An improved hardware implementation of the one hot Residue Number System

Residue Number System (RNS) is a kind of numerical representation that allows to divide a given arithmetic operation done over a binary numerical representation with a determined number of bits, into several smaller operations that are performed in parallel, and use binary numerical representations of smaller number of bits. There are many possible implementations of RNS, but the one of highest processing speed is the so called One Hot Residue Number System (OHRNS). The main disadvantage of this implementation is that it requires order m² number of transistors for a modulo-m operation. In this paper a modified version of OHRNS, called OHRNS2 is presented, which perform as well as the original OHRNS, but with significant less hardware requirements. A generalized system is also presented, and called OHRNSn.