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In keeping with the experimental nature of the Illinois Pattern Recognition Computer (ILLIAC III), the arithmetic units are intended to be a practical testing ground for recent theoretical work in computer arithmetic. This paper describes the use of redundant number systems and the design of a structure with which multiplication and division are executed radix 256. The heart of the unit is the stored-sign subtracter, a recently discovered member of the family of borrow-save subtracters and carry-save adders. A cascade of these subtracters, controlled by a multiplier recoder, provides multiplication. The same structure, controlled by a "model division" (a quotient recoder), performs division.