Abstract
Pipelined two-operand modular adder (TOMA) is one of basic components used in digital signal process- ing (DSP) systems that use the residue number system (RNS). Such modular adders are used in binary/residue and residue/binary converters, residue multipliers and scalers as well as within residue processing channels. The structure of pipelined TOMAs is usually obtained by in- serting an appropriate number of pipeline register layers within a nonpipelined TOMA structure. Hence the area of pipelined TOMAs is determined by the nonpipelined TOMA structure and by the total number of pipeline registers. In this paper we propose a new pipelined TOMA, that has a considerably smaller area and the attainable pipelining frequency comparable with other known pipelined TOMA structures. We perform comparisons of the area and pipe- lining frequency with TOMAs based on ripple carry adder (RCA), Hiasat TOMA and parallel-prefix adder (PPA) using the data from the very large scale of integration (VLSI) standard cell library. n m m m X X X with i m i x Z . This mapping is the bijection and for X, Y ZM and for i m i i y x Z , , we have i m i i i y x z ,where denotes addition, subtraction or
Highlights
Modular addition plays an important role in the implementation of digital signal processing systems that use the residue number system [1,2,3,4] as well as its derivatives like the quadratic residue number system (QRNS) [5] and modified quadratic residue number system (MQRNS) [6]
The paper has the following structure: in Sec. 2 we review the basic two-operand modular adder (TOMA) structures, in Sec. 3 we consider the TOMA-ripple carry adder (RCA), and in Sec. 4 Hiasat TOMA, in Sec. 5 we present the TOMA based on the parallel-prefix adder (PPA) adder and in Sec. 6 a new TOMA
The Brent-Kung TOMA can be relatively easy transformed to the pipelined form, the use of the Brent-Kung PPA allows one to simplify the adder used in the second stage when one of addends is a constant
Summary
Modular addition plays an important role in the implementation of digital signal processing systems that use the residue number system [1,2,3,4] as well as its derivatives like the quadratic residue number system (QRNS) [5] and modified quadratic residue number system (MQRNS) [6]. The principal advantage of the RNS with respect to the high-speed DSP is due to the replacement of large multipliers that limit the pipelining frequency, by small multipliers modulo mi If their binary size l = (log2mi) , where denotes rounding off to an integer, does not exceed six bits, multiplications by a constant can be performed by look-up with small ROMs or using combinatorial networks. Hiasat [23] proposed a TOMA with the reduced area based on the carry-look-ahead (CLA) adder. A novel delay-powerarea-efficient approach to the TOMA design was given by Patel et al [24] Their TOMA structure was based on the cascaded connection of the modified carry-save adder. In each section we analyze a nonpipelined and pipelined form
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