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Finite word length arithmetic computational errors (due to roundoff, chopping, etc.), in on-line applications of the Widrow-Hoff LMS adaptive algorithm, result in statistical variations in the weight vector from the infinite precision arithmetic weight vector. These errors can be modeled as an additive driving noise in the weight computation algorithm, effecting weight mean and covariance convergence. Assuming stationary, independent Gaussian input data, the mean and covariance convergence conditions and bounds on the errors due to the additive noise are obtained. These bounds are tested for roundoff and chopping using 2's complement, fixed-point arithmetic with an adaptive noise canceller of Gaussian noise.