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The main factors that affect the performance of residue number system (RNS) are speed and hardware complexity of the residue-to-binary converter. In this paper, two efficient reverse converters are proposed for the moduli sets [Formula: see text] and [Formula: see text] based on two-level approach. In the first level, a reverse converter is implemented based on new Chinese remainder theorem-I for the moduli set [Formula: see text]. The fourth modulus is joined in the second level for each converter and only simple binary adders are used in this level. The architecture of novel circuits mainly consists of simple adders thus leading to implementing efficient converters. To have a fair comparison, both unit gate model and simulation are used. The proposed converters and the recently represented converters have been implemented on Xilinx ISE 13.1 field-programmable gate array (FPGA) simulator to derive area and delay that are measured for the various ranges up to 256 bits. The experimental results show that the proposed converters have lower area–time complexity comparing to the state-of-the-art converter for similar moduli sets.

In this paper, a high speed residue to binary converter for three moduli set {2n - 1, 2n + 1, 2n} is presented in this paper, which uses two-part RNS and is based on mixed radix conversion (MRC). By using two-part RNS, the number of modulus in each part decreases; therefore the complexity of reverse converter is reduced. Also, the architecture of the proposed converter is based on subtractors and Multiplexers which are suitable for VLSI implementation. Reducing the number of modulus and simplifying the structure of the proposed converter lead to improvement of the latest presented converter in terms of area and delay. In order to obtain an accurate comparison, the proposed converter and the fastest designs were implemented on Xilinx 12.1 FPGA simulator, area and delay of each converter was measured for various word widths up to 64-bit. As the results indicated the novel proposed method has better Area and conversion time comparing to the previous designs.

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