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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
4.9 FACTORIZATION, RESUBSTITUTION, AND DECOMPOSITION METHODS 179
As a practical example of the application of Shannon’s expansion theorem, consider the
function
F(A, B, C, D) =
m(1, 3, 4, 5, 9, 10, 13, 14, 15), (4.71)
which is represented in the truth table of Fig. 4.48a and in the K-map of Fig. 4.48b. Applying
Eq. (4.69) for decomposition with respect to variables C and D gives the cofactors
F
0
=(A, B, 0, 0) =
¯
AB
F
1
=(A, B, 0, 1) = 1
F
2
=(A, B, 1, 0) = A
F
3
=(A, B, 1, 1) = A B
,
from which the function F can be written as
F
CD
(A, B, C, D) =
¯
C
¯
D(
¯
AB) +
¯
CD(1) +C
¯
D(A) +CD(A B)
=
¯
AB
¯
C
¯
D +
¯
CD + AC
¯
D + (A B)CD,
which could have been deduced ...
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Publisher Resources

ISBN: 9780126912951