Page 257 - Engineering Digital Design

228 CHAPTER 5 / FUNCTION MINIMIZATION

The OR operators in Eqs. (5.71) add an extra level of path delay compared to forms
that are exclusively EXSOP/SOP. This can be demonstrated by avoiding the partitioning of
function F\ . When this is done the CRMT g coefficients become
go = x © z g4 = z

gl=l g 5=0

1©F = Y.

Introducing these g coefficients into Eq. (5.66) gives the EXSOP/SOP result

F 1 =X©Z©C©£ 7 © AZ ®ABXY® ABCY
= (X e C) ©AZ© BY @ABY(X © C)
= [ABY(X © C)] © (AZ) © (BY), (5.72)

which is a four-level function with a gate/input tally of 7/15, exclusive of inverters. This
compares to the mixed five-level function FI in Eqs. (5.71), which has a gate/input tally of
8/16.
Subfunction partitioning in maxterm code is equally effective in facilitating the min-
imization process. As a simple example, consider the function FCD in Fig. 5.8b and the
EQPOS CRMT form

FCD = go O (D + £,) O (C + # 2) O (C + D + g 3), (5.73)

which follows Eq. (5.20). Proceeding with the CRMT minimization, with B partitioned out
of the term A • B in cell 10, gives the CRMT g coefficients

go = A # 2 = A O A = 0
g l=AQBQA = B g 3 = AOBQAQB = l.

Introducing these coefficients into Eq. (5.73) and adding the two-level result gives

F CD = [A O (B + D) O C] • (B + C + D), (5.74)

which is exactly the same as the K-map minimum result in Eqs. (5.60).
Notice that the mixed CRMT/two-level method requires that the partitioning be carried
out in either minterm or maxterm code form. Thus, if subfunctions of the type X + Y are
partitioned, the entire minimization process must be carried out in minterm code. Or, if terms
such as X • Y are partitioned, the minimization process must be carried out in maxterm code.
Note that either X or Y or both may represent multivariable functions or single literals of
any polarity.