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Arithmetic units are usually designed to perform addition and subtraction as quickly as possible, with multiplication as a good second. Division is sometimes added later, and a few workers have proposed hardware for other mathematical functions. The paper describes an attempt to design a combined division and square-root unit, drawing on the similarities of algorithm to be seen in comparing the pencil and paper calculations. The unit which results turns out to be capable of implementing a simple multiplication algorithm, and to be capable of fixed-point addition and subtraction. Speed of division and square root are very respectable, considering the simplicity of the approach and the technology used for the implementation. A custom-IC implementation would be very cost effective.