Modeling of Probabilistic Ripple-Carry Adders

Abstract

This paper proposes a mathematical model for probabilistic ripple-carry adders. The model gives explicit expressions for calculating error probabilities of sum and carry bits. The expressions show how errors propagate through the carry, which accumulate and eventually influence the correctness of a ripple-carry adder's outputs. The proposed model is flexible since it only requires mild assumptions on the probability distribution of noise. Hence, in addition to Gaussian, it is applicable to a wide class of distributions. We validate the model through HSPICE simulation. The model is able to predict error-rates of a simulated probabilistic ripple-carry adder with reasonable accuracy.