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214 CHAPTER 5 / FUNCTION MINIMIZATION

offers another comparison and is

Z = BCD + ABD + BCD + BCD + ABC (5.34)

with a gate/input tally of 6/20, again excluding inverters.
Comparing the results for the four methods used to minimize function Z given by
Eqs. (5.28) through (5.34), it is clear that the CRMT results in Eqs. (5.28) and (5.30) are
competitive with the other methods. However, only the CRMT result in Eq. (5.30) is an exact
EXSOP minimum result. As will be demonstrated further by other examples, the CRMT
and EV K-map methods of minimization tend to yield results that are typically competitive
with or more optimum than those obtained by the other methods, including computerized
two-level results. These observations are valid for relatively simple expressions amenable to
classroom methods. No means are yet available for making a fair comparison of the CRMT
approach with related computer algorithmic methods.

AN EQPOS EXAMPLE Consider the four variable function G and its canonical R-M
transformation

G(W, X, Y, Z) = [~J M(0, 1, 6, 7, 8, 10, 13, 15) = Q M(0, 1, 6, 7, 8, 10, 13, 15),
(5.35)

which follows from Eqs. (5.19). The conventional (1's and O's) K-map for this function
is shown in Fig. 5.5a. Begin with the CRMT minimization method applied to bond set
{W, X} as depicted in Fig. 5.5b, which is a second-order compression of the function G.
From Eqs. (5.20) and (5.21) and for bond set {W, X}, this function is represented in the

\YZ Y)
WX\ 00 01 11 10 (v

00 0 0 (z z)

01 0 0 (b)

11 0 0

10 0 0

(a)

FIGURE 5.5
(a) Conventional K-map for function G. (b), (c) Compressed EV K-maps of function for bond sets
{W, X} and {Y, Z} showing minimum cover by using XOR-type patterns.