Digital Systems: Principles and Design

116

Digital Systems

Solution

Recall ORing rule; Y +

Y

= 1. (Equation 4.10d) We have the expression X + Y.Z. We first

convert it into standard SOP format using this rule. Therefore, SOP S is as follows:

S = X.(

Y

+ Y).(

Z

+ Z) + (X +

X

).Y.Z

= X.

Y

.

Z

+ X.Y.

Z

+X.

Y

.Z + X.Y.Z +

X

.Y.Z + X.Y.Z

= X.

Y

.

Z

+ X.Y.

Z

+ X.

Y

.Z +

X

.Y.Z + X.Y.Z

(Remove fourth term X.Y.Z occurring twice using rule X + X = X).

= S m(3, 4, 5, 6, 7). (Above expression first term is m(4), second is m(6), third m(5),

fourth m(3) and fifth m(7)).

We have to put 1s in cells 011, 100, 101, 110 and 111 for forming the SOP Karnaugh

map.

Now recall Table 5.5 and put 1s at appropriate minterm positions