ic
Section 8.2 Logic Networks
651
x 1
(x 1 + x 2 )'
1
1
0
0
1
0
1
0
0
1
1
1
x 2
x 1
x 2
figure 8.16
1 Exercises 51 and 52 of Section 1.1 give truth tables for binary connectives that agree with the NAND and
NOR truth functions. There you were asked to prove that either of these two connectives is sufficient to write
any propositional wff; that is, you can write ~ , `, and ′ in terms of one of these connectives.
(x' 1 x' 2 )' = x 1 + x 2
(x 1 x 2 )'
(x 1 x 2 )'
((x 1 x 2 )'(x 1 x 2 )')' = x 1 x 2 + x 1 x 2 = x 1 x 2
(a)
(b)
(c)
(x 1 x 1 )' = x' 1
x 1
x 1
x 1
x 2
x 2
x' 2
x' 1
figure 8.17
The NOr gate (the NOT OR gate) and its truth function appear in Figure 8.18. An
exercise at the end of this section asks you to construct networks using only NOR
gates for inverters, OR gates, and AND gates.
1