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

406 BOOLEAN ALGEBRA [CHAP. 15

15.71. Find all possible minimal sums for each Boolean expressionEgiven by the Karnaugh maps in Fig. 15-41.

Fig. 15-41

15.72. Use a Karnaugh map to find a minimal sum for the Boolean expression:

(a)E=xy+x′y+x′y′; (b)E=x+x′yz+xy′z′.

15.73. Find the minimal sum for each Boolean expression:

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

15.74. Use Karnaugh maps to redesign each circuit in Fig. 15-42 so that it becomes a minimal AND-OR circuit.

Fig. 15-42

15.75. Suppose three switchesA,B,Care connected to the same hall light. At any moment a switch may be “up” denoted

by 1 or “down” denoted by 0. A change in any switch will change the parity (odd or even) of the number of 1’s. The

switches will be able to control the light if it associates, say, an odd parity with the light being “on” (represented

by 1), and an even parity with the light being “off” (represented by 0).

(a) Show that the following truth table satisfies these conditions:

T(A,B,C)=T( 00001111 , 00110011 , 01010101 )= 01101001

(b) Design a minimal AND-OR circuitLwith the above truth table.