The residue number system (RNS) is popular in high performance computation applications because of its carry-free nature. The challenges of RNS systems design lie in the moduli set selection and in the reverse conversion from residue representation to weighted representation. In this paper, we proposed a fully parallel reverse conversion algorithm for the moduli set {r – 2, r – 1, r}, based on ...

In this paper, we propose a novel high speed memoryless reverse converter for the moduli set {22n+1 − 1,2n,2n − 1}. First, we simplify the traditional Chinese Remainder Theorem in order to obtain a reverse converter that only requires arithmetic mod-(22n+1 − 1). Second, we further improve the resulting architecture to obtain a reverse converter that only uses Carry Save Adders and Carry Propaga...

The 4-moduli{ } set has been recently proposed for large dynamic range of 6n-bits .for this 4moduli set reverse converter design based on New CRT-1 and MRC has already been proposed. In this paper we propose reverse converter design for 4-moduli set{ }based on New CRT-II theorem to achieve more efficient residue number system(RNS) than the former one. The design is achieved using carry save add...

Abstract The three-modulus residue number system (RNS) based on the moduli set {2, 2–1, 2–1} has been recently introduced. The modulo (2+1)-free feature of this set enables it to provide fast realization of modular addition and multiplication circuits of RNS arithmetic unit. But, the latest design of the RNS to binary (reverse) converter for the moduli set {2, 2–1, 2–1} relies on large hardware...

The increasing usage of Residual Number System (RNS) in signal processing applications demands the development of new and more adaptable RNS moduli sets and arithmetic units. In this paper, a new reverse converter for moduli set {22n+1−1,22n ,2n− 1}, which can offers large dynamic range, is presented. We improved a previously introduced Mixed-Radix Converter architecture [1] for a high speed ha...

In this paper, a new four-moduli set {2n − 1, 2n, 2n+1 − 1, 2n+1 + 2n − 1} is proposed. The new moduli set choice because of a fast modulo 2n+1 + 2n − 1 adder has been proposed in literature. In order to work out the reverse converter for this moduli set, we introduce the technique for modulo 2n+1+2n−1 of a negative number and modulo 2n+1+2n−1 multiplication of a residue number by 2 and design ...

In this paper, a novel 3-moduli set { 2 − 1, 2, 2 − 1 } , which has larger dynamic range when compared to other existing 3-moduli sets is proposed. After providing a proof that this moduli set always results in legitimate RNS, we subsequently propose an associated reverse converter based on the New Chinese Remainder Theorem. The proposed reverse converter has a delay of (4n + 6)tFA with an area...

The reverse converter is the most complex and essential part of residue number system (RNS), and has a significant role in the general performance of RNS. Recently, it is showed that the reverse converter performance could be significantly improved using different adder’s type in the architecture of reverse converters, rather than just using one type of adder topology. This technical report aim...

In this paper, we propose the new moduli set { − , , + } with an efficient reverse converter. Experiments were performed on our converter and the state of the art using Xilinx ISE 14.3 software to target a Spartan 3 FPGA board. The results from these experiments suggest that on the average, the proposed converter outperforms the state of the art converters for the moduli sets { − , , + } and { ...