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5.11 K-MAP SUBFUNCTION PARTITIONING FOR COMBINED CRMT 227

After partitioning, CRMT coefficients for function F\ become

g 0 = X®Z g 4 = X®Z

g\ = 1 g5 = 1
82 = Y g(, = Y
£3= 0 g 7 =0 .

The two-level minimization result for cells 100, 101, 111, and 1 10 is simply

ACX + ACX + ABY = A(X @ C + BY). (5.67)

Introducing the g coefficients into Eq. (5.66) and adding the two-level result gives the mixed
minimum result
FI = x © z © c © BY © AX © AZ © AC © ABY + A(x © c + BY)

= (x © o e AZ © Afly © A(x © c) + A(X © c + BY)
(5.68)

Applying the same procedure to the partitioned F 2 function gives the CRMT g coeffi-
cients

go = g4 = XZ g 2 = g6 = YZ
g { = g 5 = Z £3 = £7 = 0.

From the K-map for p2, the two-level minimum result is easily seen to be

ABCXY + ABCXY = ABY(X © C). (5.69)

Now introducing the g coefficients into Eq. (5.66) and adding the two-level result yields an
EXSOP/SOP minimum,

F 2 = XZ © CZ © BYZ © AXZ © ACZ © AfiFZ + Afi7(X © C)
= AXZ © ACZ © ABYZ + ABY(X © C)

= AZ[(X © C) © (BY)] + A(BY)(X © C). (5.70)

The combined two-function minimum result is now given by

f FI = A[Z © (X © C) © (BY)] + A(X © C + BY)]
\ - - \ , (5.71)
( F 2 = AZ[(X © C) © (BY)] + A(BY)(X © C) ]

which represents a five-level system with a combined gate/input tally of 11/24 excluding
possible inverters.