New CRT-based RNS converter using restricted moduli set

This paper presents a new RNS converter using any number of relatively prime moduli of the form 2ⁿ and 2ⁿ ± 1. With the exception of common 3 moduli sets such as {2ⁿ - 1,2ⁿ, 2ⁿ + 1}, FINS output converters based on the CRT require the computation of a sum of products modulo a large number. The new converter presented in this paper uses the fractional representation for the output and eliminates the requirement for multiplications, thereby reducing area and delay. Further area improvements are possible by exploiting the period of terms to be added. An algorithmic approach is used to obtain full adder-based architectures that are optimized for area and delay.