dynamic range partitioning

Residue number system (RNS) is considered as a prominent candidate for high-speed arithmetic applications due to its limited carry propagation, fault tolerance, and parallelism in “Addition”, “Subtraction”, and “Multiplication” operations. Whereas, “Comparison”, “Division”, “Scaling”, “Overflow Detection” and “Sign Detection” are considered as complicated operations in residue number systems, which have also received a surge of attention in a multitude of publications. Efficient realization of Comparators facilitates other hard-to-implement operations and extends the spectrum of RNS applications. Such comparators can substitute the straightforward method (i.e. converting the comparison operands to binary and comparing them with wide word binary comparators) to compare RNS numbers. Dynamic Range Partitioning (DRP) method has shown advantages for comparing unsigned RNS numbers in the 3-moduli sets {2^n,2^n±1} and {2^n,2^n-〖1,2〗^(n+1)-1}, in comparison with other methods. In this paper, we employed DRP components and designed a unified unit that detects the sign of operands and also compares numbers, for the 5-moduli set γ={2^2n,2^n±1,2^n±3}. This unit can be used for comparison of signed and also unsigned RNS numbers in the moduli set γ. Synthesized comparison results reveal 47% (54%) speed-up, 35% (32%) less area consumption, 25% (24%) lower power dissipation, and 60% (65%) less energy for n=8 (16) in comparison to the straightforward signed comparator. According to the results of this study, DRP method for sign detection and comparison operations outperforms other methods in different moduli sets including 5-moduli set γ={2^2n,2^n±1,2^n±3}.