Question

A combinational circuit has four inputs (A, B, C, D) and three outputs (X, Y, Z). XYZrepresents a binary number whose value equals the number of 1’s at the input. For example if ABCD  1011,XYZ  011. (a) Find the minterm expansions for X,Y,and Z. (b) Find the maxterm expansions for Y and Z.

Answer 1

As per the given question,

The truth table are given below,

a) Min term expansion,

$F=x'yz+x'yz+x'yz+x'yz$

$F=\Sigma(7, 11,13, 14)$

b) similarly,

Max term expansion,

$F=\Sigma(0,1,2,3,4,5, 6,8,9,10,12,15)$