Abstract: The residue number system (RNS), due to its
properties, is used in applications in which high performance
computation is needed. The carry free nature, which makes the
arithmetic, carry bounded as well as the paralleling facility is the
reason of its capability of high speed rendering. Since carry is not
propagated between the moduli in this system, the performance is
only restricted by the speed of the operations in each modulus. In this
paper a novel method of number representation by use of redundancy
is suggested in which {rn- 2,rn-1,rn} is the reference moduli set
where r=2k+1 and k =1, 2,3,.. This method achieves fast
computations and conversions and makes the circuits of them much
simpler.