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202 CHAPTER 5 / FUNCTION MINIMIZATION

B
C ' '
00 01 11 10
0 ,^X)©Y 0 Y
/o 7P 1 3 2
/ /
(X/ [ Y 0 Y
4 5 7 6
/
C
(a) (b)

AB \ 00 01 ' 11 10

00 z") 0 Y Y
/ o 1 3 2
01 ^/©/x 0 X, 0
/ 4 5 / 7 6
/x 0 x/© VY Y,e/z^
12 13 15 / 14
10 0 0 0 \
8 9 11 \ 10,
D
(C)
FIGURE 5.2
Examples of complex XOR patterns, (a) Combined XOR-type patterns, (b), (c) Compound associative
patterns.

for the adjacent pattern (Y in the A domain and Y in the A domain), while Eqs. (3.4) are
applied to the offset pattern (Yand Y in the BC domain, and Yand Y in the BCdomain).
Notice that the O's in cells 3 and 7 play no role in this offset/adjacent pattern even though
they are included in the shaded loop covering this pattern.
For comparison purposes, the two-level minimum result is

HSOP = ABCXY + ABCX + ABCY + BCXY + ABCY + ABCY, (5.8)

which has a gate/input tally of 7/31. Comparison with Eq. (5.7) makes it clear that the three-
level result provides a better gate-minimum result but not necessarily a better performance.
To evaluate the relative performance of the two approaches, fan-in restrictions and gate
propagation delays would have to be established.
Compound (interconnected) associative patterns are also possible and may lead to gate-
minimum functions, although often of a higher level (hence slower) than those where there
is no interconnection between associative patterns. Two examples are given in Figs. 5.2b and
5.2c, both third-order compressions (hence three EVs). Function / is extracted in maxterm
code, yielding the four-level, gate-minimum result

IEQV/POS = [B + (A © X)] Q [Y + (A © 5)] O [A + Z], (5.9)