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The inner product computer is a special-purpose computational unit intended to be used as an adjunct to a general-purpose digital computer to perform numerical processing tasks which previously exceeded the capacity of the general-purpose computer. The algorithmic structure of the inner product is briefly reviewed in the first section of this paper. Methods are described for computing the inner product of complex vectors with a series of four real inner products. Several hardware implementations of the inner product computer are described and then compared in terms of speed and complexity; a figure of merit is developed to simplify the comparison. The utility of this computational unit is demonstrated via the examination of a large-scale numerical problem, computerized three-dimensional x-ray reconstruction (computerized tomography) arising in the biomedical sciences. Finally, a comparison is given of the size of a general-purpose computer required to execute a large-scale processing task with that of an inner product computer to execute the same task. The inner product computer greatly reduces computational costs for the solution of a large class of problems, including computerized tomography, image restoration, weather forecasting, and economic modeling.