Exploiting redundancy in bit-pipelined rational arithmetic

Abstract

The authors develop and analyze a redundant continued-fraction representation of the rationals in the implementation of an arithmetic unit for computing the sum, difference, product, quotient, and other useful functions of two rational operands. Their representation of operands and results allows the computations of the unit to be performed in a signed bit-serial, online fashion. Several such units can then be interconnected for the computation of more complicated expressions in a pipelined manner. Redundancy is used to help achieve a small bounded online delay and uniform throughput.<>