Computationally Efficient Approach to Implementation of the Chinese Remainder Theorem Algorithm in Minimally Redundant Residue Number System

In this paper, we deal with the critical problem of performing non-modular operations in the Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used in many modern computer applications. Throughout the article, an efficient approach for implementing the CRT algorithm is described. The structure of the rank of an RNS number, a principal positional characteristic of the residue code, is investigated. It is shown that the rank of a number can be represented by a sum of an inexact rank and a two-valued correction to it. We propose a new variant of minimally redundant RNS, which provides low computational complexity for the rank calculation, and its effectiveness analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the excess residue modulo 2, the complexity of the rank calculation goes down from $O\left (k^{2}\right )$ O k 2 to $O\left (k\right )$ O k with respect to required modular addition operations and lookup tables, where k equals the number of non-redundant RNS moduli.

An Efficient Implementation of the CRT Algorithm Based on an Interval-Index Characteristic and Minimum-Redundancy Residue Code

The Chinese remainder theorem (CRT), which appeared in ancient China, is widely used in many modern computer applications. This paper presents the CRT implementation by using the interval-index characteristic and minimum redundancy residue code. The proposed algorithm does not use large modulo addition operations and provides low computational complexity compared to conventional non-redundant RNS. The efficiency factors of using the minimally redundant RNS increase with the number [Formula: see text] of non-redundant moduli, asymptotically approaching the threshold [Formula: see text]. The new approach presented here will have a significant impact on many non-modular operations in RNS arithmetic, which currently use the CRT.

An Efficient Current Mode MVL Residue Code Checker for Fault-Tolerant Arithmetic

Due to technology scaling, reliability has become one of the biggest challenges in VLSI circuits. A number of techniques have been introduced in the literature, especially for arithmetic and logic unit in computers. One of well-known schemes for fault-tolerant arithmetic is the use of arithmetic residue codes. A key problem with most of the previous works regarding residue-based checker is that these methods impose an unacceptable area penalty. In this paper, we propose a novel residue checker with current mode multi-valued logic (CMMVL). A plain design procedure with arbitrary modulo is introduced; also a more efficient integrated scheme for modulo 3 has been demonstrated. The results of the plain CMMVL scheme showed up to 19.5% and 42.9% lower delay and power consumption, respectively, compared with those of the conventional CMOS. Also, utilizing the integrated CMMVL provided, on average, about 17.7% and 80.2% lower delay and power consumption, respectively.