Design and Application of Mean and Square Root Circuits for Stochastic Computing

Stochastic computing (SC) is an unconventional computing paradigm that represents values using probabilities. This representation enables simple logic gates to perform complex arithmetic operations. This work proposes two low hardware-cost stochastic mean circuits for even and odd inputs, respectively, along with a high-accuracy stochastic square root circuit. The circuits are designed by considering correlation technique and achieve excellent performance. Experimental results demonstrate that the proposed mean circuits surpass previous counterparts in computing accuracy and hardware cost. For instance, the proposed 9-input mean circuit can achieve at least an 86.7% reduction in mean square error (MSE) and a 28.6% reduction in area. For the square root circuit, the proposed design achieves a reduction in MSE of at least 19.6%. The proposed circuits are further demonstrated with the Niblack binarization algorithm, which shows superior performance of accuracy.