Design of Multiple-Valued Programmable Logic Array with Unary Function Generators

Yutaka HATA; Naotake KAMIURA; Kazuharu YAMATO

Design of Multiple-Valued Programmable Logic Array with Unary Function Generators

Yutaka HATA, Naotake KAMIURA, Kazuharu YAMATO

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This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of the array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log₂ppv + p(n-v) + 1) p^n-1 to realize any n-variable p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form PLA is the most useful in reducing the array size among the four form PLAs.

Publication: IEICE TRANSACTIONS on Information Vol.E82-D No.9 pp.1254-1260

Publication Date: 1999/09/25

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Type of Manuscript: PAPER

Category: Computer Hardware and Design

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Yutaka HATA, Naotake KAMIURA, Kazuharu YAMATO, "Design of Multiple-Valued Programmable Logic Array with Unary Function Generators" in IEICE TRANSACTIONS on Information, vol. E82-D, no. 9, pp. 1254-1260, September 1999, doi: .
Abstract: This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of the array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log₂ppv + p(n-v) + 1) p^n-1 to realize any n-variable p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form PLA is the most useful in reducing the array size among the four form PLAs.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_9_1254/_p

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@ARTICLE{e82-d_9_1254,
author={Yutaka HATA, Naotake KAMIURA, Kazuharu YAMATO, },
journal={IEICE TRANSACTIONS on Information},
title={Design of Multiple-Valued Programmable Logic Array with Unary Function Generators},
year={1999},
volume={E82-D},
number={9},
pages={1254-1260},
abstract={This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of the array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log₂ppv + p(n-v) + 1) p^n-1 to realize any n-variable p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form PLA is the most useful in reducing the array size among the four form PLAs.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Design of Multiple-Valued Programmable Logic Array with Unary Function Generators
T2 - IEICE TRANSACTIONS on Information
SP - 1254
EP - 1260
AU - Yutaka HATA
AU - Naotake KAMIURA
AU - Kazuharu YAMATO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 9
JA - IEICE TRANSACTIONS on Information
Y1 - September 1999
AB - This paper describes the benefit of utilizing the unary function generators in a multiple-valued Programmable Logic Array (PLA). We will clarify the most suitable PLA structure in terms of the array size. The multiple-valued PLA considered here has a structure with two types of function generators (literal and unary function generators), a first-level array and a second-level array. On investigating the effectiveness to reduce the array size, we can pick up four form PLAs: MAX-of-TPRODUCT form, MIN-of-TSUM form, TSUM-of-TPRODUCT form and TPRODUCT-of-TSUM form PLAs among possible eight form PLAs constructing from the MAX, MIN, TSUM and TPRODUCT operators. The upper bound of the array sizes with v UGs is derived as (log₂ppv + p(n-v) + 1) p^n-1 to realize any n-variable p-valued function. Next, experiments to derive the smallest array sizes are done for 10000 randomly generated functions and 21 arithmetic functions. These results conclude that MAX-of-TPRODUCT form PLA is the most useful in reducing the array size among the four form PLAs.
ER -