# Help! Combinational Circuit Design

#### jdimpas

Joined Nov 8, 2011
1

Here's the given:

Design a circuit which will yield the product of two binary numbers n and m, where 00
n
11 and 000
m
101. For example, if n = 10 and m = 001, then the product is n x m = 10 x 001 = 0010.

Let the variables A and B represent the first and second digits of n ,respectively (i.e., in the above example A = 1 and B = 0). Let the variables C, D, and E represent the first, second, and third digits of m, respectively (in the above example C = 0, D = 0, and E = 1). Also let the variables W, X, Y, and Z represent the first, second, third, and fourth digits of the product. (In the above example W = 0, X = 0, Y = 1, and Z = 0.) Assume that m > 101 never occurs as a network input.

Design the network using only 2- and 3-input NOR gates and inverters. Try to minimize the total number of gates and inverters required. The variables A, B, C, D, and E will be available from toggle switches. Any solution that uses 16 or fewer gates and inverters (not counting the 5 inverters for the inputs) is acceptable.

here the original given scanned file from the book: http://i155.photobucket.com/albums/s318/jdimpas/logic1.jpg

#### Georacer

Joined Nov 25, 2009
5,182
Fair enough. Have you done any efforts towards solving the problem? You should post any thoughts or schematics you have come up so far, even if they are wrong.

The way I would go with it, is to notice that factor n is only two bits long. Thus, I could multiply m with both n's bits and then add the two results in an adequate way.

#### kwso

Joined Jan 3, 2012
2
You may solve it by drawing a complete truth table, ....then you will find each output as,

W = A.C
X = A.D + B.C
Y = A.E + B.D
Z = B.E

#### Georacer

Joined Nov 25, 2009
5,182
@kwso

Generally, it is a good practice to let the inquirer make an effort or two before handing him the answer.

If a ready answer is given straight from the beginning, no learning process takes place.