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222 CHAPTER 5 / FUNCTION MINIMIZATION

5.10 MULTIPLE OUTPUT FUNCTIONS WITH DON'T CARES

The problem of selecting an optimum bond set is further complicated by the presence of
don't cares in multiple output systems. Application of the CRMT minimization procedure
given earlier to such systems is illustrated by minimizing the following two four-variable
functions containing don't cares:

F(A, B, C, D) = y^ra(3,6, 8,9, 12, 15) + 0(1, 4, 5, 11)
and (5.53)
H(A, B, C, D) = ^m(l, 4, 7, 10, 12, 13) + 0(2, 5,6, 8, 11, 15).

The conventional fourth-order K-maps for functions F and H are shown in Fig. 5.8a.
The don't cares are so chosen as to best meet the requirements of the CRMT minimization
procedure for both functions, but with no guarantee of a two-function optimal result. The
bond sets are arbitrarily chosen to be {C, D} and {A, B}, respectively, for functions F and

\CD
AB\ 00 01 11 10

0 # 1 0
</> 4> 0 1

1 0 1 0

1 1 * 0

\CD
AB\ 00 01 11 10

00 0 0 1 1 0 0 m $ \B
A\ 0
1 t
01 1 m D WC
1 1 #
11 0
/
t 0 # 1
10
ZH
(a) (b)
FIGURE 5.8
(a) Conventional K-maps for functions F and H of Eqs. (5.53) and (b) their second-order compressions
for bond sets {C, D} and {A, B} showing minimum cover for each by using XOR-type patterns.