Synthesis Method for Ternary Logic Function Based on NOR-Type Polypheck
Summary :
This paper is concerned with the synthesis of ternary logic function based on NOR-type polypheck. The system of fundamental operators consists of cyclic, inverse cyclic, logical sum and logical product. It is shown that any ternary logic function is represented by the logical sum of at most 2n-order terms. The simplification method in the binary logic system is extendedly applied to the ternary logic system. In synthesizing a ternary logic function based on NOR-type polypheck, the efficient tool, size of term, is newly-introduced. Size of term is defined by the total arithmetic sum of truth values of a term over all assignments of variable values. It has such characteristic that the decreased order of a term results in the increase of the size of the term. The utility of NOR-type polypheck is also discussed. The proposed method is applied to the ternary half-adder function as an example.
- Publication
- IEICE TRANSACTIONS on transactions Vol.E66-E No.5 pp.313-320
- Publication Date
- 1983/05/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Automata and Languages
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Michiaki YANAGITA, Yoshiaki MIYOSHI, Kyoichi NAKASHIMA, Kazuharu YAMATO, "Synthesis Method for Ternary Logic Function Based on NOR-Type Polypheck" in IEICE TRANSACTIONS on transactions,
vol. E66-E, no. 5, pp. 313-320, May 1983, doi: .
Abstract: This paper is concerned with the synthesis of ternary logic function based on NOR-type polypheck. The system of fundamental operators consists of cyclic, inverse cyclic, logical sum and logical product. It is shown that any ternary logic function is represented by the logical sum of at most 2n-order terms. The simplification method in the binary logic system is extendedly applied to the ternary logic system. In synthesizing a ternary logic function based on NOR-type polypheck, the efficient tool, size of term, is newly-introduced. Size of term is defined by the total arithmetic sum of truth values of a term over all assignments of variable values. It has such characteristic that the decreased order of a term results in the increase of the size of the term. The utility of NOR-type polypheck is also discussed. The proposed method is applied to the ternary half-adder function as an example.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e66-e_5_313/_p
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@ARTICLE{e66-e_5_313,
author={Michiaki YANAGITA, Yoshiaki MIYOSHI, Kyoichi NAKASHIMA, Kazuharu YAMATO, },
journal={IEICE TRANSACTIONS on transactions},
title={Synthesis Method for Ternary Logic Function Based on NOR-Type Polypheck},
year={1983},
volume={E66-E},
number={5},
pages={313-320},
abstract={This paper is concerned with the synthesis of ternary logic function based on NOR-type polypheck. The system of fundamental operators consists of cyclic, inverse cyclic, logical sum and logical product. It is shown that any ternary logic function is represented by the logical sum of at most 2n-order terms. The simplification method in the binary logic system is extendedly applied to the ternary logic system. In synthesizing a ternary logic function based on NOR-type polypheck, the efficient tool, size of term, is newly-introduced. Size of term is defined by the total arithmetic sum of truth values of a term over all assignments of variable values. It has such characteristic that the decreased order of a term results in the increase of the size of the term. The utility of NOR-type polypheck is also discussed. The proposed method is applied to the ternary half-adder function as an example.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Synthesis Method for Ternary Logic Function Based on NOR-Type Polypheck
T2 - IEICE TRANSACTIONS on transactions
SP - 313
EP - 320
AU - Michiaki YANAGITA
AU - Yoshiaki MIYOSHI
AU - Kyoichi NAKASHIMA
AU - Kazuharu YAMATO
PY - 1983
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E66-E
IS - 5
JA - IEICE TRANSACTIONS on transactions
Y1 - May 1983
AB - This paper is concerned with the synthesis of ternary logic function based on NOR-type polypheck. The system of fundamental operators consists of cyclic, inverse cyclic, logical sum and logical product. It is shown that any ternary logic function is represented by the logical sum of at most 2n-order terms. The simplification method in the binary logic system is extendedly applied to the ternary logic system. In synthesizing a ternary logic function based on NOR-type polypheck, the efficient tool, size of term, is newly-introduced. Size of term is defined by the total arithmetic sum of truth values of a term over all assignments of variable values. It has such characteristic that the decreased order of a term results in the increase of the size of the term. The utility of NOR-type polypheck is also discussed. The proposed method is applied to the ternary half-adder function as an example.
ER -
English
