Optimized Multiplier Based upon 6-Input Luts and Vedic Mathematics

Authors: Zulhelmi Zakaria, Shuja A. Abbasi

Abstract:

A new approach has been used for optimized design of multipliers based upon the concepts of Vedic mathematics. The design has been targeted to state-of-the art field-programmable gate arrays (FPGAs). The multiplier generates partial products using Vedic mathematics method by employing basic 4x4 multipliers designed by exploiting 6-input LUTs and multiplexers in the same slices resulting in drastic reduction in area. The multiplier is realized on Xilinx FPGAs using devices Virtex-5 and Virtex-6.Carry Chain Adder was employed to obtain final products. The performance of the proposed multiplier was examined and compared to well-known multipliers such as Booth, Carry Save, Carry ripple, and array multipliers. It is demonstrated that the proposed multiplier is superior in terms of speed as well as power consumption.

Keywords: Multiplier, Vedic Mathematics, LUTs, FPGAs.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084518

References:

[1] J.Senthil Kumar , G.Sriram, G.Lakshminarayanan , B.Venkataramani, " Design and Implementation of FPGA based Fast Multipliers with Optimum Placement & Routing Using Structure Organizer", National Conference on VLSI design & Testing, PSG College of Technology, Coimbatore, 21-22 February, 2003
[2] T. V. More and R. V. Kshirsagar, "Design of low power column bypass multiplier using FPGA," in Electronics Computer Technology (ICECT), 2011 3rd International Conference on, 2011, pp. 431-435.
[3] G. C. T. Chow, K. Eguro, W. Luk, and P. Leong, "A Karatsuba-Based Montgomery Multiplier," in Field Programmable Logic and Applications (FPL), 2010 International Conference on, 2010, pp. 434- 437.
[4] Michael John Sebastian Smith, "Application-specific integrated circuits", Addison-Wesley, (1997).
[5] S. K. Mangal, R. B. Deshmukh, R. M. Badghare, and R. M. Patrikar, "FPGA Implementation of Low Power Parallel Multiplier," in VLSI Design, 2007. Held jointly with 6th International Conference on Embedded Systems., 20th International Conference on, 2007, pp. 115- 120.
[6] S. Bhattacharjee, S. Sil, B. Basak, and A. Chakrabarti, "Evaluation of power efficient adder and multiplier circuits for FPGA based DSP applications," in Communication and Industrial Application (ICCIA), 2011 International Conference on, 2011, pp. 1-5.
[7] P. R. Aparna and N. Thomas, "Design and implementation of a high performance multiplier using HDL," in Computing, Communication and Applications (ICCCA), 2012 International Conference on, 2012, pp. 1-5.
[8] S. Akhter, "VHDL implementation of fast NxN multiplier based on vedic mathematic," in Circuit Theory and Design, 2007. ECCTD 2007. 18th European Conference on, 2007, pp. 472-475.
[9] K. S. Gurumurthy and M. S. Prahalad, "Fast and power efficient 16 X16 Array of Array multiplier using Vedic Multiplication," in Microsystems Packaging Assembly and Circuits Technology Conference (IMPACT), 2010 5th International, 2010, pp. 1-4.
[10] H. D. Tiwari, G. Gankhuyag, K. Chan Mo, and C. Yong Beom, "Multiplier design based on ancient Indian Vedic Mathematics," in SoC Design Conference, 2008. ISOCC '08. International, 2008, pp. II-65-II- 68.
[11] P. Mehta and D. Gawali, "Conventional versus Vedic Mathematical Method for Hardware Implementation of a Multiplier," in Advances in Computing, Control, & Telecommunication Technologies, 2009. ACT '09. International Conference on, 2009, pp. 640-642.
[12] V. Kunchigi, L. Kulkarni, and S. Kulkarni, "High speed and area efficient Vedic multiplier," in Devices, Circuits and Systems (ICDCS), 2012 International Conference on, 2012, pp. 360-364.
[13] L. Sriraman and T. N. Prabakar, "Design and implementation of two variable multiplier using KCM and Vedic Mathematics," in Recent Advances in Information Technology (RAIT), 2012 1st International Conference on, 2012, pp. 782-787.
[14] Ahmed et. al, "Architecture-Specific Packing for Virtex-5 FPGAs," FPGA-08, February 24-26, 2008, Monterey, California, USA.
[15] Xilinx, "ds100, Virtex-5 Family Overview," February 6, 2009, Xilinx. Inc.
[16] Xilinx, "ds150, Virtex-6 Family Overview," March 24, 2011, Xilinx. Inc.