Schaum's Outline of Discrete Mathematics, Third Edition (Schaum's Outlines)

CHAP. 15] BOOLEAN ALGEBRA 397

15.25. Express the outputYas a Boolean expression in the inputsAandBfor the logic circuit in Fig. 15-29.

Here a small circle in the circuit means complement. Thus the output of the three gates on the left areAB′,

(A+B)′, and(A′B)′. Hence

Y=AB′+(A+B)′+(A′B)′

Fig. 15-29

15.26. Draw the logic circuitLwith inputsA,B,Cand outputYwhich corresponds to each Boolean expression:

(a) Y=ABC+A′C′+B′C′; (b) Y=AB′C+ABC′+AB′C′.

These are sum-of-products expressions. ThusLwill be an AND-OR circuit which has an AND gate for each

product and one OR gate for the sum. The required circuits appear in Fig. 15-30(a)and(b).

Fig. 15-30

TRUTH TABLES

15.27. Find the output sequenceYfor an AND gate with inputsA,B,C(or equivalently forY=ABC) where:

(a) A= 111001 ;B= 100101 ;C=110011.

(b) A= 11111100 ;B= 10101010 ;C=00111100.

(c) A= 00111111 ;B= 11111100 ;C=11000011.