Abstract

The four-moduli Residue Number System (RNS) sets such as $(2^n-1, 2^n, 2^n+1, 2^{n+1}-1)$ have attracted a lot of researches during recent years. However, nowadays applications require higher dynamic range. This study introduces the RNS four-moduli set $(2^n, 2^n-1, 2^n+1, 2^{n+1}-1)$ which is obtained by enhancing the moduli set $(2^n-1, 2^n, 2^n+1, 2^{n+1}-1)$. This enhancement didn’t increase the total speed of RNS arithmetic unit since the critical modulo in both of the moduli sets $(2^n-1, 2^n, 2^n+1, 2^{n+1}-1)$ and $(2^n, 2^n-1, 2^n+1, 2^{n+1}-1)$ is $2^n+1$. Besides, an efficient RNS-to-binary converter for the proposed moduli set is designed using a two-level architecture where a previous converter design for subset $(2^n, 2^n-1, 2^n+1)$ is used in the first level and then a two-channel Mixed-Radix Conversion (MRC) algorithm is considered to achieve the final result. Comparison with a recently introduced RNS-to-binary converter for a four-moduli set with the same dynamic range show that the proposed design results in higher speed.

Keywords:

Mixed-Radix Conversion (MRC), Residue Number System (RNS), reverse converter,

References

Competing interests

The authors have no competing interests.

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Copyright

The authors have no competing interests.