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This paper gives a detailed description of coefficient quantization errors of the distributed arithmetic, which means a recently introduced technique for the realization of the inner product of two vectors where conventional multipliers and adders are replaced by a memory and an accumulator. For systems excited by uniformly distributed white noise, an expression for the total power of the output error is derived. It may be compared with an earlier error analysis which, as will be shown, is too pessimistic for small vector lengths. In that case the total round-off error is partly correlated with the input signals while for large vector lengths usual errors due to the quantization of individual coefficients vanish and thus the total error can be described by an independent noise source at the output.