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Engineering Digital Design
book

Engineering Digital Design

by Richard F. Tinder
January 2000
Intermediate to advanced content levelIntermediate to advanced
884 pages
29h 39m
English
Academic Press
Content preview from Engineering Digital Design
208 CHAPTER 5 / FUNCTION MINIMIZATION
(uncomplemented f
i
) R-M expansion (PPRME). Each R-M coefficient is the set
g
i
=
%
ji
f
j
. (5.18)
obtained from the subnumbers of i by replacing m 1’s with 0’s in 2
m
possible ways in the
binary number corresponding to decimal i:
g
0
= f
0
···000
g
1
=⊕f (1, 0) = f
1
f
0
···001 ···000
g
2
=⊕f (2, 0) = f
2
f
0
···010 ···000
g
3
=⊕f (3, 2, 1, 0) = f
3
f
2
f
1
f
0
···011 ···010 ···001 ···000
g
4
=⊕f (4, 0) = f
4
f
0
···100 ···000
g
5
=⊕f (5, 4, 1, 0) = f
5
f
4
f
1
f
0
···101 ···100 ···001 ···000
·
·
·
g
2
n
1
=
2
n
1
%
i=0
f
i
.
Note that any g
i
in Eq. (5.18) is 1 if an odd number of f coefficients are logic 1, but is
0 if an even number of f coefficients are logic 1. If a Karnaugh map (K-map) of F
n
is
available, the values for the g
i
are easily determined by counting ...
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Publisher Resources

ISBN: 9780126912951