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

CHAP. 15] BOOLEAN ALGEBRA 405

Fig. 15-39

15.64. Find the output sequenceYfor an OR gate with inputsA,B,C(or equivalently forY=A+B+C) where:

(a) A=100011;B=100101;C=1000001.

(b) A=10000001;B=00100100;C=00000011.

(c) A=00111100;B=11110000;C=10000001.

15.65. Find the output sequenceYfor a NOT gate with inputAor, equivalently, forY=A′, where:

(a)A= 11100111 ; (b)A= 10001000 ; (c)A= 11111000.

15.66. Consider a logic circuitLwithn=6 inputsA,B,C,D,E,F, or, equivalently, consider a Boolean expressionE

with six variablesx 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6.

(a) How many different ways can we assign a bit (0 or 1) to each of then=6 variables?

(b) Find the first three special sequences for the variables (inputs).

15.67. Find the truth tableT=T(E)for the Boolean expressionE=E(x, y, z)where:

(a)E=xy+x′z; (b)E=xyz′+y+xy′.

15.68. Find the truth tableT=T(E)for the Boolean expressionE=E(x, y, z)where:

(a)E=x′yz′+x′y′z; (b)E=xyz′+xy′z′+x′y′z′.

15.69. Find the Boolean expressionE=E(x, y, z)corresponding to the truth tables:

(a) T (E)= 10001010 ; (b) T (E)= 00010001 ; (c) T (E)= 00110000.

15.70. Find all possible minimal sums for the each Boolean expressionEgiven by the Karnaugh maps in Fig. 15-40.

Fig. 15-40