Prime and nonprime implicants in the minimization of multiple-valued logic functions
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Authors
Tirumalai, Parthasarathy
Butler, Jon T.
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Date of Issue
1989-05
Date
May 1989
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Abstract
We investigate minimal sum-of-products expres-
sions for multiple-valued logic functions for realization
by programmable logic arrays. Our focus is on expres-
sions where product terms consist of the MIN of inter-
val literals on input variables and are combined using
one of two operations - SUM or MAX. In binary
logic, the question of whether or not prime implicants
are sufficient to optimally realize all functions has been
answered in the affiimative. We consider the same
question for higher radix functions. When the combin-
ing operation is MAX, prime implicants are sufficient.
However, we show that this is not the case with SUM.
There is also the question of whether all functions can
be optimally realized by successively selecting impli-
cants that are prime with respect to the intermediate
functions. We show that this is not true either. In fact,
the number of implicants in a solution using prime
implicants successively can be sigmficantly larger than
the number of implicants in a minimal solution.
Type
Article
Description
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.
Proceedings of the 19th International Symposium on Multiple-Valued Logic, May 1989, pp. 272-279
Proceedings of the 19th International Symposium on Multiple-Valued Logic, May 1989, pp. 272-279
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Department of Electrical and Computer Engineering
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Citation
Prime and nonprime implicants in the minimization of multiple-valued logic functions", Proceedings of the 19th International Symposium on Multiple-Valued Logic, May 1989, pp. 272-279