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A bit-level systolic array for computing matrix x vector products is described. The operation is carried out on bit parallel input data words and the basic circuit takes the form of a 1-bit slice. Several bit-slice components must be connected together to form the final result, and the paper outlines two different ways in which this can be done. The basic array also has considerable potential as a stand-alone device, and its use in computing the Walsh-Hadamard transform and discrete Fourier transform operations is briefly discussed.