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This paper describes the theory and design of digital high-radix multiplier-dividers (Patent Pending). The theory of high-radix division is extended to high-radix multiplier-dividers that can perform fused multiplication and division operations using a single recurrence relation. With the fused implementation of multiplication and division, the two operations can be executed using a single instruction, implying only a single rounding operation. The recurrence relation is described, the quotient digit selection function derived, and important design parameters together with their optimal values and relations are defined. Efficient design procedure and implementation hardware are described and important system parameter values for various radix systems computed. Compared to pure dividers, the multiplier-divider requires a slightly more complex data path and quotient digit selection function.