Stochastic Logic Implementations of Polynomials with All Positive Coefficients by Expansion Methods

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Abstract

This brief addresses computing polynomials with all positive coefficients whose sum is less than or equal to one using unipolar stochastic logic. The contributions of this brief are twofold. First, we present novel approaches to expanding polynomials that can be implemented using multiplexers in unipolar stochastic logic. These expansions are based on ascending-order, and Horner's rule based on descending-order. It is shown that the Horner's rule expansion is equivalent to OR-AND expansion. We also present another new expansion, referred as AND-OR. These expansions have not been presented in any prior work. Second, we also show that the proposed AND-OR expansion is logically equivalent to the prior double-NAND expansion. Furthermore, we show that the OR-AND circuits can be transformed into equivalent double-NOR circuits.

Original languageEnglish (US)
Article number8049504
Pages (from-to)1698-1702
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Volume65
Issue number11
DOIs
StatePublished - Nov 1 2018

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Keywords

  • AND-OR expansion
  • Horner's expansion
  • OR-AND expansion
  • Stochastic logic
  • ascending-order expansion
  • double-NAND expansion
  • double-NOR
  • multiplexers
  • polynomial expansion
  • tree expansion

Cite this

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title = "Stochastic Logic Implementations of Polynomials with All Positive Coefficients by Expansion Methods",
abstract = "This brief addresses computing polynomials with all positive coefficients whose sum is less than or equal to one using unipolar stochastic logic. The contributions of this brief are twofold. First, we present novel approaches to expanding polynomials that can be implemented using multiplexers in unipolar stochastic logic. These expansions are based on ascending-order, and Horner's rule based on descending-order. It is shown that the Horner's rule expansion is equivalent to OR-AND expansion. We also present another new expansion, referred as AND-OR. These expansions have not been presented in any prior work. Second, we also show that the proposed AND-OR expansion is logically equivalent to the prior double-NAND expansion. Furthermore, we show that the OR-AND circuits can be transformed into equivalent double-NOR circuits.",
keywords = "AND-OR expansion, Horner's expansion, OR-AND expansion, Stochastic logic, ascending-order expansion, double-NAND expansion, double-NOR, multiplexers, polynomial expansion, tree expansion",
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