SU758149A1 - Device for multiplying binary code by number represented in unitary code - Google Patents

Description

The invention relates to computing, in particular, to analog-to-digital converters, and can be used in digital measurement technology. ^uh

A device for multiplying, containing counters, elements AND, elements OR [1].

This device is characterized by insufficient speed and high hardware costs.

The closest to the invention to the technical essence is a device containing counters and elements (5 AND, which can multiply a binary number by a number represented in a sequential unit code. However, this device requires additional equipment costs 20 due to the need for a register of code storage operand and element groups AND [2D.

The aim of the invention is to reduce hardware costs. 25

This is achieved by the fact that the device containing counters and elements And, additionally introduced delay elements and elements of the ban, and the counting output of each ϊ-th counter 30

2

(ΐ = 1 — t-1, where t is the number of counters corresponding to the groups of digits of the multiplicand code), connected to the prohibition input of the ΐth BAN element, the output of which is connected to the (1 + 1) -th counter, and the information input to the output of the ίth delay element, the inputs of the delay elements and the counting input of the first counter are connected to the input of the device, the counting output of the 1st and counting input of the second discharge (1 + 1) -th counter, working on addition, are connected respectively to the input and output of the corresponding the element And, the other input of which is connected to the output of the 1st ale delay-coagulant.

The drawing shows a diagram of the proposed device containing counters b, ~ 1 _tons , delay elements 2) —2 _tons . _y , elements of prohibition 3, -Z _tm

element and 4.

Let us explain the arithmetic on the basis of which the proposed device operates. To do this, we take the binary number of the pn “179 or in the binary code n ₃ “ 11001101 (lower-order digits from the left) and create the production table

this binary number on the natural series of numbers. Initial number η _Λ ра3

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zobyem on the group, as indicated above.

Table 1

Value of the work The sequence number of discharge groups five one 2 3 four five Ro 00 00 00 0 0000 ten p, = 179 ^eleven 00 eleven 0 1000 P ₂ = 358 01 ten 01 one 0100 R _? = 537 ten 01 ten 0 0010 15 RD = 716 00 eleven 00 one 1010 P ₅ = 895 eleven eleven eleven one it 20 R ₆ = 1074 01 00 eleven 0 0001 R ₇ = 1253 'ten .ten 01 one 1001 P _e = 14 32 00 οι ten 0 1101 25 R ₉ = 1611 eleven 01 00 one UN ^R y = 1790 01 .eleven Th one 1011 thirty Group view ΰ / " " th I

discharges

Analyzing the table. 1, we see that in the transition from to P _{a + 1} ^! the information 35 in the groups of digits changes sequentially with an increment of plus or minus the transfer unit from the lower digits. Moreover, within each group the information (not counting the transfer) is changed independently of the change in other groups. The meaning of the works of I} within each of the groups changes as follows: in the groups represented in P _{1 by a} sequence of units (P type), it decreases cyclically; in groups represented in Р ^ by a sequence of zeros or by an isolated zero (δ kind) or one with _ one. or several nu-: lami. (b-view) increases cyclically. The transition from 1 to 0 in the highest order of groups 4 and I »of the types corresponds to the transfer of the unit to addition to the following groups, and the transition from 0 to 1 in the most senior category of the type II groups corresponds to the transfer of the unit to the subtraction to the following groups, for example, the initial state is all zeros, then when going from P _p to Ru without taking into account the transfer, if one impulse is added to all groups in parallel, ¹ we would get the number

ΪΊ

eleven

f ίίι Τ

10 11 ϊ 10 * 00 65

Taking into account transfers from the second category to the third and from the sixth to the seventh for subtraction, we obtain the desired P, =

= 179.

11 00 11 0 1000

When splitting any binary number into the indicated three types of symbol groups, the types of hyphenation and the groups into groups, taking into account the sign of the hyphenation, are exhausted by the following five types

table 2

II '- +

ι ——-- a

Sh - ± "T" -ί-►!

As can be seen from tables 1 _? and 2, in the event that the hyphenation sign from the previous group is opposite to the sign of the channel used in this group, information in this group at this multiplication step is saved, for example, when going from P ₄ = 716 to Rd = 895 in the first and third order groups of the second type generate transfer pulses with a minus sign, while at the same time, in the second and fourth groups, the unit code is entered in addition. At the same time, information in the second and fourth groups is kept unchanged. Similarly, when going from P ₀ = 1432 to Rd = 1611, the information in the second group of the third type does not change or when going from Rd = 895 to = 1074 in the second group of type w, a transfer pulse with a plus sign is formed, and the unit code to the third group of the second type entered in the subtraction - the information in the third group, does not change.

In the event that the hyphenation sign from the previous Group coincides with the sign of the channel used in this group, then the information in this group at this multiplication step changes by 2. Such a change occurs if the given group is type I, and the previous one is} or n ”type. For example, when moving from p ^ = 358 to P _& = 537 in the fourth group of the third type, a transfer momentum is formed with the familiar sign and the unit code in the fifth group is'

T of the form is entered on the addition - the information in the fifth group changes by 2. Similarly, when moving from P ₆ to P ₆ and from P _? To Ρθ, the information of the fifth group changes to 2.

Thus, the correct formation of works will occur with parallel recording in all groups of 3 units, while the transfer sign from the previous group is opposite to the sign of the channel used in

five

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this group, the information in this group should be preserved regardless of the receipt of a single code, and if the transfer symbol from the previous group matches the sign of the channel used in this group, then the information in this group should change to 2 when a single code arrives. Intergroup relations in the multiplication process can be characterized by the following table.

Table 3

Transfer from previous group to this Information in this group and- - H1 preserved is changing on 2 one one! preserved 1and AND preserved and, 7 is changing on 2 Time delays of each from lines delays more time of setting

previous discharges counter.

Thus, parallel-sequential insertion of a sequential single code into the corresponding bits is ensured, at which transfer signals arrive before information pulses. The duration of the transfer signals does not exceed the repetition period of a single code. The counters 1 ,, 1 ₂ contain two digits each (see Table 1), the counter 1 ₄ contains one digit and the counter 1§ contains the highest bits.

Consider the operation of the device on the example of multiplying a fixed number of 179 (transfer signal conditioners are not shown in the drawing).

For this example, the operation of the proposed device is as follows.

Initial state of the device

00 00 00 0 0000 ·

1 2 3 4 5

The counters 1, and C 'informational. Impulses of a single code are entered into the subtraction (for this example t = 5), the counters 1 ₂ , 1e, 5 - to addition. In counters 1-, 1¾, transfer signals are formed during the transition "zeros in all digits - ones in all digits", counters, C - in the transition "units in all digits - zeros in all digits". The polarity of the transfer signals in both cases is the same and corresponds to the polar

impulses of a single code. After the arrival of the first impulse of a single code on the subtracting counter 1t, the state of the device will change to:

11 00 00 0 0000

1 2 3 4 5

In this case, the transfer signal from counter 1 will go to the prohibition input of prohibition element 3-, prohibiting the arrival of the first impulse of a single code through the delay line 2, to the input of summing counter 1 ₂ .

Device status will remain.

The impulse from the delay line 2 ₂ through the prohibition element Зg will be fed to the input of the reading counter 1. The state of the device will be as follows

11 .00 11 O ^- 0000

1 2 3 4 5

The transfer signal from counter 1¾ goes to the input of element 3 ^, prohibiting the arrival of a pulse of a single code from delay element 2¾ to the input of summing counter 1 ₄ . Device status will remain.

The impulse of a single code from the delay line 2 ₄ through the element of the prohibition 3 _{5 is} fed to the input of the summing counter Ι5. Device status will become

as follows 11 00 eleven 0 1000 12 · 3 four 5> i.e. equal to P, - 179

When the next (second) pulse of a single code arrives at the input of the counter 1 ₁ and through delay elements 2, -2d, prohibition elements 3, -31, to the inputs of counters 1, -15, the state of the devices

roystva will become to those who 01 ten 01 1 0100 one 2 3 4 five,

i.e. equal to P ₂ = 358

When the third impulse of a single code arrives at the input of counter 1 (and through delay elements 2 ,, 2%, 2 $ and prohibition elements 3 ₁ , 3 ₂ , 3 ¾ to inputs of counters Ι2; C, 1 ₄ , the device will become as follows:

10 01 10 0 0100

In this case, the transfer signal from the counter Ι4 will go to the input of the prohibition of the element 3§, prohibiting the arrival of the third pulse of a single code to the input of the counter Ι5. The same transfer signal will be sent to one of the inputs of the circuit And 4, allowing the arrival of the third impulse of a single code and a 2t — 1 delay element to the input of the second discharge of the counter 1t · The device state will change

10 01 10 О 0010

12 34 5,

i.e. will be equal to Pn, - 537.

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You can also check the operation of the proposed device at any stage of the multiplication process.

Thus, in the proposed device, the value of the product is set by the arrival of the 3rd pulse of a single code.

Thus, by grouping and eliminating end-to-end transfers, the frequency of switching the discharges of the counter does not decrease while reducing the amount of equipment.

Claims (1)

Claim A device for multiplying a binary number by a number, represented in a unitary code, containing counters and elements AND, characterized in that, in order to reduce hardware costs, it additionally introduces delay elements and prohibition elements, with the counting output of each-th counter ( = 1 — t-1, where t is the number of counters corresponding to groups of digits of the multiplicand code), is connected to the prohibition input of the ΐth element BANGE, the output of which is connected to (ί + 1) -nm counter, and the information input is from stroke v-th delay element, the inputs ^e ale ntov delay count input and The first counter is connected to the input of the device, the counting output of the ί-th and the counting input of the second digit of the (ΐ + 1) -th counter, working in addition, are connected respectively to the input and output of the corresponding element And, the other input of which is connected to the output of the ϊ-th element delays.