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This paper examines a number of stochastic computational elements employed in artificial neural networks, several of which are introduced for the first time, together with an analysis of their operation. We briefly include multiplication, squaring, addition, subtraction, and division circuits in both unipolar and bipolar formats, the principles of which are well-known, at least for unipolar signals. We have introduced several modifications to improve the speed of the division operation. The primary contribution of this paper, however, is in introducing several state machine-based computational elements for performing sigmoid nonlinearity mappings, linear gain, and exponentiation functions. We also describe an efficient method for the generation of, and conversion between, stochastic and deterministic binary signals. The validity of the present approach is demonstrated in a companion paper through a sample application, the recognition of noisy optical characters using soft competitive learning. Network generalization capabilities of the stochastic network maintain a squared error within 10 percent of that of a floating-point implementation for a wide range of noise levels. While the accuracy of stochastic computation may not compare favorably with more conventional binary radix-based computation, the low circuit area, power, and speed characteristics may, in certain situations, make them attractive for VLSI implementation of artificial neural networks.