Use of gray decoding for implementation of symmetric functions

Osnat Keren; Ilya Levin; Radomir S. Stankovic

doi:10.1109/VLSISOC.2007.4402467

Use of gray decoding for implementation of symmetric functions

Osnat Keren, Ilya Levin, Radomir S. Stankovic

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity Reed-Muller (FPRM) expansions. The suggested method reduces the number of product terms, correspondingly, the implementation cost of symmetric functions based on these expressions by exploiting Gray decoding of input variables. Although this decoding is a particular example of all possible linear transformation of Boolean variables, it is efficient in the case of symmetric functions since it provides a significant simplification of SOPs and FPRMs. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method.

Original language	English
Title of host publication	2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC
Pages	25-30
Number of pages	6
DOIs	https://doi.org/10.1109/VLSISOC.2007.4402467
State	Published - 2007
Event	2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC - Atlanta, GA, United States Duration: 15 Oct 2007 → 17 Oct 2007

Publication series

Name	2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC

Conference

Conference	2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC
Country/Territory	United States
City	Atlanta, GA
Period	15/10/07 → 17/10/07

Keywords

Autocorrelation
Gray code
Linear transformation
Symmetric function

Access to Document

10.1109/VLSISOC.2007.4402467

Cite this

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title = "Use of gray decoding for implementation of symmetric functions",

abstract = "This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity Reed-Muller (FPRM) expansions. The suggested method reduces the number of product terms, correspondingly, the implementation cost of symmetric functions based on these expressions by exploiting Gray decoding of input variables. Although this decoding is a particular example of all possible linear transformation of Boolean variables, it is efficient in the case of symmetric functions since it provides a significant simplification of SOPs and FPRMs. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method.",

keywords = "Autocorrelation, Gray code, Linear transformation, Symmetric function",

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Keren, O, Levin, I & Stankovic, RS 2007, Use of gray decoding for implementation of symmetric functions. in 2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC., 4402467, 2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC, pp. 25-30, 2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC, Atlanta, GA, United States, 15/10/07. https://doi.org/10.1109/VLSISOC.2007.4402467

Use of gray decoding for implementation of symmetric functions. / Keren, Osnat; Levin, Ilya; Stankovic, Radomir S.
2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC. 2007. p. 25-30 4402467 (2007 IFIP International Conference on Very Large Scale Integration, VLSI-SoC).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Use of gray decoding for implementation of symmetric functions

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Keywords

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