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Reciprocals and reciprocal square roots are used in several digital signal processing, multimedia, and scientific computing applications. This paper presents high-speed methods for computing reciprocals and reciprocal square roots. These methods use a table lookup, operand modification, and multiplication to obtain an initial approximation. This is followed by a modified Newton-Raphson iteration, which improves the accuracy of the initial approximation. The initial approximation and Newton-Raphson iteration employ specialized hardware to reduce the delay, area, and power dissipation. The application of these methods is illustrated through the design of reciprocal and reciprocal square root units for operands in the IEEE single precision format. These designs are pipelined to produce a new result every clock cycle.