A Fault Tolerant Scheme for Detecting Overflow in Residue Number Microprocessors (International Journal of Engineering and Computer Science, 2018)
The decomposition of larger numbers into smaller ones termed as residues is the main operation behind the concept of Residue Number System (RNS); it possesses inherent features such as parallelism and independent digit arithmetic computations. These features of the RNS has made it desirable for applications that require intensive computations such as Digital Signal Processing (DSP), Digital Filtering and Convolutions. Overflow detection is one of the major challenges that confront the efficient implementation of RNS in general purpose computer processors. Overflow occurs in RNS when an illegitimate value is represented within legitimate range – Dynamic Range (DR) as if it is legitimate value. This misrepresentation of results, which usually arises during addition operations ultimately affects systems built on this Number System. It is therefore imperative that steps are taken not to only detect but correct the occurrence of overflow whenever it occurs. In this paper, an additive overflow detection and correction scheme for the moduli set  is presented. The scheme uses a redundant modulus to extend the DR of the moduli set. The proposed scheme is demonstrated theoretically to be an efficient scheme by comparing it to previous similar works.