Prime and nonprime implicants in the minimization of multiple-valued logic functions
Butler, Jon T.
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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.
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
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Kerkhoff, Hans G.; Butler, Jon T. (1987-07);As in binary, a multiple-valued programmable logic array (PLA) realises a sum-of-products, expression specified by the user. However, in multiple-valued logic, there are many more operations than in binary, and an important ...
Bender, Edward A.; Butler, Jon T. (1989-01);While the use of programmable logic arrays in modern logic design is common, little is known about what PLA size provides reasonable coverage in typical applications. We address this question by showing upper and ...
Schueller, Kriss A.; Butler, Jon T. (1991-05);A symmetric multiple-valued function can be realized as the disjunction of fundamental symmetric functions. A simpler disjunction can be formed when the latter functions combine in the same way that minterms combine to ...