Discrete Mathematical Structures by Pearson

9-20 Discrete Mathematical Structures

(b) (1) The AND gate receives input x = 1, y = 0 and so xy = 0. The NOT produces the

result 1.

(2) The AND gate receives the signal x = 0 and y = 1 and hence output is 0 and NOT

gate changes it 1. Thus, the output is 1.

(3) The NOT gate receives the output 1 and hence changes it to 0. Consequently, the

output is 0.

Example 2 Draw the circuit for the function f (x, y) = x′y + xy′ and find the output for the input

x = 1 and y = 1.

x

y

x′y

xy′

x′

x

y′

f(x,y )=x′y+xy

′

Figure 9.7

Example 3 Construct a circuit that produces the function

f (x, y, z) = (x + y + z′)(xyz)

and find out the output corresponding to input ...