We built and tested the first hardware implementation of Phatak’s Quotient-First Scaling (QFS) algorithm in the reduced-precision residue number system (RP-RNS). This algorithm is designed to expedite division in the Residue Number System for the special case when the divisor is known ahead of time (i.e., when the divisor can be considered to be a constant, as in the modular exponentiation requ...

n ±1 are the most popular moduli in Residue Number Systems (RNS), a large variety of modulo 2 n ±1 adder designs have been proposed based on different number representations. However, in most of the cases, these encodings do not allow the implementation of a unified adder for all the moduli of the form 2 n-1, 2 n , and 2 n +1. In this paper, we address the modular addition issue by introducing ...

In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2 ± 1 and modulo 2 . The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2 − 1, 2, 2 +1). This approach allows using many smal...

A novel signaling scheme is presented, where a set of orthogonal signals is transmitted in parallel. The signals are selected according to the so-called residue number system (RNS). Hence the system is essentially a multiple code parallel communication scheme using high-modulation alphabets. It is demonstrated that the system performance can be substantially improved by exploiting a number of a...

With the current advances in VLSI technology, traditional algorithms for Residue Number System (RNS) based architectures should be reevaluated to explore the new technology dimensions. In this brief, we introduce A @(log n ) algorithm for large moduli multiplication for RNS based architectures. A systolic array has been designed to perform the modulo multiplication Algorithm. The proposed modul...

Recently a renewed interest is seen in RNS (Residue Number System) which stems out from the fact that these systems are inherently parallel and modular and thus are fast and simple. In many DSP applications Multiply-Accumulate (MAC) operation turns out to be the most basic one and hence an RNS based 36-bit MAC architecture is presented in this paper to speed up the whole operation. A further en...

In this paper, memory optimization and architectural level modifications are introduced for realizing the low power <span lang="EN-US">residue number system (RNS) with improved flexibility electroencephalograph (EEG) signal classification. The proposed RNS framework is intended to maximize reconfigurability of high-performance finite impulse response (FIR) filter design. By replacing exis...

In this paper, we present a high-speed pairing coprocessor using Residue Number System (RNS) which is intrinsically suitable for parallel computation. This work improves the design of Cheung et al. [11] using a carefully selected RNS base and an optimized pipeline design of the modular multiplier. As a result, the cycle count for a modular reduction has been halved. When combining with the lazy...

Residue number system (RNS) arithmetic has a promising role for fault-tolerant high throughput superconducting single flux quantum (SFQ) circuits for digital signal processing (DSP) applications. We have designed one of the basic computational blocks used in DSP circuits, one-decimal-digit RNS adder. A new design for its main component, the single-modulus adder, has been developed. It combines ...

The free action for the massless sector of the Type II superstring was recently constructed using closed RNS superstring field theory. The supersymmetry transformations of this action are shown to satisfy an N=2 D=10 SUSY algebra with Ramond-Ramond