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An exact representation of the multiplying property of a binary rate multiplier (BRM) is derived. The equations are in a simple matrix form with a common multiplier matrix, the order and elements of which are easily predicted for BRM's of any given bit magnitude. Equations are developed for particular input constraints and may be combined when more than one input constraint condition exists. The equations are of a form which is particularly useful in the analysis of digital feedback systems using BRM's.