Set the Domain for Using 3-moduli set {2^n-1, 2^n, 2^n +1}

In special purpose circuits, the amount of energy consumed and the speed of operation are the main challenges. There are wide researches and methods to improve the performance of these types of circuits. One of these methods is to use a Residue Number System (RNS). In the RNS, there are a number of modules (channels) as a set to represent the number and perform parallel arithmetic operations. The most famous set is the 3-modlui set {2n-1, 2n, 2n +1}. The form of modules to the power of 2 makes it easier to perform binary computational operations. To use this system, you need to perform conversion operations from binary to residue (forward conversion) and residue to binary (reverse conversion). The greater the number of modules (channels) in the set, the higher the degree of parallelism of computational operations. In contrast, more complex forward and reverse conversion circuits are required. The overhead of conversion computing can reduce the efficiency of using this system, unless the number of consecutive operations is large enough to cover the conversion overhead time. In this paper, based on 3-moduli set {2n-1, 2n, 2n +1} evaluation, it was determined that for how many consecutive addition or multiplication operations, the use of RNS operations leads to greater speed. In this paper, we evaluate the carry propagation adder as the most popular adder and parallel prefix adder as the high speed adder. Also, the parallel block multiplier circuit was used to evaluate the multiplication operations. First, modular adder/multiplier, binary, and forward and reverse conversion circuits were implemented and synthesized. We used Synopsys Design Compiler, K-2015.06 version and 45nm technology. The results show that if the carry propagation adder is used, in modules with a width of more than 8 bits (n≥8), if the number of consecutive operations is at least 4, it will speed up the calculations. Likewise, in the multiplication operation and parallel prefix addition, the number of sequences is reduced to two.