2014 International Conference on Computer Communication and Informatics (ICCCI -2014), Jan. 03 – 05, 2014, Coimbatore, INDIA
[978-1-4799-2352-6/14/$31.00 ©2014 IEEE]
A Modified Novel Compressor based Urdhwa
Tiryakbhyam Multiplier
N.Rajasekhar
M. Tech II year student
Department of Electronics Engineering
Pondicherry University
Pondicherry, India
rajpdtrkad.atr@gmail.com
Dr.T.Shanmuganantham
Asst. Professor
Department of Electronics Engineering
Pondicherry University
Pondicherry, India
shanmuga.dee@pondiuni.edu.in
Abstract—With the advent of new technology in the domain
of VLSI, communication and signal processing, there is an
ever going demand for the high speed processing and low
area design. In this paper, introduces modified compressor
based multiplier architecture. This modified structure uses
the 4:2 compressor and 7:2 compressor architectures. In
addition to that it uses Vedic mathematics to get a high speed
multiplication operation and low area design. The design
and experiments carried were carried out on a Xilinx
Spartan 3E series of FPGA and discussed about the results
of area and speed.
Keywords—High speed multiplier, 4:2 compressor, 7:2
compressor, modified architecture, vedic mathematics.
I. INTRODUCTION
The Processor speed greatly depends on its
multiplier’s performance. This in turn raises the demand for
multipliers high speed, at the same time maintaining low area
and moderate power dissipation [1]. Over the past few
decades, several new novel architectures are come for
multipliers and have been designed and explored. Booth’s [2]
and modified Booth’s algorithm based multipliers are quite
popular in modern VLSI design but come along with their
own set of disadvantages. In these multiplier algorithms, the
multiplication process, involves several transitional operations
before received at the finishing answer. The intermediate
stages include several additions, subtractions and comparisons
which reduce the speed exponentially with the total number of
bits present in the multiplier and the multiplicand [6]. Since
the speed is major concern, utilizing such type of architectures
is not good approach since it involves several time consuming
operations.
In order to address the disadvantages of the above
mentioned methods [7, 8] with respect to speed of opera
ration, explored a new approach for multiplier design based on
ancient vedic mathematics. Vedic mathematics is an Indian
ancient and eminent approach which acts as a foundation to
solve many mathematical challenges faced in the current day
scenario. Vedic mathematics was existed in ancient India and
re discovered by a popular great mathematician, Sri Bharati
Krishna Tirthaji [9]. He divided the Vedic mathematics into
16 simple sutras (formulae). These Sutras deals with
Arithmetic, Analytical, Algebra, Geometry, Trigonometry, etc.
The simplicity in the Vedic mathematics sutras pays a way for
its application in several prominent domains of engineering
and technology like Signal Processing, Control Engineering
and VLSI [10].
One of the highlights in Vedic mathematics approach
is that the calculation of all partial products required for
multiplication, are obtained well in development, much before
that the actual operations of multiplication begin. These
intermediate partial products are then added based on the
Vedic mathematics algorithm to obtain the ending product.
This in turn indications to a very high speed approach to
achieve multiplication [11]. In this paper, explore a novel
method to further enhance in speed of a Vedic multiplier by
replacing the existing full adders and half adders of the Vedic
mathematics based multipliers with compressors based adders.
Compressors, in its several variants, are logic circuits which
are skilled of adding more than 3 bits at a time as divergent to
a full adder and capable of acting with a lesser gate count and
higher speed in comparison with an equivalent full adder
circuit [13].
II. VEDIC MATHEMATICS
A. Urdhwa Tiryakbhyam Sutra
Vedic mathematics is divided into 16 different sutras
to perform to perform mathematical calculations. Among
these sutras Urdhwa Tiryakbhyam is the most preferable and
good enough algorithm to perform multiplication of integers
as well as binary numbers. The term "Urdhwa Tiryakbhyam”
originated from 2 Sanskrit words Urdhwa and Tiryakbhyam
which means that “vertically” and “crosswise” respectively.
Let us consider the two 8 bit numbers X7-X0and Y7-
Y0, where 0 to 7 represent bits from the Least Significant Bit
(LSB) to the Most Significant Bit (MSB). P0to P15represent
each bit of the multiplied result [1]. It can be seen from