Minimization of Multiple-Valued Logic Expressions with Kleenean Coefficients
Summary :
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.
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- IEICE TRANSACTIONS on Information Vol.E79-D No.3 pp.189-195
- Publication Date
- 1996/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Computer Hardware and Design
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Yutaka HATA, Takahiro HOZUMI, Kazuharu YAMATO, "Minimization of Multiple-Valued Logic Expressions with Kleenean Coefficients" in IEICE TRANSACTIONS on Information,
vol. E79-D, no. 3, pp. 189-195, March 1996, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/information/10.1587/e79-d_3_189/_p
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@ARTICLE{e79-d_3_189,
author={Yutaka HATA, Takahiro HOZUMI, Kazuharu YAMATO, },
journal={IEICE TRANSACTIONS on Information},
title={Minimization of Multiple-Valued Logic Expressions with Kleenean Coefficients},
year={1996},
volume={E79-D},
number={3},
pages={189-195},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={March},}
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TY - JOUR
TI - Minimization of Multiple-Valued Logic Expressions with Kleenean Coefficients
T2 - IEICE TRANSACTIONS on Information
SP - 189
EP - 195
AU - Yutaka HATA
AU - Takahiro HOZUMI
AU - Kazuharu YAMATO
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E79-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 1996
AB - 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.
ER -
English
