Abstract
Number Systems are media for representing numbers; the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations. The other category, Un-Weighted Number Systems, of which the Residue Number System (RNS) belongs, do not carry weights but have not yet found widespread usage in general purpose computing as a result of some challenges; one of the main challenges of RNS is overflow detection and correction. The presence of errors in calculated values due to such factors as overflow means that systems built on this number system will continue to fail until serious steps are taken to resolve the issue. In this paper, a scheme for detecting and correcting overflow during RNS addition is presented. The proposed scheme used mixed radix digits to evaluate the magnitude of the addends in order to detect the occurrence of overflow in their sum. The scheme also demonstrated a simplified technique of correcting the overflow in the event that it occurs. An analysis of the hardware requirements and speed limitations of the scheme showed that it performs considerably better in relation to similar state of art schemes.
Highlights
Number Systems are media for representing numbers; the popular ones being the Weighted Number Systems (WNS), which sometimes propagate carries during arithmetic computations
Notwithstanding the fact that, Residue Number System (RNS) is currently being applied in Digital Signal Processing (DSP) intensive computations like digital filtering, convolutions, correlations, Discrete Fourier Transform (DFT) computations, Fast Fourier Transform (FFT) computations and Direct Digital Frequency synthesis [1] [2] [3]; researchers in the area are still working hard around the clock in order that the RNS becomes a general purpose processor
{ } the addition of two RNS numbers for the moduli set 2n −1, 2n, 2n +1 is presented; the technique evaluates the sign of an RNS number by performing a partial reverse conversion using the mixed radix conversion method
Summary
The Residue Number System (RNS) has gained prominence in recent years due to its seemingly inherent features such as parallelism and carry-propagation free. The scheme in [10] presented a scheme by an Operands Examination Method for overflow detection for ( ) the moduli set 2n −1, 2n , 2n +1 during RNS addition All these schemes either relied on complete reverse conversion process as in the case of [3], or other costly and time consuming procedures such as base extension, group number and sign detection as in [8] and [10]. { } the addition of two RNS numbers for the moduli set 2n −1, 2n , 2n +1 is presented; the technique evaluates the sign of an RNS number by performing a partial reverse conversion using the mixed radix conversion method.
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