Reversible and Fault Tolerant Reversible Gates by editorijettcs


More Info
									       Web Site: Email:,
Volume 1, Issue 3, September – October 2012                                    ISSN 2278-6856

     Reversible and Fault Tolerant Reversible Gates
                                Jaspreet Kaur1, Harpreet Kaur2 and Sheenu Thapar3
                                                Assistant Professor Department of ECE
                                          CIET, Jalvehra, Fatehgarh Sahib,Punjab, India
                                                 Assistant professor Department of ECE
                                                 BBSBEC, Fatehgarh Sahib, Punjab, India

Abstract: Reversible Logic is becoming more and more               reversible. This approach is a radical departure from both
prominent technology having its applications in Low Power          traditional logic design and traditional low energy design
CMOS,       Nanotechnology,      and     Optical     Computing.    techniques.
Reversible logic has emerged as one of the most important          For the computation to be physically reversible, and
approaches for the power optimization with its application in
low power VLSI design. In contrast to conventional gates,
                                                                   therefore not dissipate any energy, the computing engine
reversible logic gates have the same number of inputs and          must be logically reversible and implemented in a
outputs, each of their output function is equal to 1 and their     physically reversible technology [7]. Any system that
fan-out is always equal to 1. It is interesting to compare both    transitions from a state A to state B is physically
reversible and conventional gates. It allows any fault that        reversible if the state B uniquely determines state A,
affects no more than a single signal readily detectable at the     implying that the transition was logically reversible, and
circuit’s primary outputs. In addition to this there are few
                                                                   the energy is available to make the reverse transition,
families of reversible gates which offer fault tolerant
technique. The paper is focused on the major VLSI                  implying that the transition was made in a physically
limitations like delay and area of different reversible logic      reversible technology. Logical reversibility imposes
gates which are simulated in Xilinx8.1li and by writing the        architectural constraints not met by conventional
code in VHDL HDL and also compared reversible gates to             processors. A conventional computing engine performs
conventional gates.                                                irreversible computations. These computations destroy
Keywords: Reversible gate, Fault tolerant, delay, power            information, and the second law of thermodynamics
                                                                   requires minimum energy dissipation when a bit of
1. INTRODUCTION                                                    information is discarded. In the decimal arithmetic
Quantum computation has come to the forefront of                   domain it is receiving significant attention as the
theoretical and applied research. Investigation into               financial, commercial, and internet-based applications
reversibility and reversible circuits is assumed to have a         cannot tolerate errors generated by conversion between
more prevalent role; because reversibility is a                    decimal and binary formats [8].
precondition of quantum computation. Fortuitously, the
restrictive nature of reversibility induces a structure on         2. MOTIVATION
the circuits such as a microprocessor design much more             Logic computation in computers erases bit information;
amenable to analysis; both within the framework of                 this is done inefficiently and heat dissipates while erasing
reversible circuit design as well as for circuit complexity        bit. According to Landauer, KTln 2 energy is dissipated
in general. Reversible circuits [1-3] and reversible               per bit operation, where k is Boltzmann’s constant, and T
computation [4, 5] constrain every gate and every step of          is the absolute temperature of the environment. At room
the computation to be completely reversible, so that no            temperature the dissipating heat is very small but not
information may be lost at any step of the computation             negligible. This computation procedure is irreversible. It
and this does not contribute to heat dissipation in circuits.      is true that high degree of integration and advancement in
Therefore, they potentially help to solve at least two             fabrication process have helped in better hardware; but
problems: overheating and power saving, which implies              this energy loss due to irreversible computation will be a
longer life for batteries. The reversible logic solution may       great impediment in the next decade. Bennett [4] showed
be especially important in low-voltage designs of mobile           that zero energy dissipation would be possible if the
systems, where both power saving and overheating are               network consists of reversible gates only. Thus
very important due to the need for light weight and                reversibility will be an essential property for the future
independent power supply. Computing devices such as                circuit design. The power loss due to irreversible gates is
processors can be designed that do not require energy              negligible for current logic technologies using adiabatic
dissipation [4, 6], but only if the computation is logically       design. But the information that is lost because of

Volume 1, Issue 3, September – October 2012                                                                         Page 236
       Web Site: Email:,
Volume 1, Issue 3, September – October 2012                                    ISSN 2278-6856

irreversible circuits is not recoverable. Thus, it is good     low cost there are design approaches and tools that
motivation for any researcher to design using reversible       incorporate them separately or in combination with each
logic.                                                         other.
The main differences of synthesizing a circuit with
reversible gates, as compared to synthesizing a standard
circuit are as follows:
   > The number of outputs of a logic gate is equal to the
     number of inputs. It is possible to find solutions
                                                                      (a) Feyman Gate                (b) Peres Gate
     sacrificing one or more gate outputs for garbage, but
     such solution is of less value.
   > A heavy price is paid for every garbage output if the
     garbage output is left unattended.
   > In reversible logic, fan out of any gate output is not                        c) Toffoli Gate
     allowed; every output can be used only once.                      Figure 1 Few preferred Reversible Gates
For example- Feynman gate is good solution for copying
circuit. However, inclusion of Feynman gate definitely         3.2. Parity Preserving Reversible Gates
increases the delay and cost but emerging technologies         Fault tolerance is the property that enables a system to
                                                               continue operating properly in the event of the failure of
asks for power reduction.
                                                               some its components. If the system itself made of fault
One of the major constraints in reversible logic is to
                                                               tolerant components, then the detection and correction of
minimize the number of reversible gates used and
                                                               faults become easier and simple. In communication and
garbage outputs produced (Garbage output refers to the         many other systems, fault tolerance is achieved by parity.
output that is not used for further computations). Any         Therefore, parity preserving reversible circuits will be the
reversible gate performs the permutation of its input          future design trends to the development of fault tolerant
patterns only and realizes the functions that are              reversible systems in nanotechnology. And a gating
reversible. If a reversible gate has k inputs, and therefore   network will be parity preserving if its individual gate is
k outputs, then it is a k*k reversible gate. Any reversible    parity preserving [13].
circuit design includes only the gates that are reversible.
An efficient design should keep the number of garbage
outputs to minimum. Parity checking is one of the widely
used error detection mechanisms in digital logic and data
communication systems. This is because most of the
arithmetic functions is not parity preserving. If the parity
of the input data is maintained throughout the                 (a) Feyman Double Gate (F2G) (b) Fredkin Gate (FRG)
computation, no intermediate checking would be required               Figure 2 Parity preserving reversible Gates
[9]. A sufficient requirement for parity preservation of a     A few parity preserving logic gates have been proposed in
reversible circuit is that each gate be parity preserving      the literature. Among them 3*3 Feynman Double gate
[9]. Thus, we need parity preserving reversible logic gates    (F2G) [10] depicted in Fig. 2(a) and 3*3 Fredkin gate
to construct parity preserving reversible circuits. This       (FRG) [13] depicted in Fig. 2(b) are one-through gates,
paper presents few existing parity preserving reversible       which means one of the inputs is also output.
gates. Such gates can be used to realize any arithmetic
module such as ripple carry adder, carry look-ahead            Table 1: Table of Parity Preserving Feyman Double Gate
adder, carry-skip logic, and multiplier/divisors.                                        (F2G)
The paper is organized as follows: the section II covers
the detail on some reversible gates followed by fault
tolerant gates. Section III covers the simulation results of
fault tolerant gates. Section IV is the results and
discussion part followed up by conclusion in section V.

  3.1. Basic Reversible Gates
There exist many reversible gates in the literature.
Among them 2*2 Feynman gate (FG) [10], depicted in
Fig. 1(a), 3*3 Peres gate (PG) [11], depicted in Fig. 1(b),    Table 2: Table of Parity Preserving Fredkin Gate (FRG)
3*3 Toffoli gate (TG) [12], depicted in Fig. 1(c), have
been studied extensively. Because of their simplicity and
Volume 1, Issue 3, September – October 2012                                                                     Page 237
       Web Site: Email:,
Volume 1, Issue 3, September – October 2012                                    ISSN 2278-6856

From Table 1 and 2, it can be seen that the gates F2G and
FRG are parity preserving respectively; since they satisfy

                A B C P Q R
and any k*k reversible logic gate where the EX-OR of the
inputs matches the EX-OR of the outputs will be parity
                                                                  Figure 5 Simulation result for toffoli gate
The reversible & fault tolerant reversible architectures is
modeled using VHSIC hardware description language
(VHDL). The coding is done on Xilinx ISE8.2i for Virtex
4 target device: 4vlx60ff668-12. For simulation purpose
the Modelsim6.2h has been used.

       Figure 3 Simulation result for feyman gate             Figure 6 Simulation result for feyman double gate

        Figure 4 Simulation result for peres gate                Figure 7 Simulation result for fredkin gate

Volume 1, Issue 3, September – October 2012                                                               Page 238
       Web Site: Email:,
Volume 1, Issue 3, September – October 2012                                    ISSN 2278-6856

The simulation result for reversible gates is shown in Fig.    [4] Charles H.Bennett, "Logical Reversibility of
3, Fig. 4, and Fig. 5 for feyman, peres, and toffoli gate        Computation," IBM Journal of Research and
respectively. The simulation results shown in Fig. 6, and        Development, vol. 17, no. 6, pp. 525 532, 1973.
Fig. 7 corresponds to fault tolerant reversible feyman         [5] Charles H.Bennett, "Time/Space Trade Offs for
double gate, and fredkin gate respectively. The                  Reversible Computation," SIAM Journal of
comparison table for reversible gates is detailed in table 3     Computation, vol. 18, pp. 766 776, 1989.
                                                               [6] Rolf Landauer, "Uncertainty principle and
        Table3. Comparison table for Reversible gates            minimal energy dissipation in the computer,"
    Reversible Delay (nS)     Slice    4-i/p    Nature           International Journal of Theoretical Physics, vol. 21,
    Gates                              LUT                       no. 3/4, pp. 283 297, 1982.
    Feyman      5.120         1        1        -----          [7] Charles H.Bennett, "The Thermodynamics of
                (4.156 logic,                                    Computation A Review," International Journal of
                0.964 route)                                     Theoretical Physics, vol. 21, no. 12, pp. 905 940,
    Peres       5.133         1        2        ------           1982.
                (4.156 logic,                                  [8] M.F. Cowlishaw, “Decimal Floating-Point:
                0.977 route)                                     Algorithm for Computers”, Proc. 16th IEEE Symp.
    Toffoli     5.133         1        1        ------           Computer Arithmetic, pp. 104-111, June, 2003.
                (4.156 logic,                                  [9] B. Parhami , “Fault tolerant reversible circuits”,
                0.977 route)                                     in Proceedings of 40th Asimolar Conf. Signals,
    Feyman      5.120         1        2        Fault            Systems, and Computers, Pacific Grove, CA, pp.
    Double      (4.156 logic,                   Tolerant         1726-1729, October 2006.
                0.964 route)                                   [10] R. Feynman, “Quantum mechanical computers”,
    Fredkin     5.132         1        2        Fault            Optical News, vol. 11, 1985, pp. 11-20.
                (4.156 logic,                   Tolerant       [11] A. Peres, “Reversible logic and quantum
                0.967 route)                                     computers”, Physical Review: A, vol. 32, no. 6, pp.
.                                                                3266-3276, 1985.
                                                               [12] T. Toffoli, “Reversible computing”, In Automata,
5. CONCLUSION                                                    Languages and Programming, Springer-Verlag, pp.
                                                                 632-644, 1980.
Computer hardware has grown in power at an amazing             [13] E. Fredkin and T. Toffoli, “Conservative logic”,
pace ever since. One of the most important computational         Intl. Journal of Theoretical Physics, pp. 219-253,
resources is energy. The energy consumption in                   1982.
computation turns out to be deeply linked to the               [14] R. Landauer, “Irreversibility and Heat Generation
reversibility of the computation [14-18]. A computation is       in the Computational Process”, IBM Journal of
called reversible if its inputs can always be deduced from       Research and Development, 5, pp. 183-191, 1961.
its outputs. The primary objective of this paper was to        [15] C.H. Bennett , “Logical Reversibility of
gain insight into the Reversible Computation and its use         Computation”, IBM J. Research and Development,
for making devices energy efficient for long life. All           pp. 525-532, November 1973.
computations can be done, in principle, for zero cost in       [16] M. S. Islam, and M. Rafiqul Islam, “Minimization
energy. Using reversible gates & having parity preserving        of reversible adder circuits”, Asian Journal of
nature can help to build arithmetic circuits for energy          Information Technology, vol. 4, no. 12, pp. 1146-
efficient processor design with easy debugging nature.           1151, 2005.
                                                               [17] D. Maslov, G. W. Dueck, and D. M. Miller,
                                                                 "Synthesis of Fredkin-Toffoli reversible networks,"
REFERENCES                                                       IEEE Trans. VLSI Systems, vol. 13, no. 6, pp. 765-
     [1] Rolf Landauer, "Irreversibility and Heat                769, 2005.
       Generation in the Computing Process," IBM Journal       [18] J. W. Bruce, M. A. Thornton, L. Shivakumaraiah,
       of Research and Development, vol. 5, pp. 183 191,         P.S. Kokate, X. Li, “Efficient adder circuits based on
       1961.                                                     a conservative reversible logic gates”, In Proceedings
     [2] Tommaso Toffoli, "Reversible Computing,"                of IEEE Computer Society Annual Symposium on
       Automata, Languages and Programming, 7th                  VLSI, Pittsburg, PA, pp. 83-88, 2002.
       Colloquium of Lecture Notes in Computer Science,
       vol. 85, pp. 632 644, 1980.
     [3] Edward Fredkin and Tommaso Toffoli,
       "Conservative Logic," International Journal of
       Theoretical Physics, vol. 21, pp. 219 253, 1982.

Volume 1, Issue 3, September – October 2012                                                                 Page 239

To top