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Comparison of numbers represented in residue number systems (RNS) is considered as a difficult RNS operation. However, RNS comparators faster than the straightforward “convert-to-binary and compare” alternative have been recently reported. Nevertheless, we present improved RNS comparators for three balanced 4-moduli sets (listed in the title, above) based on shortcut mixed radix conversion. Synthesis results show considerable improvements regarding some figures of merit. For example, 29% (24%) speedup (cost reduction) for the first moduli set, 18% cost reduction for the second, 28% lower power dissipation and 64% energy saving regarding the third one in comparison to previous works are achieved.

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RNS Comparison via Shortcut Mixed Radix Conversion: The Case of Three 4-Moduli Sets {2                     n  +  k                  , 2                     n                   ± 1,  m } ( m  ϵ {2                     n  + 1  ± 1, 2                     n  − 1  − 1})