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5.7 EXAMPLES OF MINIMUM FUNCTION EXTRACTION 211

CD
AB\ 00 01 11 10 C ® D
00 1 1

01 1 1 1
(b)
11 1 0 1
t\
10 1 1 1 B« D i D1+ B
D© B
D . . ,
/'Z
(a) (c)
FIGURE 5.4
(a) Conventional K-map for function Z. (b), (c) Compressed EV K-maps for function Z representing
bond sets {A, B} and (A, C} showing minimum cover by using XOR-type patterns.

for a tractable CRMT minimization procedure, one that is suitable for classroom (or pencil-
and-paper) application.
A MORE COMPLEX EXSOP EXAMPLE Consider the function and its canonical R-M
transformation

Z 4(A, B, C, D) = ^m(l, 2, 4, 6, 7, 8, 9, 10, 15)
= 0m(l,2,4,6,7,8, 9, 10, 15). (5.26)

In Fig. 5.4a is shown the conventional K-map for function Z. In Figs. 5.4b and 5.4c are
shown the second-order compressed K-maps of function Z for bond sets {A, B} and {A, C},
respectively, which are representative of the six possible bond sets for two variables.
Considering first the bond set (A, B}, as depicted in Fig. 5.4b, and noting that the cell
entries are the / coefficients, the function Z 4 is recast into the following CRMT form:

Z AB = (AB)f 0 0 (AB)fi
= (AB)(C 8 D) © (AB)(C + D)® (AB)(C + D) © (AB)CD
= go@ Bgi © Ag 2 0 ABgi (5.27)

for which the CRMT coefficients are

go = fo = C © D

g2 - 0/(2, 0) = (C + D)eC0£)

g3 = e/(3, 2, 1, 0) = CD © (C + D) © 1 © CD = CD © CD © 0 © CD = CD,