Core function of Residue Number System (RNS) for RNS to binary conversion and sign and parity detection in RNS domain

Residue Number System is a robust system that takes advantage of parallel addition, subtraction, and multiplication in modular levels. However it suffers from some drawbacks. Sign and Parity detection of RNS numbers and RNS to binary conversion are listed as some of these critical issues. In this work, we have proposed some techniques to solve the mentioned issues. These techniques have been proved mathematically and verified through extensive simulation.; We have proposed a technique called Shift and Scale, SAS, for RNS to binary conversion. In SAS technique, the core of any given RNS number is calculated, and then it is used to compute the corresponding binary number. In similar techniques, an ambiguity arises in computing the core value, but the ambiguity problem never occurs in SAS technique.; We have also proposed several techniques for sign and parity detection in RNS domain. Factor-2 Sign Detection Algorithm or Adaptive-Factor Sign Detection Algorithm can be used once the parity of the RNS number is known through another mechanism. Otherwise either Factor-2 Sign and Parity Detection Algorithm or Adaptive-Factor Sign and Parity Detection Algorithm can be employed. These techniques are based on iterative algorithms and the algorithm must be repeated once or several times to come up with the sign or parity. The advantage of these techniques is that all computations are performed in RNS domain and it is not required to convert the RNS number to binary. In Factor-2 algorithms a constant factor 2 is used to move any RNS number from ambiguous sign or parity area to unambiguous area in the range. In Adaptive- Factor algorithms the factor is changed based on the calculated core value. A Factor Table and a Parity Table is established that is indexed by the core value of RNS number.