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

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.