ic
Section 8.2 Logic Networks
649
table 8.6
x 1
x 2
Sum
1
1
10
1
0
1
0
1
1
0
0
0
table 8.7
x 1
x 2
s
1
1
0
1
0
1
0
1
1
0
0
0
table 8.8
x 1
x 2
c
1
1
1
1
0
0
0
1
0
0
0
0
We can express the sum as a single sum bit s (the right-hand bit of the actual sum) together with a single carry bit c; doing this gives us the two truth functions of Tables 8.7
and 8.8, respectively. The canonical sum-of-products form for each truth function is
s = x 1
′x 2 + x 1 x 2
′
c = x 1 x 2
An equivalent Boolean expression for s is
s = (x 1 + x 2 )(x 1 x 2 )′
Figure 8.14a shows a network with inputs x 1 and x 2 and outputs s and c. This device, for reasons that will be clear shortly, is called a half-adder.
x 1
x 2
s
c
s
(a) Half-adder
(b) Full-adder
Half-adder
Half-adder
x 1
c i – 1
c i
x 2
x 1
x 2
x 1
x 2
figure 8.14