The non-linear characteristic of core function of RNS numbers and its effect on RNS to binary conversion and sign detection algorithms

Residue number system (RNS) has been recognized as a robust method to perform computations in a parallel fashion. RNS operations provide us with the capability of solving a precise or fuzzy system using a low resolution multi-moduli system. Despite of the advantages of RNS operations in parallel addition, subtraction, and multiplication, it suffers from some drawbacks such as RNS to binary conversion, sign detection, parity detection, overflow detection, scaling and division by Burgess (1997), and Szaho and Tanaka (1967). Several techniques have been developed to alleviate these drawbacks. For instance MRC (mixed radix conversion) by Szaho and Tanaka (1967), New CRT II (Chinese residue theorem II) by Wang et al. (1998), and core function by Burgess (1997) and Gonella (1991) are some well-known techniques used for RNS to binary conversion. Our study is oriented upon core function. Core function has a non-linear characteristic that causes an ambiguity in RNS to binary conversion as well as sign detection algorithms. Our work is a discussion about the nonlinear characteristic of the core function and its effects on these algorithms. Also, we point to some solutions to alleviate or resolve any ambiguity due to this non-linearity.