Skip to main content

Reversible Logic Based Design and Test of Field Coupled Nanocomputing Circuits

  • Chapter
  • First Online:
Field-Coupled Nanocomputing

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8280))

Abstract

Reversible computing is based on logic circuits that can generate unique output vector from each input vector, and vice versa, that is, there is a one-to-one mapping between the input and the output vectors. Reversible computing is the only solution for non-dissipative ultra low power green computing. Conservative reversible circuits are a specific type of reversible circuits, in which there would be an equal number of 1s in the outputs as there would be on the inputs, in addition to one-to-one mapping. This work illustrates the application of reversible logic towards testing of faults in traditional and reversible field coupled nanocircuits (Portions of this chapter are based on [2]. The enhancement is comprehensive treatment of: basics of reversible computing, motivation for reversible computing, background on conservative logic, basics of QCA computing, such as QCA logic devices and QCA clocking, related work etc. Several new reversible testable designs are introduced such as design of testable reversible T latch, design of testable asynchronous set/reset D latch and master-slave D flip-flop, design of testable reversible complex sequential circuits. QCA layouts of conservative logic gates are introduced with internal design details of QCA logic devices. Complete fault patterns information and analysis are provided for conservative logic gates. The synthesis of non-reversible testable design based on MX-cqca gate is extended to MX-cqca based implementation of standard functions. The significance of this work and broader prospective for future directions is also presented.). We propose the design of two vectors testable sequential circuits based on conservative logic gates. The proposed sequential circuits based on conservative logic gates outperform the sequential circuits implemented in classical gates in terms of testability. Any sequential circuit based on conservative logic gates can be tested for classical unidirectional stuck-at faults using only two test vectors. The two test vectors are all 1s, and all 0s. The designs of two vector testable latches, master-slave flip-flops, double edge triggered flip-flops, asynchronous set/reset D latch and D flip-flop are presented. The importance of the proposed work lies in the fact that it provides the design of reversible sequential circuits completely testable for any stuck-at fault by only two test vectors, thereby eliminating the need for any type of scan-path access to internal memory cells. The reversible designs of the double edge triggered flip-flop, ring counter and Johnson Counter are proposed for the first time in literature. We are showing the application of the proposed approach towards 100 % fault coverage for single missing/additional cell defect in the QCA layout of the Fredkin gate. We are also presenting a new conservative logic gate called Multiplexer Conservative QCA gate (MX-cqca) that is not reversible in nature but has similar properties as the Fredkin gate of working as 2:1 multiplexer. The proposed MX-cqca gate surpasses the Fredkin gate in terms of complexity (the number of majority voter), speed and area.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. QCADesigner. http://waluslab.ece.ubc.ca/qcadesigner/

  2. IEEE. All rights reserved. Reprinted with permission from Thapliyal, H., Ranganathan, N., Kotiyal, S.: Design of testable reversible sequential circuits. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 21(7), 1201–1209 (2013)

    Google Scholar 

  3. Alam, M.T., Kurtz, S.J., Siddiq, M.A.J., Niemier, M.T., Bernstein, G.H., Hu, X.S., Porod, W.: On-chip clocking of nanomagnet logic lines and gates. IEEE Trans. Nanotechnol. 11(2), 273–286 (2012)

    Article  Google Scholar 

  4. Anderson, N., Ercan, I., Ganesh, N.: Toward nanoprocessor thermodynamics. In: 2012 12th IEEE Conference on Nanotechnology (IEEE-NANO), pp. 1–6 (2012)

    Google Scholar 

  5. Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973)

    Article  MATH  Google Scholar 

  6. Bhanja, S., Ottavi, M., Lombardi, F., Pontarelli, S.: QCA circuits for robust coplanar crossing. J. Electron. Test. 23(2–3), 193–210 (2007)

    Article  Google Scholar 

  7. Bhanja, S., Pulecio, J.: A review of magnetic cellular automata systems. In: 2011 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2373–2376. IEEE (2011)

    Google Scholar 

  8. Bubna, M., Goyal, N., Sengupta, I.: A DFT methodology for detecting bridging faults in reversible logic circuits. In: Proceedings of 2007 IEEE Region 10 Conference, Tencon 2007, Taipei, pp. 1–4, Oct 2007

    Google Scholar 

  9. Cho, H., Swartzlander, E.: Adder designs and analyses for quantum-dot cellular automata. IEEE Trans. Nanotechnol. 6(3), 374–383 (2007)

    Article  Google Scholar 

  10. Cho, H., Swartzlander, E.: Serial parallel multiplier design in quantum-dot cellular automata. In: Proceedings of the IEEE Symposium Computer Arithmetic (ARITH), Montepellier, France, pp. 7–15 (2007)

    Google Scholar 

  11. Chuang, M.L., Wang, C.Y.: Synthesis of reversible sequential elements. J. Emerg. Technol. Comput. Syst. 3(4), 1–19 (2008)

    Article  MathSciNet  Google Scholar 

  12. Dalui, M., Sen, B., Sikdar, B.K.: Fault tolerant QCA logic design with coupled majority-minority gate. Int. J. Comput. Appl. 1(29), 81–87 (2010)

    Google Scholar 

  13. Ercan, I., Anderson, N.: Heat dissipation bounds for nanocomputing: theory and application to QCA. In: 2011 11th IEEE Conference on Nanotechnology (IEEE-NANO), pp. 1289–1294 (2011)

    Google Scholar 

  14. Farazmand, N., Zamani, M., Tahoori, M.B.: Online fault testing of reversible logic using dual rail coding. In: Proceedings of IEEE International On-Line Testing Symposium, pp. 204–205, May 2010

    Google Scholar 

  15. Fijany, A., Toomarian, B.N.: New design for quantum dots cellular automata to obtain fault tolerant logic gates. J. Nanopart. Res. 3(1), 27–37 (2001)

    Article  Google Scholar 

  16. Fijany, A., Toomarian, B.N.: New design for quantum dots cellular automata to obtain fault tolerant logic gates. J. Nanopart. Res. 3, 27–37 (2001)

    Article  Google Scholar 

  17. Frank, M.: Approaching the physical limits of computing. In: Proceedings of ISMVL 2005, The Thirty-Fifth International Symposium on Multiple-Valued Logic, Calgary, Canada, pp. 168–185, May 2005

    Google Scholar 

  18. Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21, 219–253 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  19. Frost-Murphy, S., Ottavi, M., Frank, M., DeBenedictis, E.: On the design of reversible QDCA systems. Technical Report SAND2006-5990, Sandia National Laboratories (2006)

    Google Scholar 

  20. Große, D., Wille, R., Dueck, G.W., Drechsler, R.: Exact synthesis of elementary quantum gate circuits for reversible functions with dont cares. In: Proceedings of the International Symposium on Multi-Valued Logic, Dallas, Texas, pp. 214–219, May 2008

    Google Scholar 

  21. Große, D., Wille, R., Dueck, G., Drechsler, R.: Exact multiple control toffoli network synthesis with SAT techniques. IEEE Trans. CAD 28(5), 703175 (2009)

    Article  Google Scholar 

  22. Gupta, P., Agarwal, A., Jha, N.K.: An algorithm for synthesis of reversible logic ciruits. IEEE Trans. Comput. Aided Des. 25(11), 2317–2330 (2006)

    Article  Google Scholar 

  23. Gupta, P., Jha, N.K., Lingappan, L.: A test generation framework for quantum cellular automata circuits. IEEE Trans. VLSI Sys. 15(1), 24–36 (2007)

    Article  Google Scholar 

  24. Hanninen, I., Takala, J.: Robust adders based on quantum-dot cellular automata, In: Proceedings of the IEEE International Conference Application-Specific Systems, Architectures and Processors (ASAP), Montreal, QC, Canada, pp. 391–396, Jul 2007

    Google Scholar 

  25. Huang, J., Momenzadeh, M., Lombardi, F.: Analysis of missing and additional cell defects in sequential quantum-dot cellular automata. Integr. VLSI J. 40(1), 503–515 (2007)

    Article  Google Scholar 

  26. Jin, Z.: Fabrication and measurement of molecular quantum cellular automata (QCA) device. Ph.D. thesis, University of Notre Dame (2006)

    Google Scholar 

  27. Kartschoke, P.: Implementation issues in conservative logic networks. In: M.S.E.E. Thesis, University of Virginia, Charlottesville, VA (1992)

    Google Scholar 

  28. Kim, K., Wu, K., Karri, R.: The robust QCA adder designs using composable QCA building blocks. IEEE Trans. Comput. Aided Des. 26(1), 176–183 (2007)

    Article  Google Scholar 

  29. Kong, K., Shang, Y., Lu, R.: An optimized majority logic synthesis methodology for quantum-dot cellular automata. IEEE Trans. Nanotechnol. 9(2), 170–183 (2010)

    Article  Google Scholar 

  30. Kostinski, N., Fok, M.P., Prucnal, P.R.: Experimental demonstration of an all-optical fiber-based Fredkin gate. Opt. Lett. 34(18), 2766–2768 (2009)

    Article  Google Scholar 

  31. Landauer, R.: Irreversibility and heat generation in the computational process. IBM J. Res. Dev. 5, 183–191 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  32. Chang, L., Frank, D.J., Montoye, R.K., Koester, S.J., Ji, B.L., Coteus, P.W., Dennard, R.H., Haensch, W.: Practical strategies for power-efficient computing technologies. Proc. IEEE 98(2), 215–236 (2010)

    Article  Google Scholar 

  33. Lent, C., Isaksen, B., Lieberman, M.: Molecular quantum-dot cellular automata. J. Am. Chem. Soc. 125(4), 1056–1063 (2003)

    Article  Google Scholar 

  34. Lent, C., Tougaw, P.: A device architecture for computing with quantum dots. Proc. IEEE 85(4), 541–557 (1997)

    Article  Google Scholar 

  35. Liu, W., Srivastava, S., Lu, L., O’Neill, M., Swartzlander, E.: Are QCA cryptographic circuits resistant to power analysis attack? IEEE Trans. Nanotechnol. 11(6), 1239–1251 (2012)

    Article  Google Scholar 

  36. Lu, Y., Liu, M., Lent, C.: Molecular quantum-dot cellular automata: from molecular structure to circuit dynamics. J. Appl. Phys. 102 (2007) (Article No. 034311)

    Google Scholar 

  37. Ma, X., Huang, J., Metra, C., Lombardi, F.: Reversible gates and testability of one dimensional arrays of molecular QCA. J. Elect. Test. 24(1–3), 1244–1245 (2008)

    Google Scholar 

  38. Ma, X., Huang, J., Metra, C., Lombardi, F.: Detecting multiple faults in one-dimensional arrays of reversible qca gates. J. Elect. Test. 25(1), 39–54 (2009)

    Article  Google Scholar 

  39. Mahammad, S., Veezhinathan, K.: Constructing online testable circuits using reversible logic. IEEE Trans. Instrum. Meas. 59, 101–109 (2010)

    Article  Google Scholar 

  40. Maslov, D., Dueck, G.W.: Reversible cascades with minimal garbage. IEEE Trans. Comput. Aided Des. 23(11), 1497–1509 (2004)

    Article  Google Scholar 

  41. Mathew, J., Rahaman, H., Jose, B.R., Pradhan, D.K.: Design of reversible finite field arithmetic circuits with error detection. In: 21st International Conference on VLSI Design 2008, VLSID 2008, pp. 453–459. IEEE (2008)

    Google Scholar 

  42. Momenzadeh, M., Ottavi, M., Lombardi, F.: Modeling QCA defects at molecular level in combinational circuits. In: Proceedings of DFT in VLSI Systems, Monterey, CA, USA, pp. 208–216, Oct 2005

    Google Scholar 

  43. Morita, K.: Reversible computing and cellular automata-a survey. Theor. Comput. Sci. 395(1), 101–131 (2008)

    Article  MATH  Google Scholar 

  44. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)

    MATH  Google Scholar 

  45. Niemier, M.T., Rodrigues, A.F., Kogge, P.M.: A potentially implementable FPGA for quantum dot cellular automata. In: Proceedings of the 1st Workshop on Non-Silicon Computation (NSC-1), Boston, MS (2002)

    Google Scholar 

  46. Ottavi, M., Schiano, L., Lombardi, F., Tougaw, D.: HDLQ: a HDL environment for QCA design. ACM J. Emerg. Tech. 2(4), 243–261 (2006)

    Article  Google Scholar 

  47. Parhami, B.: Fault-tolerant reversible circuits. In: Proceedings of 40th Asilomar Conference Signals, Systems, and Computers, Pacific Grove, CA, pp. 1726–1729, Nov 2006

    Google Scholar 

  48. Patel, K.N., Hayes, J.P., Markov, I.L.: Fault testing for reversible circuits. IEEE Trans. CAD 23, 410–416 (2004)

    Article  Google Scholar 

  49. Pedram, M., Wu, Q., Wu, X.: A new design for double edge triggered flip-flops. In: Proceedings of the Asia South Pacific Design Automation Conference, Yokahama, pp. 417–421 (1998)

    Google Scholar 

  50. Polian, I., Fiehn, T., Becker, B., Hayes, J.P.: A family of logical fault models for reversible circuits. In: ATS ’05: Proceedings of the 14th Asian Test Symposium on Asian Test Symposium, Kolkata, India, pp. 422–427 (2005)

    Google Scholar 

  51. Prasad, A.K., Shende, V., Markov, I., Hayes, J., Patel, K.N.: Data structures and algorithms for simplifying reversible circuits. ACM JETC 2(4), 277–293 (2006)

    Article  Google Scholar 

  52. Pulecio, J.F., Bhanja, S.: Magnetic cellular automata coplanar cross wire systems. J. Appl. Phys. 107(3), 034308 (2010)

    Article  Google Scholar 

  53. Pulecio, J., Pendru, P., Kumari, A., Bhanja, S.: Magnetic cellular automata wire architectures. IEEE Trans. Nanotechnol. 99, 1 (2011)

    Google Scholar 

  54. Rahaman, H., Kole, D.K., Das, D.K., Bhattacharya, B.B.: On the detection of missing gate faults in reversible circuits by a universal test set. In: Proceedings VLSI Design 2008, 21st International Conference on VLSI Design, Hyderabad, India, pp. 163–168, Jan 2008

    Google Scholar 

  55. Ren, J., Semenov, V.K.: Progress with physically and logically reversible superconducting digital circuits. IEEE Trans. Appl. Supercond. 21(3), 780–786 (2011)

    Article  Google Scholar 

  56. Ren, J., Semenov, V.K., Polyakov, Y.A., Averin, D.V., Tsai, J.S.: Progress towards reversible computing with nSQUID arrays. IEEE Trans. Appl. Supercond. 19, 961–967 (2009)

    Article  Google Scholar 

  57. Rice, J.: A new look at reversible memory elements. In: Proceedings of International Symposium on Circuits and Systems (ISCAS) 2006, Kos, Greece, pp. 243–246, May 2006

    Google Scholar 

  58. Semenov, V.K., Danilov, G.V., Averin, D.V.: Classical and quantum operation modes of the reversible Josephson-junction logic circuits. IEEE Trans. Appl. Supercond. 17, 455–461 (2007)

    Article  Google Scholar 

  59. Shende, V.V., Prasad, A., Markov, I., Hayes, J.: Synthesis of reversible logic circuits. IEEE Trans. CAD 22, 710–722 (2003)

    Article  Google Scholar 

  60. Swaminathan, G.: Concurrent error detection techniques using parity. In: M.S.E.E. Thesis, University of Virginia, Charlottesville, VA (1989)

    Google Scholar 

  61. Swaminathan, G., Aylor, J., Johnson, B.: Concurrent testing of VLSI circuits using conservative logic. In: Proceedings of International Conference on Computer Design (ICCD), Cambridge, MA, pp. 60–65, Sep 1990

    Google Scholar 

  62. Tahoori, M.B., Huang, J., Momenzadeh, M., Lombardi, F.: Testing of quantum cellular automata. IEEE Trans. Nanotechnol. 3(4), 432–442 (2004)

    Article  Google Scholar 

  63. Taraphdara, C., Chattopadhyay, T., Roy, J.: Machzehnder interferometer-based all-optical reversible logic gate. Opt. Laser Technol. 42(2), 249–259 (2010)

    Article  Google Scholar 

  64. Taskin, B., Chiu, A., Salkind, J., Venutolo, D.: A shift-register-based QCA memory architecture. ACM J. Emerg. Tech. Comput. Sys. 5(1) (2009) (Article No. 4)

    Google Scholar 

  65. Thapliyal, H.: Design, synthesis and test of reversible logic circuits for emerging nanotechnologies. Ph.D. thesis, University of South Florida, Tampa, Dec 2011

    Google Scholar 

  66. Thapliyal, H., Ranganathan, N.: Reversible logic-based concurrently testable latches for molecular QCA. IEEE Trans. Nanotechnol. 9(1), 62–69 (2010)

    Article  Google Scholar 

  67. Thapliyal, H., Srinivas, M.B., Zwolinski, M.: A beginning in the reversible logic synthesis of sequential circuits. In: Proceedings of the Military and Aerospace Programmable Logic Devices International Conference Washington, Sep 2005

    Google Scholar 

  68. Thapliyal, H., Vinod, A.P.: Design of reversible sequential elements with feasibility of transistor implementation. In: Proceedings of the 2007 IEEE International Symposium on Circuits and Systems, New Orleans, USA, pp. 625–628 (May 2007)

    Google Scholar 

  69. Thapliyal, H., Ranganathan, N.: Design of reversible sequential circuits optimizing quantum cost, delay and garbage outputs. ACM J. Emerg. Technol. Comput. Syst. 6(4), 14:1–14:35 (2010). (Article No. 14)

    Article  Google Scholar 

  70. Tougaw, P., Lent, C.: Logical devices implemented using quantum cellular automata. J. Appl. Phys. 75(3), 1818–1825 (1994)

    Article  Google Scholar 

  71. Tougaw, P., Lent, C.: Dynamic behavior of quantum cellular automata. J. Appl. Phys. 80(8), 4722–4736 (1996)

    Article  Google Scholar 

  72. Vasudevan, D.P., Lala, P.K., Parkerson, J.P.: Reversible-logic design with online testability. IEEE Trans. Instrum. Meas. 55(2), 406–414 (2006)

    Article  Google Scholar 

  73. Wang, P., Niamat, M., Vemuru, S.: Minimal majority gate mapping of 4-variable functions for quantum cellular automata. In: 2011 11th IEEE Conference on Nanotechnology (IEEE-NANO), pp. 1307–1312. IEEE (2011)

    Google Scholar 

  74. Wei, T., Wu, K., Karri, R., Orailoglu, A.: Fault tolerant quantum cellular array (QCA) design using triple modular redundancy with shifted operands. In: Proceedings of the 2005 Conference on Asia South Pacific Design Automation, Shanghai, China, pp. 1192–1195 (Jan 2005)

    Google Scholar 

  75. Yang, G., Song, X., Hung, W.N., Perkowski, M.A.: Bi-directional synthesis of 4-bit reversible circuits. Comput. J. 51(2), 207–215 (2008)

    Article  Google Scholar 

  76. Zhang, R., Walus, K., Wang, W., Jullien, G.: Performance comparison of quantum dot cellular automata adders. In: Proceedings of the IEEE International Symposium Circiuts and Systems, Kobe, Japan, pp. 2522–2526 (May 2005)

    Google Scholar 

  77. Zhang, R., Walus, K., Wang, W., Jullien, G.A.: A method of majority logic reduction for quantum cellular automata. IEEE Trans. Nanotechnol. 3(4), 443–450 (2004)

    Article  Google Scholar 

  78. Zhong, J., Muzio, J.: Analyzing fault models for reversible logic circuits. IEEE Congr. Evol. Comput., Vancouver, BC, pp. 2422–2427 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Himanshu Thapliyal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Thapliyal, H., Ranganathan, N., Kotiyal, S. (2014). Reversible Logic Based Design and Test of Field Coupled Nanocomputing Circuits. In: Anderson, N., Bhanja, S. (eds) Field-Coupled Nanocomputing. Lecture Notes in Computer Science(), vol 8280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43722-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43722-3_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43721-6

  • Online ISBN: 978-3-662-43722-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics