A New Representation of the Rational Numbers for Fast Easy Arithmetic

Abstract

A novel system for representing the rational numbers based on Hensel’s p-adic arithmetic is proposed. The new scheme uses a compact variable-length encoding that may be viewed as a generalization of radix complement notation. It allows exact arithmetic, and approximate arithmetic under programmer control. It is superior to existing coding methods because the arithmetic operations take particularly simple, consistent forms. These attributes make the new number representation attractive for use in computer hardware.