Thermometer code based modular arithmetic

Abstract

This paper presents a novel approach to perform modular arithmetic addition and subtraction using base-1 thermometer code data format for operands corresponding to the residues of the same modulus. Two n-bit thermometer code operands are first concatenated and logically shifted to produce a normalized 2n-bit thermometer code intermediate sum. Modulo operation is then applied to this 2n-bit intermediate sum to produce an n-bit datum corresponding to the modular sum of the two input operands. This approach greatly simplifies the modulo addition operation by eliminating the carry bit propagation during the arithmetic operation encountered when using the conventional base-2 binary code data format. It also enables practical applications of modular arithmetic for signal processing algorithms in a very efficient way. Circuit for implementing the modular arithmetic units using multiplexers and basic logic gates are also described in this paper.