Use of special modules of the residue number system for redundant representation

The residue number system (RNS), due to its properties, is used in applications in which high accuracy of computations is not required. Since carries are not transmitted between the moduli in the RNS, the performance is only restricted by the speed of the operations in each modulus. A new method of number representation using the redundancy is suggested in which $\{r^n-2, r^n-1, r^n\}$ is a set of the reference modules, where $r=2k+1$ and $k=1,2,3,\dots$. This method provides a significant reduction of delay of computations and conversions and leads to a simplification of schemes.