Adder-Only Reverse Converters for 5-Moduli Set {2 q , 2 q − 1, 2 q+1 ± 1, 2 q+2 − 1}

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We propose a balanced 5 -moduli set P = { 2 q , 2 q − 1 , 2 q + 1 − 1 , 2 q + 1 + 1 , 2 q + 2 − 1 } , for odd q ≥ 3 . Our reverse conversion scheme is based on a multi-stage new Chinese remainder theorem, where some of the difficult-to-derive multiplicative inverse coefficients are expressed as geometric series. Only carry-save and ripple-carry adders are used as components of the corresponding circuits. Analytical gate-level evaluations are performed on the proposed and reference converters, whose results are confirmed by the synthesis tool. A comparison of the converters for moduli sets with equal dynamic range shows that P is similar to previous 5-moduli set { 2 q , 2 q − 1 , 2 q + 1 , 2 q + 1 − 1 , 2 q − 1 − 1 } and shows slight advantage in delay and energy consumption.