Analysis of stochastic logic circuits in unipolar, bipolar and hybrid formats

Implementations of polynomials and functions using stochastic logic have been of interest due to their low-area and high fault-tolerance properties. In stochastic logic, numbers are represented using unary bit streams where each bit is of same weight. If a number is represented in the range [0,1], the representation is referred to as unipolar. The representation is referred as bipolar if the number lies in the range [-1, 1]. Typically, inputs and outputs are in same format. However, sometimes the input and output may be in different formats; these are referred as circuits using hybrid formats. While analysis of unipolar stochastic logic circuits and bipolar logic circuits containing ex-or, ex-nor and multiplexors are well understood, the analysis of general bipolar stochastic logic circuits and hybrid logic circuits are not well understood. This paper presents general approaches to compute outputs of bipolar and hybrid stochastic logic circuits. It is shown that the analysis approach presented in this paper can form a basis for synthesis of stochastic logic circuits in bipolar and hybrid formats.