Minimization of Multiple-Valued Logic Expressions with Kleenean Coefficients

Yutaka HATA
Takahiro HOZUMI
Kazuharu YAMATO

IEICE TRANSACTIONS on Information and Systems   Vol.E79-D    No.3    pp.189-195
Publication Date: 1996/03/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computer Hardware and Design
multiple-valued logic,  minimization,  Kleenean functions,  two-level realization,  sum-of-products expression,  

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This paper describes Kleenean coefficients that are a subset of Kleenean functions for use in representing multiple-valued logic functions. A conventional multiple-valued sum-of-products expression uses product terms that are the MIN of literals and constants. In this paper, a new sum-of-products expression is allowed to sum product terms that also include variables and complements of variables. Since the conventional sum-of-products expression is complete, so also is the augmented one. A minimization method of the new expression is described besed on the binary Quine-McCluskey algorithm. The result of computer simulation shows that a saving of the number of implicants used in minimal expressions by approximately 9% on the average can be obtained for some random functions. A result for some arithmetic functions shows that the minimal solutions of MOD radix SUM, MAX and MIN functions require much fewer implicants than those of the standard sum-of-products expressions. Thus, this paper clarifies that the new expression has an advantage to reduce the number of implicants in minimal sum-of-products expressions.