New Adder-Based RNS-to-Binary Converters for the Moduli Set

Abstract

We investigate Residue Number System (RNS) to binary conversion, which is an important issue concerning the utilization of RNS numbers in Digital Signal Processing (DSP) applications. We propose two new reverse converters for the moduli set . First, we simplify the Chinese Remainder Theorem (CRT) to obtain a reverse converter that uses mod- operations instead of mod- operations required by other state-of-the-art equivalent converters. Next, we further reduce the hardware complexity by making the resulting reverse converter architecture adder based. Two hybrid Cost-Efficient (CE) and Speed-Efficient (SE) reverse converters are proposed. These two hybrid converters are obtained by combining the best state-of-the-art converter with the newly introduced area-delay efficient scheme. The proposed hybrid CE converter outperforms the best state-of-the-art CE converter in terms of delay with similar area cost. Additionally, the proposed hybrid SE converter requires less area cost with smaller delay when compared to the best state-of-the-art equivalent SE converter.

RNS Bases in Computer Architecture for DNA Sequence Application

“…The set of residues are represented as {r 1 ,r 2 ,r 3 , … , r n } where r n is the n th residue. The residue r n is defined as the least positive remainder of an integer value X is divided by the modulus, m n [10]. This notation based on congruence is written as; X Mod m i = r i .…”

“…RNS has limitation in applications involving arithmetic operation like scaling, overflow, division, magnitude comparisms, sign detection, overflow detection, division, reverse conversion and the complexity of the system to implement etc High speed is achieve in the operation with addition, subtraction, multiplication by supporting carry free addition, borrow free subtraction and digit to digit multiplication without partial product option for processing data in the advancing Biotechnology [4], [6]. [10] 8. Rns-Swa Based Implementation In Gene Sequence Alignment In 1981, T. F. Smith and M. S.Waterman described a method, commonly known as the Smith-Waterman (SW) algorithm [4], [15] for finding common regions of local similarity.…”

A New Efficient Residue to Binary Converter for (5n+2)-bit Dynamic Range Moduli Set

“…For a milestone chalked in the application of RNS, The conversion overhead must not nullify the advantages of RNS, and hence the need for efficient conversion algorithm for data conversion either from binary/decimal to residue or from residue to binary/decimal. Data Conversion, which is usually based on either the Chinese Remainder Theorem (CRT) [6]], [7] [8] or the Mixed Radix Conversion (MRC) [9] can be categorized into forward and reverse conversions. The forward conversion is conversion of binary/decimal to a residue form while the reverse conversion involves converting the RNS number into binary or decimal [10], [5].…”

New Efficient Reverse Converters for 8n-bit Dynamic Range Moduli Set

“…By dividing both sides of (7) by and calculating the floor values in modulo we have (8) In this case the number X can be computed by Equation (8) can be written as where (11) (12)…”

“…Out of these numerous RNS challenges, Data conversion is very critical; for successful application of RNS, data conversion must be very fast so that the conversion overhead does not nullify the RNS advantages. Data Conversion, which is usually based on either the Chinese Remainder Theorem (CRT) [5], [6] [7] or the Mixed Radix Conversion (MRC) [8] can be categorized into forward and reverse conversions. The forward conversion involves converting a binary or decimal number into its RNS equivalent while the reverse conversion involves converting the RNS number into binary or decimal [9].…”