ic
Section 8.2 Logic Networks
645
Minimization
As already noted, a given truth function may be represented by more than one
Boolean expression and hence by more than one logic network composed of AND
gates, OR gates, and inverters.
■
PraCtiCe 11
a. Find the canonical sum-of-products form for the truth function
of Table 8.5.
b. Draw the network for the expression of part (a).
table 8.5
x 1
x 2
x 3
f(x 1 , x 2 , x 3 )
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
example 15
The Boolean expression
x 1 x 3 + x 2
′
has the truth function of Table 8.5. The logic network corresponding to this expression is given by Figure 8.12. Compare this with your network in Practice 11(b)!
figure 8.12
Definition eqUivALent BooLeAn exPressions
Two Boolean expressions are equivalent if they have the same truth functions.
We know that
x 1 x 2 x 3 + x 1 x 2
′x 3 + x 1 x 2
′x 3 ′ + x 1
′x 2
′x 3 + x 1
′x 2
′x 3
′