Research Journal of Applied Sciences, Engineering and Technology 4(22): 4566-4571, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: December 30, 2011 Accepted: March 10, 2012 Published: November 15, 2012
Corresponding Author: Mozhgan Shiri, Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran
4566
A Novel Nanometric Fault Tolerant Reversible Subtractor Circuit
1
Mozhgan Shiri,
2
Majid Haghparast and
1
Vahid Shahbazi
1
Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran
2
Department of Computer Engineering, Shahre-Rey Branch, Islamic Azad University,
Tehran, Iran
Abstract: Reversibility plays an important role when energy efficient computations are considered. Reversible
logic circuits have received significant attention in quantum computing, low power CMOS design, optical
information processing and nanotechnology in the recent years. This study proposes a new fault tolerant
reversible half-subtractor and a new fault tolerant reversible full-subtractor circuit with nanometric scales. Also
in this paper we demonstrate how the well-known and important, PERES gate and TR gate can be synthesized
from parity preserving reversible gates. All the designs have nanometric scales.
Keywords: Fault tolerant, nanometric circuits, nanotechnology, quantum computing, reversible logic,
subtractor
INTRODUCTION
Reversible circuits are composed of reversible gates.
In this circuits information don’t be lost. Reversible
circuits can produce unique output from each input and
vice versa, hence, there is a one-to-one correspondence
between input and output vectors (Thapliyal and Srinivas,
2006). So a reversible logic gate has an equal number of
inputs and outputs (k ×k) (Babu and Chowdhury, 2005).
In ideal conditions, a reversible circuit has zero
internal power dissipation because, it does not lose
information. Under R. Landauer’s research in the early
1960s, the amount of energy dissipated for every
irreversible bit operation is given by KTLn2 joules,
where K = 1.3806505 × 10
!23
J/K is the Boltzmann’s
constant and T is the absolute temperature at which
operation is performed. But in 1973, Bennett showed that
KTLn2 joules of energy can be saved from a system as
long as the system permits the regeneration of the inputs
from produced outputs (Haghparast et al., 2009;
Haghparast and Navi, 2008a; Thapliyal and Gupta, 2006).
A reversible gate with n-inputs and n-outputs is
called a n × n reversible gate (Sastry et al., 2006). In a n
× n reversible function, there are 2
n
input rows and 2
n
output rows in its truth table. In fact the output rows are
a permutation of the input rows in the truth table
(Kerntopf, 2002; Hung et al., 2006). Direct fan-outs from
the reversible gate and feedbacks from a gate output
directly to its inputs are not allowed (Sastry et al., 2006).
Classical logic gates are called irreversible since they
cannot uniquely reconstruct the input vector states from
the output vector states.
Synthesis and designing of a reversible gate is
different from traditional logic gates (Haghparast and
Sheikh, 2011). Therefore, constructing a fault tolerant
reversible circuit is much more difficult than a
conventional logic circuit (Parhami, 2006). In this paper,
we propose a fault detection method based on parity
preserving reversible logic gates.
PRIMARY DEFINITIONS
Some of the main measures in synthesis a reversible
logic circuit are: Number of reversible logic gates,
Number of garbage outputs, Number of constant inputs,
Total quantum cost, and total logical calculations
(Haghparast et al., 2009).
Garbage outputs: One of the most important parameters
in designing a reversible circuit is its garbage outputs
(Hasan et al., 2004). In a reversible logic gate number of
inputs and outputs is equal but all the outputs are not
expected. The number of outputs added to make an n-
input k-output function reversible is named garbage
outputs. In fact they are needed to maintain reversibility.
A heavy price is paid for every garbage output (Parhami,
2006).
So, one of the major challenges in reversible logic
synthesis is to minimize the garbage outputs (Hasan et al.,
2004; Thapliyal et al., 2009).
Quantum cost: The quantum cost of a reversible gate is
the number of 2×2 reversible gates or quantum logic gates
required in designing it. The quantum cost of all