Discrete Mathematical Structures by Pearson

Boolean Algebra 9-17

= x′(y + y′)(y + z′) (Distributive law)

= x′ 1(y + z′) (Complement law)

= x′(y + z′) = x′y + x′z′

Example 5 Simplify the following Boolean function f (x, y, z) to minimum where

f (x, y, z) = xyz + xyz′ + xy′z + x′yz + xy′z′.

Solution:

f (x, y, z) = xyz + xyz′ + xy′z + xy′z′+ x′yz

= xy(z + z′) + xy′ (z + z′) + x′yz

= xy 1 + xy′ 1 + x′yz

= xy + xy′ + x′yz

= x (y + y′) + x′yz

= x1 + x′yz

= x + x′yz

= (x + x′)(x + yz)

= 1(x + yz)

= x + yz

9.4 SWITCHING NETWORK FROM BOOLEAN EXPRESSION

The Boolean algebra helps in designing electrical circuits from Boolean expressions using logic

gates, which are simple devices that accept one or more input ...