SU1742811A1 - Device for computing symmetric boolean functions - Google Patents

Abstract

The invention relates to numeral technology and microelectronics and is intended to implement symmetric Boolean functions from n arguments. The purpose of the invention is to simplify the design of the device for calculating symmetric Boolean functions. This goal is achieved by the fact that the device for calculating symmetric Boolean functions from n arguments contains n elements NOT, n2 + n elements 2-2IL-2IL. n information inputs, n + 1 configuration inputs and output. The device works as follows. The binary inputs xi, X2xp are sent to the information inputs, the LAL ... Ln tuning settings, the values of which belong to the {0.1} set, go to the configuration inputs. At the output of the device, a symmetric Boolean function F F (XL) is realized, which is determined by the binary vector settings jr (F) (LOD1 ...., or). 1 ill., 1 tab. 3 C / V С

Description

The invention relates to computer-aided engineering and microelectronics, and is intended to implement symmetric Boolean functions (cf.) n variables.

The purpose of the invention is to simplify the construction of the device for calculating the comp.

A device for calculating sf.f. from n variables contains n elements NOT and n groups of elements 2-2И-2ИЛИ. It has n information and n + 1 configuration inputs and one output. And each; group. About 1.

2 p) contains n + 1 2-2IIL elements, and the 1st information input of the device is connected to the input of the 1st NO element, the output of which is connected to the first input of the 1st 2-2I-2IL element of the i-th group.

2n-i + 1), the second input of which is connected

with the i-th information input device. Next, the i-th setup input of the device is connected to the third input of the i-ro element 2-2I2IL of the first group, and (n + 1) -th setup input of the device is connected to the fourth input of the nth element 2-2I-2IL of the first group . The third entrance of the k-ro element 2-2I-2ILI

1st group (to 1. 2 n-l + 1; I 2, 3p)

connected to the output of the k-ro element 2-2I-2IL (1-1) -th group, the fourth input (n-l + 2) -th element 2-2I-2ILI (1-1) -th group is connected to the output ( n-l + 2) -ro element 2-2I-2IL (1-1) -th group. The output element 2-2I-2IL or n-th group is connected to the output device. The fourth input (M) of the 2-2I-2IL element of the first group is connected to the I-th tuning input of the device, the fourth input of the s-ro element of the 2-2I-2IL, or 1st group (s 1. 2 n-l) is connected to the output

(s + 1) -ro element 2-2I-2IL (1-1) -th group.

Element 2-2I-2ILI implements the Boolean function f ai33 3234, where an is binary

 00

variable assigned to the hth input of the element (h 1, 2, 3, 4),

The drawing shows a functional diagram of the device for calculating the comp. with n 5.

The device contains n 5 elements

2-2I-2ILI of the first group IIs, n-1 A

element 2-2I-2IL of the second group 2i

24, p-2 3 elements 2-2I-2IL or the third group 3i. Za and Zz. p-3 2 elements 2-2 and 2IL of the fourth group 4i and 42, one element 2-2 and 2 OR of that group 5, n 5 elements NOT 6i65, n 5 information inputs 7i7s, n + 1 6 tuning

inputs 8i8e and output 9.

A device for calculating sf.f. works as follows.

On the information inputs of the device

binary variables xi xn are supplied,

on the tuning inputs - the components of the binary vector n (F) (no, hipp), which determines the type of device realized by the sfb. n variables F in accordance with the following expression:

t

F v Hpn, tsO

where Fnl is elementary sb.f. from n variables with working number t (t 0, 1n).

At the output of the device, the value of sfb is formed. F on this set of values of variables xi, X2хп. For the considered example (item 5), binary variables xiХ5 (in arbitrary order) are fed to the information inputs 7i, ... 7s,

on the configuration inputs 8186 - the components of P5 of the binary vector n (F) (n, n,

.... p) implemented sb.f. F F (xi, X2xs).

Output 9 is implemented by sb.f. F, given by the vector n (F).

Example. Find the device configuration vector for the implementation of sb.f. F F (x i, X2. .... xs). represented by the following perfect disjunctive normal form:

F X1X2X3X4X5VxiX2X3X4X5VxiX2X3X4X X1X2X3X4X5 & 1X2X3X4X $ tf 1X2X3X4X5VX1X2X3X4X5.

The binary number N (truth table) of the given function F has the form

N (1110 1000 1000 0000 1000 0000 0000 0001).

It is obvious that N NI N2 N3, where NL N2. N3 - binary numbers of elementary sb.f. Ps. Fg, FS, respectively.

In this case, n (F) (1,1,0.0,0,1). Consequently, it is necessary to send a signal of a logical unit to the configuration inputs 8i, 82, 85 of the device, and a logical zero signal to the configuration inputs 8з, 84 and 8s.

The advantage of a device for calculating sb is a simple construction. The number of elements 2-2И-2ИЛИ, necessary for the implementation of the prototype, is

Snp 2n-1.

(one)

At the same time, the construction of the proposed device requires

S

n2 + n

(2)

elements 2-2I-2ILI.

The costs of equipment calculated by formulas (1) and (2) are tabulated.

Claims (1)

Invention Formula A device for calculating symmetric Boolean functions, containing n (n is the number of arguments of the function being implemented) of the elements NOT and n groups of elements 2-2ИИЛИ, i- (, 2п) of which contains n-i + 1 elements, with the i-th information input of the device connected to the input of the 1st element NOT, the output of which is connected to the first input of the j-ro element 2-2I-2, OR i-th group (i 1,2 n-l + 1), the second entrance which is connected to the i-th information input of the device, the 1st configuration input of the device is connected to the third input of the 1st element 2-2I-2IL, or the first group, (n + 1) - the first configuration input of the device is connected to the fourth input of the fifth item 2-2IL-2IL or the first group, the third input of the k-ro element 2-2I-2ILI of the 1st group (k 1, 2 n-l + 1.1 2.3p) connected to the output of the k-ro element 2-2I-2ILI (1-1) -th group, the fourth entrance (n-1 + 1) -th element 2-2I-2ILI (I-1) -th group yoedinen with output (p-1 + 1) element 2-2I-2ILI (1-1) -th group, the output of the element 2-2I-2ILI of the n-th group is connected to the output of the device, characterized in that, for the purpose of simplification, the fourth input of (I) -th element 2-2I-2ILI of the first group is connected to the 1st tuning input of the device, the fourth input of the s-ro element 2-2I-2ILI of the 1st group (s 1, 2n-l) is connected to the output (s + 1) -ro element 2-2 and 2 or (i) group.