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

408 BOOLEAN ALGEBRA [CHAP. 15

15.63. (a)Y=100001;(b)Y=00111000;

(c)Y=00110000.

15.64. (a)Y=100111;(b)Y=10100111;

(c)Y=11111101.

15.65. (a)A′=00011000;(b)A′=01110111;

(c)A′=00000111.

15.66. (a) 2 n= 26 =64.

(b)x 1 = 000 ··· 00111 ... 11 (32 zeros)(32 ones).

x 2 =( 00000000000000001111111111111111 )^2.

x 3 =( 0000000011111111 )^4.

15.67. (a) T (E)=01010011;(b) T (E)=00111111.

15.68. (a) T (E)=01000000;(b) T (E)=10001010.

15.69. Use truth tables for minterms in Example 15.13.

(a) E=x′y′z′+x′yz+xyz′.

(b) E=xy′z′+xyz.

(c) E=x′yz′+xy′z′.

15.70. (a)E=xy′+x′y+yz=xy′+x′y+xz′.

(b)E=xy′+x′y+z.

(c)E=x′+z.

15.71. (a)E=x′y+zt′+xz′t+xy′z

=x′y+zt′+xz′t+xy′t.

(b)E=yz+yt′+zt′+xy′z′.

(c)E=x′y+yt+xy′t′+x′zt

=x′y+yt+xy′t′+y′zt.

15.72. (a)E=x′+y; (b)E=xz′+yz.

15.73. (a)E=y′+z′t; (b)E=xy′+zt′+y′zt.

15.74. (a) See Fig. 15-45.

15.75. (b) See Fig. 15-46.

Fig. 15-45

Fig. 15-46