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

396 BOOLEAN ALGEBRA [CHAP. 15

Fig. 15-26

Fig. 15-27

15.23. Express the outputYas a Boolean expression in the inputsA,B,Cfor the logic circuit in Fig. 15-27.

The output of the first AND gate isA′BC, of the second AND gate isAB′C′, and of the last AND gate isAB′.

Thus

Y=A′BC+AB′C′+AB′

15.24. Express the outputYas a Boolean expression in the inputsA,B,Cfor the logic circuit in:

(a) Fig. 15-28(a);(b) Fig. 15-28(b).

Fig. 15-28

(a) The output of the AND gate isBCand so the inputs to the NOR gate areAandBC. Thus(A+BC)′is the

output of the NOR gate. Therefore, the inputs to the OR gate are(A+BC)′andB; henceY=(A+BC)′+B.

(b) The output of the NAND gate is(A′B)′and the output of the NOR gate is(A+C)′. ThusY=(A′B)′+(A+C)′.