基于4模集合{2~n-1,2~n+1,2~n,2^(2n-1)-1}剩余数转换器设计

An Efficient Reverse Converter for the 4-Moduli Set{ 2~n- 1,2~n+ 1,2n,2^(2n-1)- 1}

针对剩余数系统需要大动态处理范围的问题,提出了一个新的4基数模集合;并给出了相应的剩余数至二进制数转换算法和硬件实现。该算法采用4基数模集合{2n-1,2n+1,2n,22n-1-1},每个模的形式都具有2n±1的形式,模的动态范围达到5n-1;算法基于新中国剩余数定理2实现,模集合的乘法逆元全部属于闭合形式,硬件电路完全基于加法器构成。与同类模集合反向转换器相比,提出的转换器电路完全基于加法器构成,明显减小了转换器的电路延迟,有效地提高了集成度。

As residue number system（RNS） needs the moduli set with big dynamic range, a new four-moduli set and its high efficient residue to binary conversion algorithm are proposed, and the corresponding circuit is designed. The proposed algorithm uses the moduli set {2n-1,2n 1,2n,22n-1-1} which consists of four briefness modules and the dynamic range is up to 5n-1 bits. efficient RNS-to-binary converters for the proposed moduli sets based on new Chinese remainder theorem 2 （New CRT-Ⅱ） are presented. Due to the simple multiplicative inverses of the moduli set, the proposed converter employs adders as primitive operators. Experiments results indicate that the new reverse converter has superior area-time complexity in comparison with the reverse converters for several other using the 5n-1bits dynamic range moduli set.