Showing papers on "Residue number system published in 1976"

On the Design of Modulo Arithmetic Units Based on Cyclic Groups

Abstract: Many of the modulo arithmetics can be considered as cyclic groups. A generalized method for implementing the cyclic groups is established based on a decomposed mapping approach. In order to obtain efficient implementation of cyclic groups, certain mapping relations and a proper binary encoding method are investigated. Furthermore, a new class of code, called the circulative code, is developed, and two methods for generating such a code are presented. Various modulo arithmetic units can then be easily designed through a unique formula and can also be machine implemented. The modulo arithmetic units using this design approach are usually simpler than those conventional ones.

Low-cost residue number systems for computer arithmetic

Abstract: The representation of integers by their residues with respect to a set of pairwise-prime moduli is known as the residue number representation system and has been shown to have several advantages over conventional number systems for digital computers. In this paper, residue systems are considered for which each modulus is of the form 2b-1. Such systems result in relatively high storage efficiency as well as simple algorithms for addition, subtraction multiplication, conversion, and reconversion; hence the name "low-cost." The question of existence for low-cost residue number systems is examined. It is shown that the additional storage requirement with respect to binary representation is at most one bit per word. Guidelines are given for optimal selection of the set of moduli to represent a desired range of integers. Algorithms for various operations in a low-cost residue system are described.