Comparison of Logic Operators for Use in Multiple-Valued Sum-of-Products Expressions

Takahiro HOZUMI  Osamu KAKUSHO  Yutaka HATA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E82-D   No.5   pp.933-939
Publication Date: 1999/05/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Multiple-Valued Logic and Its Applications)
Category: Logic Design
Keyword: 
logic synthesis,  cost reduction,  two-level circuits,  sum-of-products expression,  Shannon expansion,  

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Summary: 
This paper shows the best operators for sum-of-products expressions. We first describe conditions of functions for product and sum operations. We examine all two-variable functions and select those that meet the conditions and then evaluate the number of product terms needed in the minimum sum-of-products expressions when each combination of selected product and sum functions is used. As a result of this, we obtain three product functions and nine sum functions on three-valued logic. We show that each of three product functions can express the same functions and MODSUM function is the most suitable for reduction of product terms. Moreover, we show that similar results are obtained on four-valued logic.