The residue number system (RNS) is an integer system capable of supporting high speed concurrent arithmetic. One of the most important consideration when designing RNS system is reverse conversion. The reverse converter for recently proposed for the four-moduli set {2n −1,2n,2n +1,22n+1 −1} is based on new Chinese remainder theorems II (New CRT-II) [6]. This paper presents an alternative archit...

This brief presents a fast sign detection algorithm for the residue number system moduli set {2 n+1 − 1, 2 n − 1, 2 n }. First, a sign detection algorithm for the restricted moduli set is described. The new algorithm allows for parallel implementation and consists exclusively of modulo 2n additions. Then, a sign detection unit for the moduli set {2 n+1 − 1, 2 n − 1, 2 n } is proposed based on t...

The aim of this note is to obtain a logarithmic asymptotics for number of periodic orbits on Veech’s space of zippered rectangles. The space of zippered rectangles is a finite cover of a set of full measure in the moduli space of abelian differentials with prescribed singularities. In particular, all periodic orbit in moduli space can be lifted to the space of zippered rectangles. Let R be a Ra...

In this paper, we investigate Residue Number System (RNS) to decimal conversion which is an important issue concerning the utilization of RNS numbers in Digital Signal Processing (DSP) applications. We propose a reverse converter using the moduli set {2n+1, 2n, 2n−1}. First, we show that this converter does not require the computation of multiplicative inverses. Next, we simplify the Chinese Re...

A finite set of residue classes ai (mod ni) with 1 < n1 < n2 < · · · < ns is called a covering system of congruences if every integer satisfies at least one of the congruences x ≡ai (mod ni). An example is the set {0 (mod 2), 1 (mod 3), 3 (mod 4), 5 (mod 6), 9 (mod 12)}. A covering system all of whose moduli are odd called an odd covering system is a famous unsolved conjecture of Erdös and Self...

This brief presents a fast sign detection algorithm for the residue number system moduli set {2n+1 − 1, 2n − 1, 2n}. First, a sign detection algorithm for the restricted moduli set is described. The new algorithm allows for parallel implementation and consists exclusively of modulo 2n additions. Then, a sign detection unit for the moduli set {2n+1 − 1, 2n − 1, 2n} is proposed based on the new s...

This paper presents an investigation into using a combination of two alternative digital number representations; the residue number system (RNS) and the signed-digit (SD) number representation in digital arithmetic circuits. The combined number system is called RNS/SD for short. Since the performance of RNS/SD arithmetic circuits depends on the choice of the moduli set (a set of pairwise prime ...

In most arithmetic systems the speed is limited by the nature of the building block which makes logic decisions and by the extent to which decisions of low order numeric significance can affect results of higher significance. In this contribution, an improved DNA representation [A. Fujiwara, K. Matsumoto, W. Chen, Procedures for logic and arithmetic operations with DNA molecules, Int. J. Found....