A new redundant method on representing numbers with moduli set {3n, 3n −1, 3n −2}

The residue number system (RNS) is a system for representing numbers. It uses the residues of numbers with respect to a moduli set. Due to the possibility of parallel operations and smaller numbers used in this system in comparison with the binary equivalents, calculations are applicable with higher speed. Because of the suitable features of RNS, this system is used in many cases such as DSP devices and filters. Summation is the most widely used operation in this system, by use of which, conversions and other operations may be done. The method that has been offered in this paper is a new definition for numbers representation, using {3ⁿ-2, 3ⁿ-1, 3ⁿ} set. We use redundancy to improve the residues representation. This method makes conversions, summation and consequently subtraction and multiplication faster and makes the circuits of them much easier.