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224 CHAPTER 5 / FUNCTION MINIMIZATION

The two CRMT optimized functions are now expressed together as

= A 0 C © BD ® ABCD ]
\ , (5.59)
=C®B®AD

representing a three-level system with a combined gate/input tally of 8/18, but with no
shared terms.
A comparison is now made with other approaches to the minimization of these functions.
The EV K-map minimum results read directly from the cover (shown by the loopings) in
Figs. 5.8b are

f F K. map = [AQCQ(B + D)](B + C + D)}
} > (5.60)

representing a three-level system having a gate/input tally of 8/17 with no shared terms.
Notice that function F is extracted (looped out) in maxterm code, whereas function H is
extracted in minterm code. The computer-optimized two-level SOP result is

f F = ACD + ABD + ACD + BD\
{ _ _ __ _ _ }, (5.61)
H=BCD+ACD+AB

with a total gate/input tally of 10/29 excluding possible inverters.
For further comparison, these two functions are minimized together as a system by using
canonical R-M forms. As a practical matter, an exhaustive search is not carried out on the
choice of don't cares and, consequently, an exact EXSOP result cannot be guaranteed.
However, a few trial-and-error attempts at minimization indicate that an exact or near-exact
result is obtained for function F if all 0's are taken as logic 1, but that for function H the
don't-care values are taken to be the same as those used by the CRMT method. Therefore,
from the conventional K-maps in Fig. 5.8a there result the following canonical R-M forms:
For F the R-M coefficients are

g\ = g 4 = g5 = gl = gS = g9 = g\0 = gl\ = g\2 = 1,

and for H they are

gl = g2 = 84 = g9 = I-

Introducing the g values for functions F and H into Equation (5.17) separately gives

F = D®B®BD® BCD ® A® AD® AC® ACD ® AB
= AD®ACD®BCD®A®AB®B
= AD®ACD®BCD®AB®B (5.62)