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Residue number system (RNS) operations have no carry between different residue digits. Addition, subtraction, and multiplication run on a residue digit independently from computations on other digits. This independency reduces the time needed to perform residue-based arithmetic operations compared with binary based operations. Therefore, RNS is used efficiently in some digital signal processing and cryptographic applications that require high-speed computations. Selecting the proper moduli set is a very important step in utilizing RNS to serve the above-mentioned applications. The moduli set selection is determined by the dynamic range, the number of moduli and the form of moduli targeted. While some applications can be well served by a three-moduli set, other applications require a wider dynamic range, a higher level of parallelism, and moduli forms that ease the residue-to-binary conversion and arithmetic operations within any RNS-based processor. The dynamic range is determined by the product of all moduli comprising the moduli set. Increasing the magnitude of a modulus within a set (i.e., vertical extension) achieves a wider dynamic range. Another way of achieving the same goal is by increasing the number of moduli (i.e., horizontal extension), which also leads to a higher level of parallelism required by specific applications like cryptography. The forms of moduli are also crucial in determining the speed of residue-to-binary conversion and residue-based arithmetic computations. This design is based on the residue-to-binary converter for the four moduli set using Verilog HDL and tested with an 8-Tap FIR filter application using Verilog HDL with Matlab.
Reference Paper-1: A Residue-to-Binary Converter for the Extended Four-Moduli Set
Author’s Name: Ahmad Hiasat
Source: IEEE TRANSACTIONS ON VERY LARGE-SCALE INTEGRATION (VLSI) SYSTEMS
Year: 2017
Reference Paper-2: Forward and Reverse Converters and Moduli Set Selection in Signed-Digit Residue Number Systems
Author’s Name: Andreas Persson and Lars Bengtsson
Source: Springer
Year: 2008
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SIMULATION VIDEO DEMO-Four Moduli
SIMULATION VIDEO DEMO-Four Moduli with 8-Tap FIR Filter
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