A New Approach to Overflow Detection in Moduli Set {2n-3, 2n-1, 2n+1, 2n+3}

Residue number system (RNS) is a non weighted number system, which speeds up arithmetic operations by dividing them into smaller parallel operations. This number system supports parallel calculations, limited carry propagation and low power consumption which is used in digital system processors. One of the problems in the above mentioned system is the issue of overflow. The previously proposed algorithms for detecting overflow need transforming numbers from residue number system to decimal system and making a comparison in decimal systems. We propose a new overflow detection algorithm for RSN moduli set {2ⁿ - 3, 2ⁿ - 1, 2ⁿ + 1, 2ⁿ + 3} which can be implemented by fewer components of circuits. In addition, the proposed method is faster than the previous ROM-based algorithms as there is no need to fully convert the number to the decimal system. Besides, having a limited number of components, delay in this circuit is lower than the previously proposed ROM-based reverse converting circuits in all moduli systems.