Combinatorial logic based forward converters in residue number systems

A. Premkumar, M. Bhardwaj
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引用次数: 2

Abstract

The Residue Number System (RNS) offers unlimited opportunities for high performance arithmetic provided efficient forward and reverse converters could be constructed for the moduli set at hand. All forward conversion proposals to date, require some form of Read Only Memory (ROM) along with computational elements like Full Adders (FA). In this paper, we show that by formulating the forward conversion problem in terms of modular exponentiation and addition, we can achieve memory free conversion. We generalize our solution such that bit serial and bit parallel implementations can be derived by simply varying a parameter, namely, multiplexers. Apart from this formulation itself, the paper makes two other contributions. Firstly, it demonstrates an entirely new set of converters that use no look up. Secondly, we show how conversion complexity can be reduced significantly by sharing circuitry over several forward converters.
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基于组合逻辑的剩余数系统正演变换器
剩余数系统(RNS)为高性能算法提供了无限的机会,只要可以为手边的模集构造有效的正向和反向变换器。到目前为止,所有前向转换建议都需要某种形式的只读存储器(ROM)以及全加法器(FA)等计算元素。在本文中,我们证明了通过用模幂和加法来表述前向转换问题,我们可以实现无内存转换。我们推广我们的解决方案,使位串行和位并行实现可以通过简单地改变一个参数,即多路复用器来推导。除了这个公式本身,这篇论文还有另外两个贡献。首先,它演示了一套全新的不查找转换器。其次,我们展示了如何通过在几个正向转换器上共享电路来显着降低转换复杂性。
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