Design and Implementation of Low Power 1 and 2 Trit Multipliers

International Journal of Electrical and Electronics Engineering
© 2024 by SSRG - IJEEE Journal
Volume 11 Issue 9
Year of Publication : 2024
Authors : R. Nagarathna, A.R. Aswatha, B.V. Srividya
pdf
How to Cite?

R. Nagarathna, A.R. Aswatha, B.V. Srividya, "Design and Implementation of Low Power 1 and 2 Trit Multipliers," SSRG International Journal of Electrical and Electronics Engineering, vol. 11,  no. 9, pp. 9-27, 2024. Crossref, https://doi.org/10.14445/23488379/IJEEE-V11I9P102

Abstract:

Multipliers are combinational logic circuits used in applications like computers, calculators, general-purpose processors and digital signal processors. They are widely used in a variety of signal-processing applications, as 70% of these applications use algorithms which include addition and multiplication operations. In VLSI/embedded applications, power consumption is an important factor to lessen the cost of the chip and enhance battery life. Traditional multipliers are implemented using binary logic, in which each line carries two signal levels, logic 0 or logic 1. In contrast, Ternary logic uses circuits, which carry three levels 0,1, and 2, known as trits. Ternary gates, which are required for ternary multipliers, are implemented using multi-threshold MOSFETs. Leakage current and, hence, static power can be reduced by a forced stack that deploys additional transistors to split the current. In this paper, low-power ternary gates are realized using the forced stack technique. This work mainly designs and implements 1-trit and 2-trit multipliers utilizing low-power ternary logic gates, using Cadence Virtuoso using 45nm Technology. The power of the 1-trit multiplier and 2-trit multiplier is compared with that of its counter binary multipliers, which show reduced power consumption. Further, this work proposes a novel technique to implement a ternary multiplier using Single Pole Triple Throw (SPTT) switches, resulting in a reduced number of transistors.

Keywords:

Ternary, Multiplier, Low power, Logic Circuit, STI.

References:

[1] A.P. Dhande, V.T. Ingole, and V.R. Ghiye, Ternary Digital System: Concepts and Applications, SM Online Publishers LLC, 2014.
[Google Scholar]
[2] Subrata Das, Partha Sarathi Dasgupta, and Samar Sensarma, “Arithmetic Algorithms for Ternary Number System,” Progress in VLSI Design and Test, pp. 111-120, 2012.
[CrossRef] [Google Scholar] [Publisher Link]
[3] V.T. Gaikwad, and P.R. Deshmukh, “Implementation of Low Power Ternary Logic Gates Using CMOS Technology,” International Journal of Science and Research, vol. 3, no. 10, pp. 2221-2224, 2014.
[Publisher Link]
[4] Furqan Zahoor et al., “Carbon Nanotube and Resistive Random Access Memory Based Unbalanced Ternary Logic Gates and Basic Arithmetic Circuits,” IEEE Access, vol. 8, pp. 104701-104717, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Elena Dubrova, “Multiple-Valued Logic in VLSI: Challenges and Opportunities,” Proceedings of NORCHIP, vol. 99, no. 1999, 1999.
[Google Scholar]
[6] A.P. Dhande, Satish S. Narkhede, and Shridhar S. Dudam, “VLSI Implementation of Ternary Gates Using Tanner Tool,” 2014 2nd International Conference on Devices, Circuits and Systems (ICDCS), Coimbatore, India, pp. 1-5, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Sneh Lata Murotiya, Anu Gupta, and Ayan Pandit, “CNTFET-Based Low Power Design of 4-Input Ternary XOR Function,” 2014 International Conference on Computer and Communication Technology (ICCCT), Allahabad, India, pp. 347-350, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Ahmet Unutulmaz, and Cem Unsalan, “Implementation and Applications of a Ternary Threshold Logic Gate,” Circuits, Systems, and Signal Processing, vol. 43, pp. 1192-1207, 2024.
[CrossRef] [Google Scholar] [Publisher Link]
[9] G. Thrishala, and K. Ragini, “Design and Implementation of Ternary Logic Circuits for VLSI Applications,” International Journal of Innovative Technology and Exploring Engineering, vol. 9, no. 4, pp. 3117-3121, 2020.
[Google Scholar] [Publisher Link]
[10] Erfan Shahrom, and Seied Ali Hosseini, “A New Low Power Multiplexer Based Ternary Multiplier Using CNTFETs,” AEU - International Journal of Electronics and Communications, vol. 93, pp. 191-207, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[11] V.T. Gaikwad, and P.R. Deshmukh, “Design of CMOS Ternary Logic Family Based on Single Supply Voltage,” 2015 International Conference on Pervasive Computing (ICPC), Pune, India, pp. 1-6, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Zarin Tasnim Sandhie, Farid Uddin Ahmed, and Masud H. Chowdhury, “Design of Ternary Logic and Arithmetic Circuits Using GNRFET,” IEEE Open Journal of Nanotechnology, vol. 1, pp. 77-87, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[13] Kushawaha Jyoti, and Satish Narkhede, “An Approach to Ternary Logic Gates Using FinFET,” Proceedings of the International Conference on Advances in Information Communication Technology & Computing (AICTC '16), pp. 1-6, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Sunmean Kim, Taeho Lim, and Seokhyeong Kang, “An Optimal Gate Design for the Synthesis of Ternary Logic Circuits,” 2018 23rd Asia and South Pacific Design Automation Conference (ASP-DAC), Jeju, Korea (South), pp. 476-481, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[15] Aiman Malik, Md. Shahbaz Hussain, and Mohd. Hasan, “An Approximate Ternary Full Adder Using Carbon Nanotube Field Effect Transistors,” 2022 5th International Conference on Multimedia, Signal Processing and Communication Technologies (IMPACT), Aligarh, India, pp. 1-6, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[16] Jongho Yoon et al., “Optimizing Ternary Multiplier Design with Fast Ternary Adder,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 70, no. 2, pp. 766-770, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[17] K.C. Smith, “A Multiple Valued Logic: A Tutorial and Appreciation,” Computer, vol. 21, no. 4, pp. 17-27, 1988.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Hurst, “Multiple-Valued Logic-its Status and its Future,” IEEE Transactions on Computers, vol. C-33, no. 12, pp. 1160-1179, 1984.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Xiao-Yuan Wang et al., “A Review on the Design of Ternary Logic Circuits,” Chinese Physics B, vol. 30, no. 12, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[20] Y. Sujatha, and K.N.V.S. Vijaya Lakshmi, “Applications of XOR Gate Using Ternary, Logic,” International Journal of Creative Research Thoughts, vol. 5, no. 4, pp. 2450-2454, 2017.
[Publisher Link]
[21] Mingqiang Huang et al., “Design and Implementation of Ternary Logic Integrated Circuits by Using Novel Two-Dimensional Materials,” Applied Sciences, vol. 9, no. 20, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[22] Vallabhuni Vijay et al., “Design of Unbalanced Ternary Logic Gates and Arithmetic Circuits,” Journal of VLSI Circuits and Systems, vol. 4, no. 1, pp. 20-26, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[23] Makani Nailesh Kishor, and Satish S. Narkhede, “A Novel Finfet Based Approach for the Realization of Ternary Gates,” ICTACT Journal on Microelectronics, vol. 2, no. 2, pp. 254-260, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[24] Tabassum Khurshid, and Vikram Singh, “Energy Efficient Design of Unbalanced Ternary Logic Gates and Arithmetic Circuits Using CNTFET,” AEU - International Journal of Electronics and Communications, vol. 163, 2023.
[CrossRef] [Google Scholar] [Publisher Link]
[25] P.A. Gowrisankar, “Design of Multi-Valued Ternary Logic Gates Based on Emerging Sub-32nm Technology,” 2017 Third International Conference on Science Technology Engineering & Management (ICONSTEM), Chennai, India, pp. 1023-1031, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[26] Badugu Divya Madhuri, and Subramani Sunithamani, “Design of Ternary Logic Gates and Circuits Using GNRFETs,” IET Circuits, Devices & Systems, vol. 14, no. 7, pp. 972-979, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[27] Sufia Banu, and Shweta Gupta, “Leakage Minimization in Semiconductor Circuits for VLSI Application,” 2021 5th International Conference on Electrical, Electronics, Communication, Computer Technologies and Optimization Techniques (ICEECCOT), Mysuru, India, pp. 65-68, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
[28] Sufia Banu, and Shweta Gupta, “Design and Leakage Power Optimization of 6T Static Random Access Memory Cell Using Cadence Virtuoso,” International Journal of Electrical and Electronics Research, vol. 10, no. 2, pp. 341-346, 2022.
[CrossRef] [Google Scholar] [Publisher Link]