A Class of Binary Divisions Yielding Minimally Represented Quotients

Abstract

Binary division methods employing a redundant quotient representation in which quotient digits assume the values 0, 1, or ?1 have been analyzed previously. The method in which partial remainders are always normalized is of particular interest; it yields quotients represented with a minimal number of nonzero digits for all divisors D in the range ??|D|??. This method is extended to yield minimally represented quotients for all normalized divisors.