Efficient Sign-Detection-Scheme Using Modular Computation Technique for the Moduli Set {2<sup>n</sup>-1, 2<sup>n</sup>, 2<sup>n</sup>+1, 2<sup>(n+1)</sup>-1, 2<sup>2n</sup>-5}

Abstract

In computer arithmetic, one of the most important things to consider in hardware design is the ability of the system to detect and display numbers with their signs. This when properly managed will reduce errors and ensure hardware reliability. But interestingly, detecting and knowing the sign of a residue number during arithmetic operation is very difficult. Magnitude Comparison, Scaling and Number conversions are some of the other difficult operations in Residue Number System (RNS). Unlike the weighted number system, it is even extremely difficult to determine the sign of a number in an RNS architecture thereby hampering the full implementation RNS in general purpose computing. In this paper, an efficient sign detection algorithm for detecting the sign of a number in an RNS architecture is presented. In formulating the algorithms, X maximum, (X_max) is computed from the Dynamic Range, M=∏^k_i=1(m_i). Modular Computation Technique is employed as a converter to compute X from the residues (r₁, r₂, r₃) with respect to a given moduli set, say S= {m₁, m₂ ..., m_n}. X is positive if X-X_max<0 otherwise X is negative and the actual value is this case is computed as X-M. The moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1, 2⁽ⁿ⁺¹⁾-1, 2²ⁿ-5} is used for the system design implementation and for numerical illustrations. It is observed that the scheme effectively detects the sign of RNS numbers and theoretical analysis showed that simple hardware resources and low-power modular adders are used in the design. It is also observed that the scheme when implemented practically can help project RNS to be used in general purpose computing.