Statistical properties of boolean variables generated by a class of binary arithmetic processes

Abstract

The statistical properties of variables generated by some common binary arithmetic operations are discussed. The binary arithmetic considered are add, subtract, two’s complement transformation, multiply, and divide. It is demonstrated that the serially generated variables for all these operations are stochastic for all conditions except when the input variables are at a maximum or minimum entropy condition. For stationary inputs, serially generated variables generally tend to become non-stationary in the wide sense. The use of Markov chain to model the add and subtract processes is also presented.