log ₂ (p _i - one).

The inventive method is intended to reduce the redundancy of the representation of residues in homogeneous blocks of the modular register and contains technological steps.

At the first stage, the first constant p = 2 ⁿ is specified. The second stage is defined a plurality of pairs (p _i, p _j) relatively prime moduli-radix modular bases, for which the following conditions:

The output block modular register contains an arbitrary even number m≥2 blocks of equal length n = log ₂ p, consisting of binary unit cells designed to accommodate the binary components of the residues modulo. An odd number of blocks can be if the module p _i = 2 ^{n is} included in the set of bases of the modular system.

для каждой пары оснований (p_i,p_j) ∀i,j=1÷n, i≠j.To represent the residues modulo in m-binary blocks of the output register, where m≥2, without redundancy, the equality

for each base pair (p _i , p _j ) ∀i, j = 1 ÷ n, i ≠ j.

The rationale for the proposed method is given as an example of one pair of numerical values of residues modulo (α _i , α _j ) for two relatively simple bases of the modular system (p _i , p _j ), p _i <p <p _j .

, α_i≤p_j-1=p+γ_j-1.For residues modulo, which are components of the modular code, the following relations are true:

_{, Α i ≤p j -1 = p} + γ j -1.

Consider the first variant of the relations. Suppose for residues modulo the inequalities _{α i ≤p i -1, α j} ≤p- 1. These inequalities are found by comparing the numerical values of the residues modulo with the first constant p = 2 ⁿ (n≥2). In this case, the modulo deductions in the blocks of the input modular register are transferred to the corresponding homogeneous blocks of the output modular register.

выполняется соотношение

Это позволяет число

передать в блок для вычета по модулю p_i<р, что обнаруживают по выполнению неравенства

, т.к. выполняется соотношение:Consider the second variant of the relations. Let for the residue modulo the greater the inequality p-1≤α _i ≤p + γ _j -1 be satisfied. The auxiliary quantity α ′ = α _j -p≤γ _j -1 is calculated, for which the inequalities 0≤α ′ _j ≤γ _j -1 hold, and also for

the relation holds

This allows the number

pass to the block for the deduction modulo p _i <p, which is found by the inequality

because the ratio is satisfied:

,

,

where δ _i = (p-p _i ) is the second constant, which is the difference between the first constant and the smaller of the base pair of the modular system.

заявляемого способа. Четвертым технологическим этапом является ротация чисел перед занесением в блоки выходного регистра:The third technological step is the calculation, using the second constant, of the expression

the proposed method. The fourth technological stage is the rotation of numbers before entering into blocks of the output register:

- in the binary block of length n = log ₂ p instead of the deduction α _j modulo p _j place the deduction α _i ≤p _i -1 <p;

.- in a binary module of length n = log ₂ p instead of subtracting α _i modulo the base p _i place the number

.

безубыточное, а при

компактное, почти безубыточное размещение в выходном модульном регистре чисел в однородных блоках одинаковой длины n=log₂ р.The result will be obtained when

breakeven, and when

compact, almost break-even placement in the output modular register of numbers in homogeneous blocks of the same length n = log ₂ p.

To unambiguously restore the numerical values of residues modulo from heterogeneous blocks of the input register, reverse rotation is performed:

- a binary block length n = log ₂ p for subtracting modulo - p _i transmitting base residue α _i ≤p _i -1 <p;

, которое может быть размещено в бинарном блоке длиной n+1=1+log₂p.- restore the numerical value of the residue α _j ≥ p modulo p _j from the relations

, which can be placed in a binary block of length n + 1 = 1 + log ₂ p.

For the claimed method, we give numerical examples.

; р=р₃=2⁸=256; р₅=p+γ₁=259=2⁸+3;

;

; p₄=p+γ₂=2⁸+1=257;

; n=log₂p=log₂2⁸=8.Example 1. Based on the standard binary byte size, we choose mutually simple base modules of the modular system: {p ₁ , p ₂ , p ₃ , p ₄ , p ₅ } = {251, 255, 256, 257, 259}. For them, the following relationships hold: modules 251, 257 are simple; for three modules the multiplicative canonical decompositions have the form: 255 = 3.5.17; 259 = 7.37; 256 = 2 ⁸ . This allows you to form two pairs (p ₁ , p ₅ ), (p ₂ , p ₄ ) of mutually simple modules, for which the relations are satisfied:

; p = p ₃ = 2 ⁸ = 256; p ₅ = p + γ ₁ = 259 = 2 ⁸ +3;

;

; p ₄ = p + γ ₂ = 2 ⁸ + 1 = 257;

; n = log ₂ p = log ₂ 2 ⁸ = 8.

The fulfillment of the relations for the base modules of the modular system allows the claimed method to place the binary values of the residues on five mutually simple modules in five homogeneous 8-bit blocks of the output register.

, которое размещают в 8-битовом блоке, предназначенном для размещения вычета по модулю р₂, который размещают в 8-битовом блоке, предназначенном для размещения вычета по модулю р₄.Suppose that a deduction α ₄ = 2 ⁸ = p modulo 257, which cannot be placed in an 8-bit block, is obtained from the input register block. Calculate the number

which is placed in an 8-bit block designed to accommodate a deduction modulo p ₂ , which is placed in an 8-bit block intended to accommodate a deduction modulo p ₄ .

A variant of the method is possible, characterized in that the non-uniform blocks of the input register contain arbitrary numbers that are not mathematically modulo residues, but varying within not multiple of the integer powers of two similar modulo residues. In this case, the analogue of the module should be one more than the maximum value of the numerical values placed in the corresponding block of the input register. For analogs of modules in this case, the condition of mutual simplicity is not required.

A variant of the method is possible, characterized in that the blocks of the input and output registers contain non-binary representations of numbers with an arbitrary set of digital symbols, i.e. numbers represented in a positional number system with an arbitrary base.

The claimed method is implemented in the claimed device.

In FIG. 1 is a structural diagram of a device in which a pair of heterogeneous blocks 1, 2 of the input register 3, a comparison block 4, data transmission blocks 5, 6, 7, a subtraction block 8, transmission conductors from a comparison block 4 control signals 4.1, 4.2, a pair of homogeneous are indicated blocks 9, 10 of the output register 11.

In the device, the output of block 1 is connected to the information inputs of blocks 5, 7; the output of block 2 is connected to the information inputs of blocks 4, 6, 8; the first output 4.1 of block 4 is connected to the control inputs of blocks 5, 6; the second output 4.2 of block 4 is connected to the control inputs of blocks 7, 8; the output of block 5 is connected to the input of block 9; the output of block 6 is connected to the input of block 10; the output of block 7 is connected to the input of block 10; the output of block 8 is connected to the input of block 9.

A device that implements the claimed method works as follows. From the block 1 of the input register 3, the values of the residues modulo in a parallel binary code are transmitted to the information inputs of the data transmission units 5, 7, and the values of the residues modulo from the block 2 of the input register 3 are likewise transferred to the information inputs of the blocks 4, subtract 8 and data transfer 6. In block 4, a comparison of the deduction from block 2 is performed with the first constant specified by the claimed method. If the compared residue is less, then after the receipt of the enabling signal 4.1 from block 4, the numerical value of the residues from blocks 5, 6 is transmitted to the information inputs of blocks 9, 10 of the output register 11, respectively. If the compared deduction is not less, then after the receipt of the enabling signal 4.2 from block 4, from block 7, the deduction modulo is transmitted to the information input of block 10 of the output register 11, and in block 8 the second constant calculated by the claimed method is subtracted, and the result is transmitted to the information input block 9 of the output register 11.

, P=2⁴=16, p_j=p+γ_j=2⁴+3=19;

; n=log₂p=4.Let us describe the operation of device blocks using an example. Given an ordered set of mutually simple base modules of the modular system: {p ₁ , ... p _i , p, p _j , ... p _m } = {..., 13, 16, 19, ...}. For a pair of modules 13 and 19, the following relations are satisfied:

, P = 2 ⁴ = 16, p _j = p + γ _j = 2 ⁴ + 3 = 19;

; n = log ₂ p = 4.

Deductions for modules 13, 19 are selected from heterogeneous blocks 2, 3 of the input modular register 1.

Deductions for modules less than or equal to 16 can be placed in four-bit binary blocks. To place the residues modulo 13 you need a four-bit binary block 2. The numerical values of the residues modulo 19, greater than or equal to 16 can only be placed in a five-bit binary block 3 of the input register 1.

We illustrate how the deductions for the selected modules 13, 19, the claimed device places in four-bit binary blocks 9, 10 of the output register 11. Let the residue modulo 19 in block 2 of register 1 is 18, this is more than 16, so the residue cannot be placed in a four-bit binary block 10.

. Полученное в блоке 8 число при поступлении управляющего сигнала 4.2 передают на информационный вход четырехбитового блока 9. Вычет по модулю 13, переданный в блок 7, при поступлении управляющего сигнала 4.2 передают на информационный вход блока 10 регистра 11, первоначально предназначенного для размещения вычетов по модулю 19 для числовых значений, меньших 16. О ротации числовых значений в блоках 9, 10 регистра 11 свидетельствует большее модуля 13 числовое значение 15 в четырехбитовом блоке 9. О передаче вычетов из блоков 1, 2 регистра 3 без ротации в блоки 9, 10 регистра 11 свидетельствовало бы размещенное в блоке 9 значение вычета, меньшее 13 по модулю 13.In block 8, calculate the number:

. The number obtained in block 8 when the control signal 4.2 arrives is transmitted to the information input of the four-bit block 9. The residue modulo 13 transmitted to block 7, when the control signal 4.2 arrives, is transmitted to the information input of the block 10 of register 11, which was originally intended to accommodate the deductions modulo 19 for numerical values less than 16. The rotation of numerical values in blocks 9, 10 of register 11 is indicated by the larger module 13, the numerical value 15 in four-bit block 9. The transfer of residues from blocks 1, 2 of register 3 without rotation to the block 9, the register 10 would indicate 11 arranged in the block 9 deducting a value less than 13 modulo 13.

The inventive device is in the form of an integrated circuit or is included in the microcircuit as part of a computing device and is intended for compact placement, storage, presentation of an ordered set of numerical values of groups of numbers or residues of the modular code used for parallel processing of discrete information.

A variant of the device is possible, characterized by the absence of separate block input and output registers and containing addressable memory cells that perform the functions of blocks of input and output registers.

A variant of the device is possible, characterized by the absence of separate block input and output registers and containing parallel independent channels of the input stream and the output stream of digital data as register blocks, respectively.

Thus, the set of technological operations of the claimed method, namely, setting the first constant, dividing into pairs of residues modulo located in the input register blocks, calculating the second constant, choosing the base pair of the modular system symmetrical with respect to the first constant, converting the residue from one of the bases with using the second constant, placing after converting a pair of numbers in homogeneous blocks of the output register, as well as the hallmarks of the claimed device, namely the presence To each pair of input register block matching blocks, subtraction, data conductors and control signals, it allows to achieve the stated technical result.

Claims (6)

1. The method of placing groups of numbers in homogeneous blocks of the digital register, in which the residues are selected modulo from the blocks of the input register, converted into groups of numbers and placed in blocks of the output register, characterized in that the residues modulo in the blocks of the input register are selected in pairs, for each of which the first constant is specified, the base pairs of the modular system are set that are symmetrical with respect to the first constant, the second constant is calculated - the difference between the first constant and the lower of the bases, the residue modulo transform for shego of bases using a second constant, and then the converted pair of numbers placed in the output register homogeneous blocks, followed by a repetition of these steps for each pair of residues modulo. 2. The method according to p. 1, characterized in that the pairs of numbers are placed in the blocks of the input register, varying within a multiple of integer powers of two, similar to the limits of the modulus residue deduction. 3. The method according to p. 1, characterized in that the blocks of the input and output registers contain non-binary representations of numbers with an arbitrary set of digital characters. 4. A device for placing groups of numbers in homogeneous blocks of a digital register, containing an input block register for selecting residues modulo, in which in each pair of blocks the output of the odd block is connected to the information inputs of the first and second odd data transfer blocks, the outputs of which are connected to the inputs of the odd and even blocks, respectively, in a pair of blocks of the output register, the output of the even block of the input register is connected to the information inputs of the comparison unit, the even data transfer unit and the subtraction unit, the first the course of the comparison block is connected to the control inputs of the first even and odd data transmission blocks, the second output of the comparison block is connected to the control inputs of the second odd data transmission block and subtraction block, the output of the subtraction block is connected to the input of the odd block in a pair of blocks of the output register, the output of the even transmission block data is connected to the input of an even block in a pair of blocks of the output register. 5. The device according to p. 4, characterized in that as blocks of input and output registers contains addressable memory cells. 6. The device according to p. 4, characterized in that as blocks of the input and output registers contains independent parallel channels of the input and output digital data streams, respectively.

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