ASIC Design of Reversible Multiplier Circuit
Hatkar A. P., Hatkar A. A.
E&TC Engineering Department
Sir Visvesvaraya Institute of Technology
Nasik, India
arvind_hatkar@yahoo.com
Narkhede N. P.
Electronics Engineering Department
Shri Ramdeobaba College of Engineering & Management
Nagpur, India
narkheden@rknec.edu
Abstract—Reversible logic is very much in demand for the
future computing technologies as they are known to produce low
power dissipation having its applications in Low Power CMOS,
Quantum Computing, Nanotechnology, and Optical Computing.
Adders and multipliers are fundamental building blocks in many
computational units. In this paper we have presented and
implemented reversible Wallace signed multiplier circuit in ASIC
through modified Baugh-Wooley approach using standard
reversible logic gates/cells, based on complementary pass-
transistor logic and have been validated with simulations, a
layout vs. schematic check, and a design rule check. It is proved
that the proposed multiplier is better and optimized, compared to
its existing counterparts with respect to the number of gates,
constant inputs, garbage outputs, hardware complexity, and
number of transistors required. It has also been shown in
Cadence’s tools that the reversible multiplier outperform the
irreversible multiplier in terms of power dissipation.
Keywords: - Reversible logic, Low Power CMOS, Wallace signed
multiplier, Baugh-Wooley approach, standard reversible logic cells.
1. INTRODUCTION
Power dissipation and therewith heat generation is a serious
problem for today’s computer chips. The 30-year-long trend in
microelectronics has been to increase both speed and density
by scaling of device components. During this trend higher
level of integration and new fabrication processes reduced the
heat generation in the last decade. A more fundamental reason
for power dissipation arises from the observations made by
Landauer already in 1961 [1]. Landauer proved that using
conventional logic, gate operations always lead to energy
dissipation regardless of the underlying technology. More
precisely, exactly kTln2 Joule of energy is dissipated for each
“lost” bit of information during an irreversible operation. This
phenomenon can be attributed to the fact that erasing a bit
amounts to ignoring its present contents, which may in fact be
unknown and resetting it to some standardized state (usually
0). This means that the system moves from a random state to
an ordered state thus bringing down the entropy of the system.
But according to second law of thermodynamics entropy of a
system cannot decrease and hence heat is dissipated into the
surrounding environment [2].
In contrast, Bennett [3] showed that energy dissipation can
be reduced or even eliminated if computation becomes
information-lossless. This does not hold for irreversible
(conventional) circuits. But, reversible circuits, i.e. circuits
where all operations are performed in an invertible manner,
satisfy this criterion. Moreover, as also shown by Bennett,
zero power dissipation on circuits will only be possible if the
respective computation is made reversible.
As a consequence, Landauer [1] (and later Bennett [3],
Fredkin [4], Toffoli [5]) suggested the use of reversible
circuits. These circuits have an equal number of input and
output signals, whereby each input assignment maps to a
unique output assignment. Since reversible circuits are by
definition information-lossless, power dissipation resulting
from Landauer’s principle, as described above, can be
decreased or even eliminated.
In the computational units, multiplication is one of the
useful operations. Therefore, developing a signed multiplier
circuit is necessary. In this paper, we have proposed Wallace
reversible signed multiplier circuit by Toffoli gate (TG) [5],
Peres gate (PG) [6], and Haghparast-Navi gate (HNG) [7, 8].
We implemented basic standard reversible cells in Cadence
tool and used them in the design of Wallace reversible signed
multiplier.
The paper is organized as follows. Section 2 presents an
overview of reversible logic and multiplier circuits. In Section
3 we introduced design of reversible and irreversible Wallace
sign multiplier circuit. Section 4 described the CMOS
implementation of reversible and irreversible circuits.
Furthermore, we have analyzed and evaluated the proposed
reversible signed multiplier circuit in Section 5, Section 6
suggest some future extensions and Section 7 concludes the
paper.
2. BASIC CONCEPTS
A. Reversible logic
Quantum gates which are represented by unitary matrices
have potentials to implement reversible logic circuits. Each
Quantum gate represents a valid Quantum operation, which
must be unitary and hence must be reversible. That is
Quantum gates are reversible, unlike many classical logic
gates. Reversible logic gate/circuit can be defined as follows:
Definition 1: For an n input, m output logic gate, if there is a
one-to-one correspondence between its inputs and outputs, and
then this logic gate is reversible.
Definition 2: A gate is reversible if and only if the (Boolean)
function is bijective i.e. a gate is reversible if it maps each
input vector into a unique output vector and vice versa.
2014 International Conference on Electronic Systems, Signal Processing and Computing Technologies
978-1-4799-2102-7/14 $31.00 © 2014 IEEE
DOI 10.1109/ICESC.2014.16
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