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 ⅗≤|D|≤¾. This method is extended to yield minimally represented quotients for all normalized divisors.