ic
Section 8.2 Logic Networks
653
x 1 x 3 x 4 + x 2 also represents the function. Figure 8.19 shows the logic network for
this expression.
table 8.9
x 1
x 2
x 3
x 4
f( x 1 , x 2 , x 3 , x 4 )
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
figure 8.19
■
PraCtiCe 14 A hall light is controlled by two light switches, one at each end of the hall. Find (a) a
truth function, (b) a Boolean expression, and (c) a logic network that allows the light to be
switched on or off by either switch.
In some problems the corresponding truth functions have certain undefined
values because certain combinations of input cannot occur (see Exercise 35 at
the end of this section). Under these “don’t-care” conditions, any value may be
assigned to the output.
In a programming language where the Boolean operators AND, OR, and
NOT are available, designing the logic of a computer program may consist in part
of choosing appropriate truth functions and their corresponding Boolean expressions (see Exercise 36 of Section 1.1).