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226 CHAPTER 5 / FUNCTION MINIMIZATION

\B( •N
A \ 00 01 11 10
0 x ez x ez xeY©z X0Y0Z

1 i x x X+Y X+Y :

(a)

\BC
AX oo 01 11 / 10 •-..

0 XZ XZ Z(XeY) +iXY i Z(x©Y) + ;XY;
u. * ' * >j
1
h
/ 2
(b)
FIGURE 5.9
Combined CRMT and two-level minimization of a two-output system of six variables, (a) Third-order
compression of function FI, (b) third-order compression of function FI.

the minimum result

Z = [B © D © CD © AD] + A CD,
AC
= [fl©CD©AD]+ACD, (5.65)

where Z Ac is now a four-level function with a gate/input tally of 6/13. Recall that the CRMT
result in Eq. (5.30) is only a three-level function. The extra level in Eq. (5.65) compared to
Eq. (5.30) is due to the OR operator of the mixed form.
A more interesting example is the EXSOP/SOP partitioning of the two function system
shown in Figs. 5.9a and 5.9b. In this case, all entries in cells 100, 101, 111, and 110 for
function F\ are partitioned out (set to logic 0) for CRMT minimization, but are extracted
optimally as shown by the two-level minimum cover. Similarly, for function FI, terms XY
and XY in cells Oil and 010 are partitioned out of the CRMT minimization but are extracted
optimally in SOP logic. Also, the don't cares in the F^ K-map are set to logic 0 for both the
CRMT and two-level minimizations.
The minimization process is now carried out on both the function FI and F^ in such a
manner as to make effective use of any shared terms that may occur. By using Figs. 5.9a
and 5.9b, the function FI and F 2 are cast in the form of Eq. (5.17) to give

F\, F 2 = go 0 Cgi © Bg 2 © BCg 3 © Ag 4 0 ACss © A£g 6 © ABCgj. (5.66)