A modular technique of Booth encoding and Vedic multiplier for low-area and high-speed applications.


Journal

Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288

Informations de publication

Date de publication:
16 Dec 2023
Historique:
received: 25 08 2023
accepted: 13 12 2023
medline: 17 12 2023
pubmed: 17 12 2023
entrez: 16 12 2023
Statut: epublish

Résumé

A technique for efficiently multiplying two signed numbers using limited area and high speed is presented in this paper. This work uses both the Booth and Vedic multiplication sutra methodologies to enhance the speed and reduction in the area by using two VLSI architectures of radix encoding techniques-Radix-4 and Radix-8-with the Vedic multiplier. The functionality of the proposed methods is tested using an Artix-7 Field Programmable Gate Array (FPGA-XC7A100T-CSG324) in Xilinx Vivado 2019.1 and ASIC 45 nm technology. Two methods of Booth encoding using Vedic multiplier (Urdhva-Tiryakbhyam sutra) were used to develop, and examine the benefits of rapid computational multiplier. The results of the proposed multiplier for Booth-Vedic-Radix-4 encoding (BVR-4) decrease area by 89% and improve Area-Delay Product (ADP) by 72% for a 16-bit multiplier when subjected to other existing multipliers. The Booth-Vedic-Radix-8 (BVR-8) method shows that there will be an 89% reduction in area and an improvement in ADP by 72% for the 16-bit multiplier. The performance is evaluated regarding area occupancy (i.e., LUTs number) and propagation delay (output time). In terms of resource utilization, the proposed BVR-4 and BVR-8 multipliers outperform all the current designs with a marginal effect on speed and area for narrower bit-width ranges.

Identifiants

pubmed: 38104192
doi: 10.1038/s41598-023-49913-5
pii: 10.1038/s41598-023-49913-5
doi:

Types de publication

Journal Article

Langues

eng

Sous-ensembles de citation

IM

Pagination

22379

Informations de copyright

© 2023. The Author(s).

Références

Thakur, G., Sohal, H. & Jain, S. A novel parallel prefix adder for optimized Radix-2 FFT processor. Multidimens. Syst. Signal Process. 32(3), 1041–1063 (2021).
doi: 10.1007/s11045-021-00772-1
Vassiliadis, S., Schwarz, E. M. & Hanrahan, D. J. A general proof for overlapped multiple-bit scanning multiplications. IEEE Trans. Comput. 38(2), 172–183 (1989).
doi: 10.1109/12.16494
Pour Ali Akbar, E. & Mosleh, M. An efficient design for reversible Wallace unsigned multiplier. Theor. Comput. Sci. 773, 43–52 (2019).
doi: 10.1016/j.tcs.2018.06.007
Chang, Y.-J., Cheng, Y.-C., Liao, S.-C. & Hsiao, C.-H. A low power radix-4 booth multiplier with pre-encoded mechanism. IEEE Access 8, 114842–114853 (2020).
doi: 10.1109/ACCESS.2020.3003684
Abrar, M., Elahi, H., Ahmad, B. A., Ghayasudin, M. & Mughal, M. R. An area-optimized N-bit multiplication technique using N/2-bit multiplication algorithm. SN Appl. Sci. 1(11), 1–6 (2019).
doi: 10.1007/s42452-019-1367-6
Abed, S., Khalil, Y., Modhaffar, M. & Ahmad, I. High-performance low-power approximate Wallace tree multiplier. Int. J. Circuit Theory Appl. 46(12), 2334–2348 (2018).
doi: 10.1002/cta.2540
Waters, R. S. & Swartzlander, E. E. A reduced complexity Wallace multiplier reduction. IEEE Trans. Comput. 59(8), 1134–1137 (2010).
doi: 10.1109/TC.2010.103
Jain, R. & Pandey, N. Approximate Karatsuba multiplier for error-resilient applications. AEU-Int. J. Electron. Commun. 130, 153579 (2021).
doi: 10.1016/j.aeue.2020.153579
Gnanasekaran, R. A fast serial-parallel binary multiplier. IEEE Trans. Comput. 34(08), 741–744 (1985).
doi: 10.1109/TC.1985.1676620
Kang, J.-Y. & Gaudiot, J.-L. A simple high-speed multiplier design. IEEE Trans. Comput. 55(10), 1253–1258 (2006).
doi: 10.1109/TC.2006.156
Rubinfeld, L. P. A proof of the modified Booth’s algorithm for multiplication. IEEE Trans. Comput. 100(10), 1014–1015 (1975).
doi: 10.1109/T-C.1975.224114
Lo, H.-Y. High-speed signed digital multipliers for VLSI. Microprocess. Microprogramm. 29(4), 205–215 (1990).
doi: 10.1016/0165-6074(90)90339-B
Ullah, S., Nguyen, T. D. A. & Kumar, A. Energy-efficient low-latency signed multiplier for FPGA-based hardware accelerators. IEEE Embed. Syst. Lett. 13(2), 41–44 (2020).
doi: 10.1109/LES.2020.2995053
Fu, C., Zhu, X., Huang, K. & Gu, Z. An 8-bit Radix-4 non-volatile parallel multiplier. Electronics 10(19), 2358 (2021).
doi: 10.3390/electronics10192358
Monica, Y., Naresh Kumar, K. & Veeramachaneni, S. Energy efficient signed and unsigned radix 16 booth multiplier design. Comput. Electr. Eng. 90, 106892 (2021).
doi: 10.1016/j.compeleceng.2020.106892
Boro, B., Manikantta Reddy, K., Nithin Kumar, Y. B. & Vasantha, M. H. Approximate Radix-8 booth multiplier for low power and high-speed applications. Microelectron. J. 101, 104816 (2020).
doi: 10.1016/j.mejo.2020.104816
Jose, B. A. & Radhakrishnan, D. Redundant binary partial product generators for compact accumulation in Booth multipliers. Microelectron. J. 40(11), 1606–1612 (2009).
doi: 10.1016/j.mejo.2009.03.005
Moss, D. J. M., Boland, D. & Leong, P. H. W. A two-speed, radix-4, serial-parallel multiplier. IEEE Trans. Very Large-Scale Integr. Syst. 27(4), 769–777 (2018).
doi: 10.1109/TVLSI.2018.2883645
Ruiz, G. A. & Granda, M. Efficient implementation of 3X for radix-8 encoding. Microelectron. J. 39(1), 152–159 (2008).
doi: 10.1016/j.mejo.2007.10.006
Jiang, H., Han, J., Qiao, F. & Lombardi, F. Approximate radix-8 booth multipliers for low-power and high-performance operation. IEEE Trans. Comput. 65(8), 2638–2644 (2015).
doi: 10.1109/TC.2015.2493547
Patali, P. & Kassim, S. T. Efficient modular hybrid adders and Radix-4 booth multipliers for DSP applications. Microelectron. J. 96, 104701 (2020).
doi: 10.1016/j.mejo.2020.104701
Cui, X., Liu, W., Chen, X., Swartzlander, E. E. & Lombardi, F. A modified partial product generator for redundant binary multipliers. IEEE Trans. Comput. 65(4), 1165–1171 (2015).
doi: 10.1109/TC.2015.2441711
Tomar, G. S. & George, M. L. Modified binary multiplier architecture to achieve reduced latency and hardware utilization. Wirel. Person. Commun. 98(4), 3549–3561 (2018).
doi: 10.1007/s11277-017-5028-z
Paramasivam, M. E. & Sabeenian, R. S. An efficient bit reduction binary multiplication algorithm using Vedic methods. In 2010 IEEE 2nd International Advance Computing Conference (IACC) 25–28 (IEEE, 2010).
Deepa, A. & Marimuthu, C. N. Design of a high speed Vedic multiplier and square architecture based on Yavadunam Sutra. Sādhanā 44(9), 1–10 (2019).
doi: 10.1007/s12046-019-1180-3
Biji, R. & Savani, V. Performance analysis of Vedic mathematics algorithms on reconfigurable hardware platform. Sādhanā 46(2), 1–5 (2021).
doi: 10.1007/s12046-021-01605-4
Tiwari, H. D., Gankhuyag, G., Kim, C. M. & Cho, Y. B. Multiplier design based on ancient Indian Vedic mathematics. In 2008 International SoC Design Conference, Vol. 2, II-65 (IEEE, 2008).
Kasliwal, P. S., Patil, B. P. & Gautam, D. K. Performance evaluation of squaring operation by Vedic mathematics. IETE J. Res. 57(1), 39–41 (2011).
doi: 10.4103/0377-2063.78327
Prabhu, E., Mangalam, H. & Gokul, P. R. A delay efficient Vedic multiplier. Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 89, 257–268 (2019).
doi: 10.1007/s40010-017-0464-4
Bansal, Y. & Madhu, C. A novel high-speed approach for 16 × 16 Vedic multiplication with compressor adders. Comput. Electr. Eng. 49, 39–49 (2016).
doi: 10.1016/j.compeleceng.2015.11.006
Huddar, S. R., Rupanagudi, S. R., Kalpana, M. & Mohan, S. Novel high speed Vedic mathematics multiplier using compressors. In 2013 International Multi-conference on Automation, Computing, Communication, Control and Compressed Sensing (iMac4s) 465–469 (IEEE, 2013).
Padma, C., Jagadamba, P. & Ramana Reddy, P. Design of FFT processor using low power Vedic multiplier for wireless communication. Comput. Electr. Eng. 92, 107178 (2021).
doi: 10.1016/j.compeleceng.2021.107178
Barik, R. K., Pradhan, M. & Panda, R. Time efficient signed Vedic multiplier using redundant binary representation. J. Eng. 2017(3), 60–68 (2017).
doi: 10.1049/joe.2016.0376
Srividya, B. V. & Kiran Kumar, T. A novel multiplier using vedic mathematics and booth encoding. J. Adv. Math. Comput. Sci. 26, 1–9 (2018).
doi: 10.9734/JAMCS/2018/37931
Reddy, B. N. K. Design and implementation of high performance and area efficient square architecture using Vedic Mathematics. Analog Integr. Circuits Signal Process. 102(3), 501–506 (2020).
doi: 10.1007/s10470-019-01496-w
Thamizharasan, V. & Kasthuri, N. High-speed hybrid multiplier design using a hybrid adder with FPGA implementation. IETE J. Res. 1, 1–9 (2021).
Barik, R. K., Pradhan, M. & Panda, R. Efficient conversion technique from redundant binary to non-redundant binary representation. J. Circuits Syst. Comput. 26(09), 1750135 (2017).
doi: 10.1142/S0218126617501353
Reddy, K. M., Vasantha, M. H., Nithin Kumar, Y. B. & Dwivedi, D. Design and analysis of multiplier using approximate 4-2 compressor. AEU Int. J. Electron. Commun. 107, 89–97 (2019).
doi: 10.1016/j.aeue.2019.05.021
Shirzadeh, S. & Forouzandeh, B. High accurate multipliers using new set of approximate compressors. AEU Int. J. Electron. Commun. 138, 153778 (2021).
doi: 10.1016/j.aeue.2021.153778
Perumal, V. K., Jayabalan, R. & Krishnan, T. VLSI implementation of high speed multiplier architecture using VHBCSE algorithm for DSP applications. Analog Integr. Circuit Signal Process. 113, 307–313 (2022).
doi: 10.1007/s10470-022-02090-3
Sabeenian, D. R., Harirajkumar, J. & Akshaya, B. Review paper of multipliers-driven perturbation of coefficients for low power operation in reconfigurable FIR filter. Turk. J. Physiother. Rehabil. 32, 2 (2017).
Sabeenian, D., Paramasivam, D. & Versni, R. Implementation of speech command recognition for mathematical calculation using fpga—A literature. Turk. J. Physiother. Rehabil. 32, 2 (2017).
Paul, E. & Sabeenian, R. S. Modified convolutional neural network with pseudo-CNN for removing nonlinear noise in digital images. Displays 74, 102258 (2022).
doi: 10.1016/j.displa.2022.102258
Vijayashaarathi, S., Tamilselvam, V., Saranya, K., Harirajkumar, J. & Satheeskumar, L. Optimized arithmetic and logical unit design using reversible logic gates. In 2023 2nd International Conference on Applied Artificial Intelligence and Computing (ICAAIC), Salem, India, 2023 1597–1603 (2023).
Gowreesrinivas, K. V. & Samundiswary, P. Comparative analysis of single precision floating point multiplication using compressor techniques. In 2017 International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET) 2428–2433 (IEEE, 2017).
Rahnamaei, A. & Fatin, G. Z. High speed 16× 16 bit booth multiplier based on novel 4-2 compressor structure. In 2018 1st International Conference on Advanced Research in Engineering Sciences (ARES) 1–5 (IEEE, 2018).
Bianchi, V. & De Munari, I. A modular Vedic multiplier architecture for model-based design and deployment on FPGA platforms. Microprocess. Microsyst. 76, 103106 (2020).
doi: 10.1016/j.micpro.2020.103106
Elango, S. & Sampath, P. Implementation of high-performance hierarchy-based parallel signed multiplier for cryptosystems. J. Circuits Syst. Comput. 29(13), 2050214 (2020).
doi: 10.1142/S021812662050214X

Auteurs

C M Kalaiselvi (CM)

Sona College of Technology, Salem, India. kalai17cm@gmail.com.

R S Sabeenian (RS)

Department of ECE, Sona College of Technology, Salem, India.

Classifications MeSH