Output probabilities of finite-state-machine elements are studied when the input of the machine elements is a random process. Delay element modulo m madder and modulo m multiplier are considered as the machine elements. A new approach to the problem is made by defining the trans¬formation matrices T and T for a modulo m adder and a modulo m multiplier respectively. By using these matrices, the output probabilities of the machine and the stochastic matrix of the output are given in explicit expressions, assuming that the input process is a finite-state, time-invariant Markov process. A few examples of the combinatorial circuit of these elements are also studied.
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