Radix-4 Recoded Multiplier on Quantum-Dot Cellular Automata

  • Ismo Hänninen
  • Jarmo Takala
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5657)


This paper describes the implementation of an advanced multiplication algorithm on quantum-dot cellular automata (QCA) nanotechnology, promising molecular density circuits with extreme operating frequencies, using a single homogeneous layer of the basic cells. The multiplier layout is verified with time-dependent quantum mechanical simulation, to ensure stable ground state computation under the fine-grained pipelining constraints of the technology. The novel design utilizes radix-4 modified Booth recoding and ultra-fast carry-save addition, resulting in stall-free pipeline operation, with twice the throughput of the previous sequential structure and minimized active circuit area.


QCA nanotechnology arithmetic multiplication 


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  1. 1.
    Lent, C., Tougaw, P., Porod, W.: Quantum cellular automata: the physics of computing with arrays of quantum dot molecules. In: Proc. Workshop Phys. Comp., Dallas, TX, November 17-20, pp. 5–13 (1994)Google Scholar
  2. 2.
    Lent, C., Tougaw, P.: A device architecture for computing with quantum dots. Proc. IEEE 85(4), 541–557 (1997)CrossRefGoogle Scholar
  3. 3.
    Snider, G., Orlov, A., Amlani, I., Bernstein, G., Lent, C., Merz, J., Porod, W.: Quantum-dot cellular automata. In: Dig. Papers of Microprocesses and Nanotechnology Conf., Yokohama, Japan, July 6-8, pp. 90–91 (1999)Google Scholar
  4. 4.
    Orlov, A., Kummamuru, R., Ramasubramaniam, R., Lent, C., Bernstein, G., Snider, G.: Clocked quantum-dot cellular automata devices: experimental studies. In: Proc. IEEE Conf. Nanotechnology, Maui, HI, October 28-30, pp. 425–430 (2001)Google Scholar
  5. 5.
    Kummamuru, R., Orlov, A., Ramasubramaniam, R., Lent, C., Bernstein, G., Snider, G.: Operation of a quantum-dot cellular automata (QCA) shift register and analysis of errors. IEEE Trans. Electron Devices 50(9), 1906–1913 (2003)CrossRefGoogle Scholar
  6. 6.
    Blair, E., Lent, C.: Quantum-dot cellular automata: an architecture for molecular computing. In: Proc. Int. Conf. Simulation of Semiconductor Processes and Devices, Boston, MA, September 3–5, pp. 14–18 (2003)Google Scholar
  7. 7.
    Lent, C., Liu, M., Lu, Y.: Bennett clocking of quantum-dot cellular automata and the limits to binary logic scaling. Nanotechnology 17(16), 4240–4251 (2006)CrossRefGoogle Scholar
  8. 8.
    Frost-Murphy, S., DeBenedictis, E., Kogge, P.: General floorplan for reversible quantum-dot cellular automata. In: Proc. ACM Int. Conf. Computing Frontiers, Ischia, Italy, May 7-9, pp. 77–81 (2007)Google Scholar
  9. 9.
    Kim, K., Wu, K., Karri, R.: The robust QCA adder designs using composable QCA building blocks. IEEE Trans. Computer-Aided Design 26(1), 176–183 (2007)CrossRefGoogle Scholar
  10. 10.
    Walus, K., Jullien, G.: Design tools for an emerging SoC technology: quantum-dot cellular automata. Proc. IEEE 94(6), 1225–1244 (2006)CrossRefGoogle Scholar
  11. 11.
    Walus, K., Jullien, G., Dimitrow, V.: Computer arithmetic structures for quantum cellular automata. In: Conf. Rec. 37th Asilomar Conf. Signals, Systems and Computers, Pacific Grove, CA, November 9-12, pp. 1435–1439 (2003)Google Scholar
  12. 12.
    Cho, H., Swartzlander, E.: Serial parallel multiplier design in quantum-dot cellular automata. In: Proc. IEEE Symp. Computer Arithmetic, Montepellier, France, June 25-27, pp. 7–15 (2007)Google Scholar
  13. 13.
    Hänninen, I., Takala, J.: Binary multipliers on quantum-dot cellular automata. Facta Universitatis 20(3), 541–560 (2007)CrossRefGoogle Scholar
  14. 14.
    Wang, W., Walus, K., Jullien, G.: Quantum-dot cellular automata adders. In: Proc. IEEE Conf. Nanotechnology, San Francisco, CA, August 11-14, pp. 461–464 (2003)Google Scholar
  15. 15.
    Hänninen, I., Takala, J.: Binary adders on quantum-dot cellular automata. J. Sign. Process. Syst. (to appear),
  16. 16.
    Hänninen, I., Takala, J.: Robust adders based on quantum-dot cellular automata. In: Proc. IEEE Int. Conf. Application-Specific Systems, Architectures and Processors, Montréal, QC, Canada, July 8-11, pp. 391–396 (2007)Google Scholar
  17. 17.
    Fijany, A., Toomarian, N., Modarress, K., Spotnitz, M.: Bit-serial adder based on quantum dots. Tech. Rep. NPO-20869, NASA’s Jet Propulsion Laboratory, Pasadena, CA (2003)Google Scholar
  18. 18.
    Zhang, R., Walus, K., Wang, W., Jullien, G.: Performance comparison of quantum-dot cellular automata adders. In: IEEE Int. Symp. Circ. and Syst., Kobe, Japan, May 23-26, pp. 2522–2526 (2005)Google Scholar
  19. 19.
    Cho, H., Swartzlander, E.: Adder designs and analyses for quantum-dot cellular automata. IEEE Trans. Nanotechnol. 6(3), 374–383 (2007)CrossRefGoogle Scholar
  20. 20.
    Hänninen, I., Takala, J.: Pipelined array multiplier based on quantum-dot cellular automata. In: Proc. European Conf. Circuit Theory and Design, Seville, Spain, August 26-30, pp. 938–941 (2007)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2009

Authors and Affiliations

  • Ismo Hänninen
    • 1
  • Jarmo Takala
    • 1
  1. 1.Department of Computer SystemsTampere University of TechnologyTampereFinland

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