Reversible Booth’s Multiplication Implementation using Reversible Gates

Authors

  • Anup Kumar Biswas  Assistant Professor, Computer Science and Engineering, Kalyani Govt. Engineering College, Kalyani, Nadia, West Bengal, India

Keywords:

Quantum Cost, Reversible Logic Booth’s Multiplier, Permutation Matrix, Garbage Value

Abstract

One of the attractive research area in Engineering and Technology is Reversible Computing / Reversible logic. The attraction of scientists and researchers in this field in the last decade is strongly due to low-power consumption for the execution of operations. To minimize the width of circuit, garbage, total gate numbers and delay are the objectives of the reversible logic synthesis. This paper explains the design methodology regarding reversible Booth’s multiplier to be realized. Researchers’ attempts are thus making complete reversible logic circuits made up of reversible gates. Reversible Booth’s multiplication process as considered to be a speediest multiplier method. Being inspired in it, an efficient design-methodology for reversible paradigm is shown. The proposed architecture for reversible multiplication is capable of performing over signed and unsigned number multiplications for two input numbers without keeping any feedbacks. But the existing reversible mode of multiplication thinks of the feedback loop that is strongly prohibited in our present reversible multiplication mode. Theoretical underpinnings are able to show the efficiency of a reversible logic calculation and accordingly it is observed that our proposed circuit is more efficient with respect to the design viewpoint of a reversible circuit.

References

  1. R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. Res. Dev., vol. 5, no. 3, pp. 183–191, Jul. 1961. [Online]. Available: http://dx.doi.org/10.1147/rd.53.0183
  2. M. P. Frank, “Introduction to reversible computing: Motivation, progress, and challenges,” in Conference on Computing Frontiers, 2005, pp. 385– 390. [Online]. Available: http://doi.acm.org/10.1145/1062261.1062324
  3. H. Thapliyal and M. B. Srinivas, “Novel reversible multiplier architecture using reversible tsg gate,” in IEEE Conference on Computer Systems and Applications, 2006, pp. 100–103. [Online]. Available: http://dx.doi.org/10.1109/AICCSA.2006.205074
  4. K. Bhardwaj and B. M. Deshpande, “K-algorithm: An improved booth’s recoding for optimal fault-tolerant reversible multiplier,” in VLSI Design, 2013, pp. 362–367. [Online]. Available: http://dx.doi.org/10.1109/VLSID.2013.215
  5. H. H. Babu, R. Islam, A. R. Chowdhury, and S. M. A. Chowdhury, “Reversible logic synthesis for minimization of full-adder circuit,” in Euromicro Symposium on Digital Systems Design, 2003, pp. 50–54. [Online]. Available: http://dl.acm.org/citation.cfm?id=942792.943112
  6. H. H. Babu, R. Islam, S. M. A. Chowdhury, and A. R. Chowdhury, “Synthesis of full-adder circuit using reversible logic,” in VLSI Design, 2004, pp. 757–760. [Online]. Available: http://dl.acm.org/citation.cfm?id=962758.963476
  7. A. R. Chowdhury, R. Nazmul, and H. M. H. Babu, “A new approach to synthesize multiple-output functions using reversible programmable logic array,” in International Conference on VLSI Design (VLSID), 2006, pp. 6–11.
  8. S. Mitra and A. Chowdhury, “Minimum cost fault tolerant adder circuits in reversible logic synthesis,” in International Conference on VLSI Design (VLSID), 2012, pp. 334–339.
  9. R. P. Feynman, “Quantum mechanical computers,” Optics News, vol. 11, no. 2, pp. 11–20, Feb 1985. [Online]. Available: http//www.osa-opn.org/abstract.cfm?URI=on-11-2-11
  10. T. Toffoli, “Reversible computing,” in Colloquium on Automata, Languages and Programming, 1980, pp. 632–644. [Online]. Available: http://dl.acm.org/citation.cfm?id=646234.682540
  11. E. Fredkin and T. Toffoli, “Collision-based computing,” vol. 21, pp. 219–253, 1983. [Online]. Available: http://dl.acm.org/citation.cfm?id=644307.644311[12] 
  12. A. Peres, “Reversible logic and quantum computers,” Phys. Rev. A, vol. 32, pp. 3266–3276, Dec 1985. [Online]. Available:http://link.aps.org/doi/10.1103/PhysRevA.32.3266
  13. H. Thapliyal, S. Kotiyal, and M. B. Srinivas, “Novel bcd adders and their reversible logic implementation for ieee 754r format,” in VLSI Design, 2006, pp. 387–392. [Online]. Available: http://dx.doi.org/10.1109/VLSID.2006.122
  14. H. Thapliyal and M. B. Srinivas, “A novel reversible tsg gate and its application for designing reversible carry look-ahead and other adder architectures,” in Asia-Pacific Conference on Advances in Computer Systems Architecture, 2005, pp. 805–817. [Online]. Available: http://dx.doi.org/10.1007/11572961 66
  15. A. K. Biswas, M. M. Hasan, A. R. Chowdhury, and H. M. H. Babu, “Efficient approaches for designing reversible binary coded decimal adders,” Microelectronics Journal, vol. 39, no. 12, pp. 1693–1703, 2008.
  16. M. Perkowski, M. Lukac, P. Kerntopf, M. Pivtoraiko, D. Lee, H. Kim, W. Hwangbo, J.-w. Kim, and Y. W. Choi, “A hierarchical approach to computer-aided design of quantum circuits,” in International Symposium on Representations and Methodology of Future Computing Technology, 2002, pp. 201–209.
  17. J. P. Hayes, “Computer organization and architecture,” 1998 McGraw Hill international Editions.

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Published

2019-03-30

Issue

Section

Research Articles

How to Cite

[1]
Anup Kumar Biswas "Reversible Booth’s Multiplication Implementation using Reversible Gates " International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 6, Issue 2, pp.849-859, March-April-2019.