The residue number system (RNS) is a carry-free number system which can support high-speed and parallel arithmetic. Two major issues in efficient design of RNS systems are the moduli set selection and the residue to binary conversion. In this paper, we present two efficient residue to binary converters for the new three-moduli set {2, 2 + 1, 2 – 1}. This moduli set consists of pairwise relative...

This paper presents a general architecture for designing efficient reverse converters based on the moduli set {2α, 22β+1-1, 2β-1}, where β ≺ α 2β, by using a parallel implementation of mixed-radix conversion (MRC) algorithm. The moduli set {2α, 22β+1-1, 2β-1} is free from modulo (2k+1)-type which can result in an efficient arithmetic unit for residue number system (RNS). The values of α and β c...

Automatic detection and correction of errors in the residue number system involves the conversion of residue representations to integers and base extension. The residue number system is generally restricted to moduli that are pairwise relatively prime. In this paper we consider error detection and correction using a moduli set with common factors. A method to construct a moduli set that leads t...

Residue Number System is a kind of numerical systems that uses the remainder of division in several different moduli. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers will increase the speed of the arithmetic operations in this system. However, the main factor that affects performance of system is hardware complexity of reverse converter. Reverse co...

String theoretic axion is a prime candidate for the QCD axion solving the strong CP problem. For a successful realization of the QCD axion in string theory, one needs to stabilize moduli including the scalar partner (saxion) of the QCD axion, while keeping the QCD axion unfixed until the low energy QCD instanton effects are turned on. We note that a simple generalization of KKLT moduli stabiliz...

In this paper, we propose a new 4-moduli set {2n+ 3, 2n+ 2, 2n+ 1, 2n} that increases the dynamic range and the processing parallelism enabling efficient reverse conversion. First, we assume a general 4-moduli set {mi}i=1,4, m1 > m2 > m3 > m4, with the dynamic range M = ∏4 i=1 mi and introduce a modified Chinese Remainder Theorem (CRT) that requires mod-m4 instead of mod-M calculations. Subsequ...

We prove there is no infinite set of congruences with: every integer satisfying exactly one congruence, distinct moduli, the sum of the reciprocals of the moduli equal to 1, the lcm of the moduli divisible by only finitely many primes, and a prime greater than 3 dividing any of the moduli.

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...

In this paper we first study the moduli spaces related to Calabi-Yau manifolds. We then apply the results to the following problem. Let C be a fixed Riemann surface with fixed finite number of points on it. Given a CY manifold with fixed topological type, we consider the set of all families of CY manifolds of the fixed topological type over C with degenerate fibres over the fixed points up to i...

In this paper, a new reverse converter for the moduli set {2n, 2n–1, 2n–1–1} is presented. We improved a previously introduced conversion algorithm for deriving an efficient hardware design for reverse converter. Hardware architecture of the proposed converter is based on carry-save adders and regular binary adders, without the requirement for modular adders. The presented design is faster than...