SU1388843A1 - Device for comparing boolean derivatives - Google Patents

Abstract

This invention relates to the field of development tools for testing and instrumental control of digital devices. The purpose of the invention is to increase speed. The device contains two groups of inputs 1, 2, register 3, computing unit 4, containing n groups of arithmetic cells 5, outputs 6. It permits one to calculate the value vector of the Boolean derivative in one clock cycle. The code supplied to the first group of inputs determines the nature of differentiation (oriented, non-oriented, or refusal of differentiation) for each variable. Under the control of the code, the computing unit converts the vector of values of the Boolean function, nocTjmaroshchy to the second group of inputs, and the truth vector of the Boolean derivative. At the end of the clock cycle, the values of the Boolean derivative are written to the register triggers and removed from its outputs. 1 3.p. f-ly, 4 ill. S (L from 00 00 00 4 00 lit, iff - fi.g. {

Description

The invention relates to automation and computing and can be used in the design of test and instrumental control systems for digital devices.

The aim of the invention is to increase the speed.

FIG. 1 shows a block diagram of the proposed device for calculating Boolean derivatives in FIG. 2, an arithmetic cell structure; FIGS. 3 and 4; - signal graphs corresponding to various examples of differentiation of Boolean functions.

When the device for calculating ™ no Boolean derivatives (Fig. 1) contains inputs 14 t 9 ° Ie forming the first group of inputs, the second group of inputs 2,, 2, .. o, 2g (2 8) devices, eight-bit register 3, The unit of 2 8D triggers 3.32, ... Ze, computing unit 4, consisting of 3 sub-blocks 44,42,4j,

And it is equal to unity on those in the races on which the variable x x is functioning (decreasing) with increasing). At izvodna defined. dx;

mule

3 f (x) / Q

-d - i.x „,. . . , ,their

Eh.

.f (:

-u ui

, 1 5Xj ,, ..

and is equal to one in those in the bora, in which the function r (a) decreases (decreases) with decreasing

The arithmetic cells 5, 2 8 of the device outputs and the clock input of the device are denoted by 6, 6, respectively. , ..., 6g and 7.

Arithmetic cell 5 (Fig. .2). 30 consists of two multiplexers 8, and 8j, two elements AND 9, and 9, two elements OR 10 (and Yu, the UNEQUALITY element 11, two control inputs 12i and 12g, ..., two information-jg planting) of the variable x; 13i and 13, two outputs 14, and 14.

 The device is controlled by applying to the inputs 1,, 1, .., l, s the devices of the control: li, 40 hj, ..., h ;. According to the code combination h. ,, f, 3), the device performs the following transformations of the Boolean function with respect to the variable 00 — the Boolean function is not differentiated; -j 01 - the boolean function differentiates to increase; 10, the Boolean function is differentiated oriented to decrease; 11 - Boolean function differentiates neorien50

tirovano.

Consider the algorithm for calculating Boolean derivatives implemented by the device.

Derived -5 ---- Boolean function- 55

OH;

f (x), where,. .., x, 5 in the variable X; is called a function defined by the formula

Determining derivatives or several function variables can be considered a transformation using n n operators :.

... v.V, where. ®Ii, ® ... ®

At the same time, ® is the sign of the mode, 1 (, п) - the support does not change the vector of encapsulation. For example.

V, 1 „®1„., ® ... ®12® l; ., ® ..) u®I,;

, ® ... ®1, ®1,.

The operator and can be represented by signaling graphs

but). f (O) .- f (0);

fd) - fd),

if the Boolean function fails;

1 -f (x X. o

-g-- -I

S- (

, x.

@f (:

n

jXj + i 9 i-i:

Derivative ----- characterizes e xj

changing the function f (x) when changing the variable x; and is equal to one on those input sets on which the change in variable X; leads to a change in function.

a fCx)

Incremental derivative

UH;

is determined by the formula

fM

Eh

f (x.

-f (, .l e, 5... jX,. "

(+) 1

And it is equal to unity on those input sets on which the function f (x) increases (decreases) with increasing (decreasing) of the variable x ;. The decreasing derivative is determined by the form. dx;

mule

3 f (x) / Q,

-d - i.x „,. . . , ,their;, , . . x

Eh.

.f (:

-u ui

, 1 5Xj ,, .. jX,)

adine) variable x;

and is equal to one on those input sets on which the function f (x) is ascending (decreasing) with decreasing (increasing) of the variable x;

adine) variable x;

The derivation of derivatives with respect to all or several variables of a Boolean function can be viewed as its transformation using the product of the n operators :.

... v.V, where. ..®1 ;, ®й® ®Ii, ® ... ®

Moreover, ® is the sign of the direct product, 1 (, п) is an operator that does not change the vector of the Boolean function. For example.

V, 1 „®1„., ® ... ®12® l; ., ® ..) u®I,;

, ® ... ®1, ®1,.

The operator and can be represented by the following signal lines:

but). f (O) .- f (0);

fd) - fd),

if the boolean function is not differentiated;

(0) ®f (); f (0) ® f (l),

if differentiation is undirected, where the sign © denotes modulo two summation;

c) f (0) (0) f (l); fd) - f (0) f (l),

if the differentiation is oriented towards increasing, where through and 0 are indicated the operations of inversion and logical multiplication;

d) f (0) (0) f (l)

f (l) X .f (0) f (l)

if differentiation is focused on diminishing.

Consider the operation of a device for calculating Boolean derivatives in examples for the case of h 3 variables.

Example 1, The Boolean function is differentiated oriented to increase in variable x, is not differentiated to variable x, and differentiated oriented to decrease in variable x.

In this case, the conversion of the truth vector is described by the graph shown in FIG. 3

The first information inputs of the device are supplied with control signals h,, h, j, ..., hg. The values of h,, h are fed to the control inputs arif

subblock cells 4, ah

h and hj, h to the control inputs 4 2. and 4 5, respectively.

five

subblocks 4 2. and 4 5 respectively. For an increase-oriented differentiation of a Boolean function with respect to variable X, the control signals take the values: h (l,. To the values h, 0, corresponds to the absence of differentiation with respect to the variable Xj, Differentiation, oriented reduction to the variable X ,, is defined by a code combination,.

Signals f (0,0,0), f (0,0, l) f (0, l, 0), f (0, l, l) are sent to the second group of information inputs of the device 2, 22 .. ,, 2g , f (l, 0,0), f (l, 0 ,. 1), f (l, 0, l), f (l, l, 0), f (l, l, l), defining this Boolean function. These signals arrive at inputs 13, and 13 of each arithmetic cell 5 of subblock 4,. Through pins 12 and 12z, the values of h, 1, are supplied to the address inputs of multiplexers 8, and 8g.

Thanks to this, the signals formed on the second information

and- 5

- Yu

15

.

figm

30 gf20

25

35

When eininn40

the multiplexer inputs are output to their outputs, the outputs 14) and. 14 cells 5 subblocks

8, and 8j pe- As a result, 2 arithmetic 4 (there are

f values (0,0,0). f (0,0, l); f (0,0,0) (0,0, l); f (, 0) -f (0, l, l); f (0, l, 0) f (0, l, l); f (l, 0,0). f (l, 0, i); f (l, 0,0) -f (l, 0, l); f (l, l, 0) -f (l, l, l); f (1, 1, 0) -f (l, 1,1). From the outputs 14 and the arithmetic cells 5 of the sub-block 4, information is transmitted to the inputs of the sub-block 4.

Thanks to the connections at the inputs 13, and the arithmetic cells 5 of subblock 4 J, the signals f (0,0,0). F (0,0, l) are present; f (0, l, 0). f (0, l, l); f (0,0,0). f (0,0, l); f (0, l, 0), f (0, l, l); f (l, 0,0) -f (l, p, l); f (l, i, 0). f (l, l, l); (l, 0,0) -f (l, 6, l); f (l, l, 0) «f (l, l, l) -, respectively. Through the outputs 12, and 122 of the address inputs of the multiplexers 8, and 8, the arithmetic cells 5 of the subblock 4 2, the code combination 00 arrives. As a result, the information from the first information inputs of the multiplexers is transmitted to their outputs. Due to the presence of cross-links, the values of f (0,0,0) f (0,0,1) are present at the outputs of subblock 2; f (0,0,0) -f (0,0, l); f (0, l, 0). f (0, l, l); f (0, l, 0) -f (0, l, l); f (1.0.0) -. f (1.0.1); f (l, 0,0). f (l, 0, l); f (l, l, 0). f (l, l, l); f (l, l, 0). f (l, l, l).

Due to connections to exits 13; and 13 arithmetic cells 5 of subblock 4, signals (0,0,0) (0,0, l) are received; f (l, 0,0). f (l, 0, l); f (0,0,0) .. f (0,0, l); f (l, 0,0). f (l, 0, l); f (0, l, 0), f (0, l, l); f (l, l, 0). f (l, l, l); f (0, l, 0) f (0, l, l); f (l, l, 0) f (l, l, l). Through pins 12, and 12 to targeted

five

0

five

multiplexer inputs 5

8, and 8 arithmetic cells of subblock 4, served

quantities.

As a result

: ignals generated at third information inputs of multiplexers

8, and 8 2 are transmitted to their outputs. Due to the presence of cross-links at the outputs of subblock 4, the values f (0,0,0) f (0,0,1) f (l, 0,0) f (l OJ), f (0,0,0 ) f (0,0, l) f (lOQ) f 1.0,1); f (0, l, 0) -f (0, l, l) “xr (i, i, o) f (1,1.0; f (o, i, o). f (0,1,1)

ff (lJ.O) fCl, l, l); f (0,0,0). f (0,0, l) f (1,0,0) f (1,0,1); f (0 , 0,0) -f (0,0, l)

fV1,0,0) f (1,1,1); f (0, l, 0) f (0, l, l)

r (1,1,0) f (1,1,1); f (0, l, 0) -f (0, l, l) f (l, l, 0) fri ,,).

The signals from the outputs of subblock 4 pod-f (1, 0,0) ft) f (1,1,0); f (0,0,1) © f (0,1, 1);

to the information inputs register-f (1,0,1) ® f (1,1,1).

pa 3 and write to it at the back To the address inputs of the multiplexers

to the front of the sync pulse from the bus 7. At the re- 8, and V. through the pins 12, and IZj according to the result at the outputs of the device 6, is the code combination 01. Following 6j, .., 6g we have signals identical to the values obtained using the signal graph in fig. 3

Actually, the values formed on the second information inputs of the multiplexers are transmitted to the outputs 14 (Example 2, the Boolean function 10, and 14, and then by means of cross-differentiation by the variable of X ,, tied connections - to the outputs of the sub-block 4. differentiates non-oriented as a result; information inputs on variable x and differentiated D-flip-flops of register 3 are signaled to increase along the transitions rT0, 0.0) G (O, 1TD Cf (1,0,0) © The variable X ,. In this case, the vector is 5 ® f (llO); f (0,0, l) ® f (0, l, 1) 11 the fineness of f (x, x, x,) is converted (. J, 0, l) fflf ( , j 01, fTO, 0,0) ® according to the signal graph, reduced - ®f (07170) 3 f (1, 0,0) ®f (1, 1, 0); in Fig. 4.ff (0 , 0.1 ° THGTTTT) f (1, 0.1) ®f (1, 1,

L; Cf (0,0, OJ®fToTl, 0) f (1,0,0) ®

To the control inputs of the device

Signals arrive: h, 0; 20 ®f (l, 1.0) 1; f (O, 0.1) ef (O, T7T) h, l; h., l; .x f (l, 0.1) PG (1, 1, 1); f-f (0,0,0) ©

@f (0, l, 0) - f (l, 0,0) ®f (1, 1, 0) 3;

Through the second group of information inputs of the device 2, 2, „.., 2d to inputs 13, and 13/2 arithmetic

f (0, O, l) © f (0 ,,) f (l, 0, l) ® f (l, 1,1).

cells 5 of subblock 4, served on the back of the clock pulse, pony f (0,0,0), f (0,0, l), f (0, l, 0), f (0, l, l) , f (l, 0,0),. f (, 0, l), f (l, 1,0), f (1,1, 1) respectively. Ha the address inputs of the multiplexers Bf and 82 arithmetic cells 5 of subblock 4, code combination 00 comes in. As a result, the signals from the first information inputs of the multiplexers are transmitted to outputs 14, and 14 ...

Due to the presence of cross-links to the inputs 13, and 13g of the arithmetic cells 5 of the sub-block 4, signals f (0,0,0), f (0, l, 0), f (0., 0, l)

f (o, a, 1), f (uo, o), f (1,1,0),

f (l, 0, l), f (1,1,1).

stepping no bus 7, these signals are recorded in the D-flip-flops 3,, 3, ..., R and are present at the outputs 6 ,, 6, ..., 6g of the register 3. Therefore, 30 at the outputs of the device there are values formed according to the graph shown in FIG. four. .

Claims (2)

1. A device for calculating Boolean derivatives, comprising a register and a computing unit, the device clock input being connected to clock input 40 of the register, the output of which is I-I-device outputs, the first At the control inputs of the arithmetic one, which is connected to the cells, there are values h, - ozo: l of the first group of the block, -1, h, -l. Hence the signals,. the outputs, which are connected to the ... .. f, DZ Formational inputs of the register, characterized in that, in order to improve speed, the computing unit contains n groups of arithmetic cells (n is the number of variables), with the second group of device inputs connected. with the information inputs of the arithmetic cells of the first group of the computing unit, the information inputs of the j-th arithmetic cell (1,) of the i-th group (, n) are connected to the corresponding outputs of the arithmetic-id) f (l, l, l)); f (0,0,1) ® f (o, 1, 1); kih cells (1-1) -th group, outputs f (1, 0.1 X9f (1,151); f (0,0,0) © f (0,1,0); the arithmetic cells of the last grouping inputs of the multiplexers 8, and 8i are transmitted to their outputs 14, and 14. The compounds provide the presence at the outputs of subblock 4 the values f (0, Q, 0) ® f (0, l, 0); f (0., 0, l) © f (0,1,1); f (0,0 , 0) d) f (0, l, 0); f (0,0, l) © f (0, l, l); 50 f (l, 0,0) ®f (l, l, 0); f (l, 0, l) ®f (1,1,1); f (l, 0,0) ®f (1,1,0); f (1,0,1) @f (1,1,1). From the inputs of subblock 4, 55 signals f (0,0,0) ® f ((, l, 0); G (1,0,0) Ф are received by the inputs of the arithmetic cells 5 of sub block 4 by means of cross-links. f (0, O, l) © f (0 ,,) f (l, 0, l) ® f (l, 1,1). about the falling edge of the clock stepping no bus 7, these signals are recorded in the D-flip-flops 3, 3, ..., R and are present at the outputs 6, 6, ..., 6g of the register 3. Consequently, at the outputs of the device there are values formed according to the graph shown in FIG. four. . Invention Formula These terminals are connected to the outputs of the computation, the inputs of the first group of which are connected to the configuration inputs of the arithmetic cells. 2. A device according to claim 1, characterized in that the arithmetic cell contains two multiplexers, two elements AND, two elements NOT and the element UNEMINABLE, the tuning inputs of the cell with the control inputs of the first and second multiplexers, the outputs of which are connected to the outputs of the cell, the first the information input of which is connected to the first information input of the first multiplexer, the first inputs Sfl the first element AND and the element is UNCHARACTER, the input of the first element is NOT, the output of which is connected to the first input of the second element AND, the second input of which is connected to the second input of the element is UNIMKABLE which is connected to the second input of the first element And the second, third and fourth information inputs of the first and second multiplexers are connected to the outputs of the second element And, the first element And and the element NOT AVNOZNACHNOST respectively. 7 f 2 12i 9l fOi L (fdi 3z South R jr / 5 fie2 then 9} f {HO.Jf f (0,1,0) Mi, i) f (lO, Of f (1.0,1) jUioj ya /, /; . , -fr-. | pg (, J) X. x0; / l «/; W. (c) .SP (111} o .w tmii) .Qmo.i) .., o, 1) o- -jjst - a / G /, io) u IJ) f JIi.}, o} MJ, J} .o), (o.o, i) ) ) jd.o.o) ,one) i (i, W -wfuj; imo) ®Mi.o), moij} j (o, i.i) (0,0,0) фМго) Mo.i) ®j- (o, ii) ЩО) ®ЛШ) f (i, o.}) ®flm} f (i, uo) ej {j.w J {lOJ) Qf {n, J) Fi. mo, o} Jo-jJ i.o.oU (w.i) jio.o, owaoj) ShoM) She1} mip) a.i, i) f (i, w) fiw} jpta }, o) tI tolMiO, 1) (10,0) M0.1) then.oSho, nJd.o.OJMQ.i) T (Q. WjflQ. I / Ш r. OUd 1.1) (o-vmw) f (i. i, i) & (oo, o ®Mi.oi) Cf {lo, Q) .OjJ LfCo.oi) .W Cf (mj) f (ii.i) LiM MUlilm ® ®fni, ffff ®f (OV) .t) uf (ofifl) .1,) ®MW) J Sho.1 ®flaii, i) Cfllo, l) f, iff CKW) ®JiuW) .WOO) ®f (lW)  ®mi.io & ii.o.i} ® (wQ