Arithmetic properties of a class of hybrid number systems

In attempts to speed-up computer arithmetic, many researchers have investigated the arithmetic properties and practical implementations of non-weighted, residue systems (RNS). However, RNS's are not successful in those applications, such as division and magnitude comparison, where the result cannot be derived from a separate consideration of operand digits. In this paper, a class of hybrid number systems, namely, residue number systems with magnitude index (RNS with MI), have been considered under a more general formulation than that previously known. In these systems, numerical information is split into two separate parts, which are given a residue and a representation, respectively. The arithmetic properties of such systems have investigated in depth and it has been shown that these systems are suitable for fast, general purpose, arithmetic implementations.