Abstract
The quantum-dot cellular automata (QCA) is considered to be one of the ground-breaking nanotechnologies developed over the last two decades. A layered T (LT) logic cell library is constructed herein, and the methodology is extended to generic adder and subtractor module designs. The two proposed algorithms lead to more efficient QCA layout designs for an n-bit ripple carry adder (RCA) and subtractor based on an effective clock zone assignment approach. The suggested one-, four-, and eight-bit RCAs and subtractors surpass most of their existing counterparts by offering lower effective area and cell complexity. A comparative analysis is presented regarding the complexity, irreversible power dissipation, and Costα of the proposed n-bit layouts from a cost estimation purview.
Similar content being viewed by others
References
Macucci, M.: Quantum Cellular Automata Theory, Experimentation and Prospects. Imperial College Press, London (2006)
Tans, S.J., Verschueren, A.R.M., Dekker, C.: Room-temperature transistor based on a single carbon nanotube. Nature 393(6680), 49–52 (1998)
Flatté, M.E., Vignale, G.: Unipolar spin diodes and transistors. Appl. Phys. Lett. 78(9), 1273–1275 (2001). https://doi.org/10.1063/1.1348317
Yang, T., Kiehl, R.A., Chua, L.O.: Tunneling phase logic cellular nonlinear networks. Int. J. Bifurcat. Chaos 11(12), 2895–2911 (2001). https://doi.org/10.1142/S0218127401004145
Heath, J.R., Ratner, M.A.: Molecular electronics. Phys. Today 56(5), 43–49 (2003). https://doi.org/10.1063/1.1583533
Lent, C.S., Tougaw, P.D., Porod, W., Bernstein, G.H.: Quantum cellular automata. Nanotechnology (1993). https://doi.org/10.1088/0957-4484/4/1/004
Kummamuru, R.K., et al.: Power gain in a quantum-dot cellular automata latch. Appl. Phys. Lett. 81(7), 1332–1334 (2002). https://doi.org/10.1063/1.1499511
Quantum mechanics classical results, modern systems, and visualized examples.
Hennessy, K., Lent, C. S.: Clocking of molecular quantum-dot cellular automata. J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 19(5), 1752–1755 (2001). doi: https://doi.org/10.1116/1.1394729.
Graziano, M., Pulimeno, A., Wang, R., Wei, X., Roch, M.R., Piccinini, G.: Process variability and electrostatic analysis of molecular QCA. ACM J. Emerg. Technol. Comput. Syst. (2015). https://doi.org/10.1145/2738041
Niemier, M.T., Kogge, P.M.: Origins and Motivations for design rules in QCA. Nano Quantum Mol. Comput. (2006). https://doi.org/10.1007/1-4020-8068-9_9
Mukherjee, C., Sukla, A.S., Basu, S.S., Chakrabarty, R., Khan, A., De, D.: Layered T full adder using quantum-dot cellular automata. 2016, doi: https://doi.org/10.1109/CONECCT.2015.7383867.
Liu, W., Lu, L., Neill, O., Member, S.: A first step toward cost functions for quantum-dot cellular automata designs. IEEE Trans. Nanotechnol. 13(3), 476–487 (2014)
Gardelis, S., Smith, C.G., Cooper, J., Ritchie, D.A., Linfield, E.H., Jin, Y.: Evidence for transfer of polarization in a quantum dot cellular automata cell consisting of semiconductor quantum dots. Phys. Rev. B Condens. Matter Mater. Phys., 67(3), 333021–333024 (2003), doi: https://doi.org/10.1103/PhysRevB.67.033302.
Orlov, A.O., Amlani, I., Bernstein, G.H., Lent, C.S., Snider, G.L.: Realization of a functional cell for quantum-dot cellular automata. Science. 277(5328), 928–930 (1997). https://doi.org/10.1126/science.277.5328.928
Isaksen, B., Lent, C.S.: Molecular quantum-dot cellular automata. Proc. IEEE Conf. Nanotechnol. 1, 5–8 (2003). https://doi.org/10.1109/NANO.2003.1231700
Cowburn, R.P., Welland, M.E.: Room temperature magnetic quantum cellular automata. Science 287(5457), 1466–1468 (2000). https://doi.org/10.1126/science.287.5457.1466
Walus, K., Jullien, G.A.: Design tools for an emerging SoC technology : quantum-dot cellular automata. Proc. IEEE 94(6), 1225–1244 (2006). https://doi.org/10.1109/JPROC.2006.875791
Snider, G.S.L., et al.: Quantum-dot cellular automata. Microelectron. Eng. 47, 261–263 (1999)
Momenzadeh, M., Huang, J., Tahoori, M.B., Lombardi, F.: Characterization, test, and logic synthesis of and-or-inverter (AOI) gate design for QCA implementation. IEEE Trans Comput. Des. Integr. Circuits Syst. 24(12), 1881–1893 (2005). https://doi.org/10.1109/TCAD.2005.852667
Das, K., De, D.: A study on diverse nanostructure for implementing logic gate design for QCA. Int. J. Nanosci. 10(1), 263–269 (2011). https://doi.org/10.1142/S0219581X11007892
Sen, B., Sengupta, A., Dalui, M., Sikdar, B.K.: Design of testable universal logic gate targeting minimum wire-crossings in QCA logic circuit. In: Proceedings 13th Euromicro Conference on Digital System Design: Architectures, Methods and Tools, DSD 2010, pp. 613–620 (2010), https://doi.org/10.1109/DSD.2010.114.
Mukherjee, C., Roy, S.S., Panda, S., Maji, B.: T-gate : concept of partial polarization in quantum dot cellular automata. Proc. VLSI Des. Test (2016). https://doi.org/10.1109/ISVDAT.2016.8064844
Khanday, F.A., Kant, N.A., Bangi, Z.A., Shah, N.A.: A novel universal (FNZ) gate in quantum dot cellular automata (QCA). In: IMPACT 2013 - Proceedings of the International Conference on Multimedia Signal Processing and Communication Technologies (2013). https://doi.org/10.1109/MSPCT.2013.6782130.
Mukherjee, C., Panda, S., Mukhopadhyay, A.K., Maji, B.: Synthesis of standard functions and generic Ex-OR module using layered T gate. Int. J. High Perform. Syst. Archit. 7(2), 70–86 (2017)
Mukherjee, C., Panda, S., Mukhopadhyay, A.K., Maji, B.: QCA gray code converter circuits using LTEx methodology. Int. J. Theor. Phys. 57(7), 2068–2092 (2018). https://doi.org/10.1007/s10773-018-3732-4
Nejad, M.Y., Mosleh, M.: A review on QCA multiplexer designs. Majlesi J. Electr. Eng. 11(2), 69–79 (2017)
Afrooz, S., Navimipour, N.J.: Memory designing using quantum-dot cellular automata: systematic literature review, classification and current trends. J. Circuits, Syst. Comput. (2017). https://doi.org/10.1142/S0218126617300045.
Singh, G., Sarin, R.K., Raj, B.: A review of quantum-dot cellular automata based adders. Int. J. Hybrid Inf. Technol. 10(4), 41–58 (2017). https://doi.org/10.14257/ijhit.2017.10.4.04
Wang, W., Walus, K., Jullien, G.A.: Quantum-dot cellular automata adders. Proc. IEEE Conf. Nanotechnol. 1, 461–464 (2003). https://doi.org/10.1109/NANO.2003.1231818
Cho, H., Swartzlander, E.E.: Adder designs and analyses for quantum-dot cellular automata. IEEE Trans. Nanotechnol. 6(3), 374–383 (2007). https://doi.org/10.1109/TNANO.2007.894839
Kim, K., Wu, K., Karri, R.: The robust QCA adder designs using composable QCA building blocks. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 176–183 (2007)
Haruehanroengra, S., Wang, W.: Efficient design of QCA adder structures (2007). https://doi.org/10.4028/www.scientific.net/ssp.121-123.553.
Javid, M., Mohamadi, K.: Characterization and tolerance of QCA full adder under missing cells defects (2010). https://doi.org/10.1109/ICMENS.2009.22.
Liu, W., Lu, L., O’Neill, M., Swartzlander, E.E.: Cost-efficient decimal adder design in Quantum-dot cellular automata. In: ISCAS 2012 - 2012 IEEE International Symposium on Circuits and Systems, pp. 1347–1350 (2012). doi: https://doi.org/10.1109/ISCAS.2012.6271491.
Pudi, V., Sridharan, K.: Low complexity design of ripple carry and Brent-Kung adders in QCA. IEEE Trans. Nanotechnol. (2012). https://doi.org/10.1109/TNANO.2011.2158006
Kianpour, M., Sabbaghi-Nadooshan, R., Navi, K.: A novel design of 8-bit adder/subtractor by quantum-dot cellular automata. J. Comput. Syst. Sci. 80(7), 1404–1414 (2014). https://doi.org/10.1016/j.jcss.2014.04.012
Farazkish, R.: A new quantum-dot cellular automata fault-tolerant full-adder. J. Comput. Electron. 14(2), 506–514 (2015). https://doi.org/10.1007/s10825-015-0668-2
Farazkish, R., Khodaparast, F.: Design and characterization of a new fault-tolerant full-adder for quantum-dot cellular automata. Microprocess. Microsyst. 39(6), 426–433 (2015). https://doi.org/10.1016/j.micpro.2015.04.004
Abedi, D., Jaberipur, G., Sangsefidi, M.: Coplanar full adder in quantum-dot cellular automata via clock-zone-based crossover. IEEE Trans. Nanotechnol. (2015). https://doi.org/10.1109/TNANO.2015.2409117
Kumar, R., Ghosh, B., Gupta, S.: Adder design using a 5-input majority gate in a novel ‘multilayer gate design paradigm’ for quantum dot cellular automata circuits. J. Semicond. (2015). https://doi.org/10.1088/1674-4926/36/4/045001
Hashemi, S., Navi, K.: A novel robust QCA full-adder. Procedia Mater. Sci. 11, 376–380 (2015). https://doi.org/10.1016/j.mspro.2015.11.133
Roohi, A., DeMara, R.F., Khoshavi, N.: Design and evaluation of an ultra-area-efficient fault-tolerant QCA full adder. Microelectronics J. (2015). https://doi.org/10.1016/j.mejo.2015.03.023
Ahmad, F., Bhat, G.M., Khademolhosseini, H., Azimi, S., Angizi, S., Navi, K.: Towards single layer quantum-dot cellular automata adders based on explicit interaction of cells. J. Comput. Sci. 16, 8–15 (2016). https://doi.org/10.1016/j.jocs.2016.02.005
Ahmad, P.Z., Quadri, S.M.K., Tantary, S.M., Wani, G.M., Ahmad, F., Bahar, A.N.: Design of novel QCA-based half/full subtractors. Nanomater. Energy (2017). https://doi.org/10.1680/jnaen.15.00020
Balali, M., Rezai, A., Balali, H., Rabiei, F., Emadi, S.: Towards coplanar quantum-dot cellular automata adders based on efficient three-input XOR gate. Res. Phys. (2017). https://doi.org/10.1016/j.rinp.2017.04.005
Barughi, Y.Z., Heikalabad, S.R.: A three-layer full adder/subtractor structure in quantum-dot cellular automata. Int. J. Theor. Phys. 56(9), 2848–2858 (2017). https://doi.org/10.1007/s10773-017-3453-0
Balali, M., Rezai, A.: Design of low-complexity and high-speed coplanar four-bit ripple carry adder in QCA technology. Int. J. Theor. Phys. (2018). https://doi.org/10.1007/s10773-018-3720-8
Wang, L., Xie, G.: Novel designs of full adder in quantum-dot cellular automata technology. J. Supercomput. (2018). https://doi.org/10.1007/s11227-018-2481-8
Adelnia, Y., Rezai, A.: A novel adder circuit design in quantum-dot cellular automata technology. Int. J. Theor. Phys. 58(1), 184–200 (2019). https://doi.org/10.1007/s10773-018-3922-0
Zoka, S., Gholami, M.: A novel efficient full adder–subtractor in QCA nanotechnology. Int. Nano Lett. (2018). https://doi.org/10.1007/s40089-018-0256-0
Raj, M., Gopalakrishnan, L., Ko, S.B.: Fast quantum-dot cellular automata adder/subtractor using novel fault tolerant exclusive-or gate and full adder. Int. J. Theor. Phys. (2019). https://doi.org/10.1007/s10773-019-04184-7
Ahmadpour, S.S., Mosleh, M.: New designs of fault-tolerant adders in quantum-dot cellular automata. Nano Commun. Netw. 19, 10–25 (2019). https://doi.org/10.1016/j.nancom.2018.11.001
Lu, L., Liu, W., O’Neill, M., Swartzlander, E.E.: QCA Systolic array design. IEEE Trans. Comput. (2013). https://doi.org/10.1109/TC.2011.234
Fazzion, E., Fonseca, O. L., Nacif, J. A. M., Neto, O. P. V., Fernandes, A. O., Silva, D. S.: A quantum-dot cellular automata processor design. In: 2014 27th Symposium on Integrated Circuits and Systems Design (SBCCI), pp. 1–7 (2014). IEEE, doi: https://doi.org/10.1145/2660540.2660997.
Ruetz, P.: Adder which employs both carry look-ahead and carry select techniques. US5898596A (1999)
Acknowledgements
The authors would like to thank Prof. Debdatta Banerjee for her literary contribution to this work.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mukherjee, C., Panda, S., Mukhopadhyay, A.K. et al. The design, analysis, and cost estimation of a generic adder and subtractor using the layered T (LT) logic reduction methodology with a quantum-dot cellular-automata-based approach. J Comput Electron 20, 1611–1624 (2021). https://doi.org/10.1007/s10825-021-01712-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-021-01712-9