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5.9 INCOMPLETELY SPECIFIED FUNCTIONS 219

e \de
oo 01 11 10 r\ 00 01 11 10
c^ i
0 ^ 1 1 0 0 1 t> 1
*
1 1 0 0 1 1 1 1 * *

e e
oo 01 11 10 oo 01 11 10
c^ c^
0 < 0 0 1 0 ^ 1 * *
1 0 1 1 0 1 0 * * <

(a)

^ o
0 c@e 1

1 c© e ®

(b)
FIGURE 5.6
K-maps for the five-variable function / given in Eq. (5.46). (a) Conventional K-map array for bond
set {a, b}. (b) Third-order compression of function / for bond set [a, b] showing minimum cover by
using the adjacent XOR pattern in maxterm code.

(third-order compression) for bond set {a, b}. Recasting this function into the CRMT form
of Eqs. (5.16) and (5.17) gives

fab = abf 0 0 dbfi © ab/2 © abf 3
= db(c ®e)®ab<$> ab(c ®e}® abe
= gQ®bg l®ag 2®abgi (5.47)

with g values

Here, don't cares are set as 0o = 024 = 026 = 030 = 0 with the remainder equal to
logic 1. Introducing the values into Eq. (5.47) and simplifying yields the mixed polarity
result

f ab = c © e © be © be © a 0 abe
= a®e®c®bc® abe
= a<$>e@(b + c)® abe
= a®e @bc @dbe, (5.48)