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5.7 EXAMPLES OF MINIMUM FUNCTION EXTRACTION 215

negative-polarity CRMT form

G wx = (W + X + f 0')0(W + X + fi)0(W + X + f2)Q(W + X + f 3)
= (W + X + Y) 0 (W + X + Y) O (W + X + Z) 0 (W + X + Z)

= go O (X + gi) O (W + g2) O (W + X + g 3), (5-36)
which are read in maxterm code. From Eq. (5.21) the g coefficients become

Introducing these coefficients into Eq. (5.36) yields the absolute minimum EQPOS
expression

G WX = YQXQ(W + ZQF )
= Y O X O (W + Y) Q (W + Z)

= X O (W + Y) O (W + Z) (5.37)

that is seen to be a three-level function with a gate/input tally of 4/8.
The CRMT minimization process is repeated for the bond set {Y, Z} as depicted in
Fig. 5.5c. The CRMT expression now becomes

G YZ = (Y + Z + go) O (Y + Z + gl ) Q (Y + Z + g 2) O (Y + Z + g 3)

= (Y + Z + X-)Q( Y + Z + WO X)Q(Y + Z + W O X) O (Y + Z + X)
= goQ(Z+ gl)(Y + 82)(Y + Z + g3) (5.38)

for which the g coefficients are found to be

go = /o = X
gi = Qf (1,0) =WQX QX = W
g2 = Q/(2, 0) = WQXO X = W
g 3 = Q/(3, 2, 1, 0) = X O W Q X Q W = 1,

where use is made of g\ = Of (I, 0) = W in the last term for g 3. Then, introducing these
coefficients into Eq. (5.38) gives the absolute minimum result
G YZ = X O (W + Z) O (W + F), (5.39)

which is again a three-level function with a gate/input tally of 4/8, inverters excluded.
The same result is, in this case, obtained by minimizing a canonical R-M expansion of
Eq. (5.35), which becomes

G 4(W, X, Y, Z) = Q M(0, 1, 6, 7, 8, 10, 13, 15)
= go O (Af, + gi) O (M 2 + g 2) O (M 3 + g 3) O • • • O (M )5 +