It has been reported in the literature on computational neuroscience that a rat’s uncanny ability to dash back to a home position in the absence of any visual clues (or in total darkness, for that matter) may stem from its distinctive method of position representation. More specifically, it is hypothesized that the rat uses a multimodular method akin to residue number system (RNS), but with con...

This paper studies the effect of the moduli number within a moduli set on the overall speed of the residue number system (RNS). Choosing a proper moduli set greatly affects the performance of the whole system. The widely known issue is that as the number of moduli increases the speed of the residue arithmetic units (RAUs) increases, whereas the residue-to-binary converters (RCs) become slower a...

A residue number system based M -ary modem is proposed and its performance is evaluated over Gaussian channels. When one or two redundant moduli are employed, a signal-to-noise ratio gain of 1.2–2 dB was achieved for a 16-ary, 32-ary and 37-ary modem, respectively, at a bit error rate of 10 .

The polynomial residue number system (PRNS) has been considered as a useful tool for digital signal processing (DSP) since it can support parallel, carry-free, high speed arithmetic with minimum multiplication count provided that an appropriate modular ring is chosen. In this paper, the properties of two-dimensional (2-D) PRNS are investigated in detail. It is shown that in the 2-D PRNS system,...

In this paper we explore the feasibility of implementing Residue Number System (RNS) based DSP algorithms on Lookup table based Field Programmable Gate Arrays (FPGAs). In this process, Binary Decision Diagrams are used for logic representation, and a new minimizing algorithm for incompletely specified functions is introduced. A sample residue arithmetic based design is presented along with prom...

The Residue Number System based on 2 n 2 k -1 moduli set is used in the proposed model. There are more number of moduli sets among them the above mentioned one is having high performance than the other. Adder is one of the key components for the application of Residue number system (RNS). Moduli set 2 n -2 k -1 where n=16 and k=14 with the form can offer excellent balance among the RNS channels...

Based on an algorithm derived from the New Chinese Remainder Theorem I, we present three new residue-to-binary converters for the residue number system (2 1 2 2 + 1) designed using 2 -bit or -bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2 -bit adder based converter is faster and requires about half the hardware required by previous...

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...

In this work, we are interested in arithmetic in large prime field and their extensions of small degree. We explain why it is very interesting to use RNS arithmetic for the base field Fp when computations in Fpk have to be done, essentially thanks to lazy reduction. This is for example the case for pairing computations on ordinary curves (as MNT or BN curves). We prove that using RNS can consid...

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.