Design of the 16-bit Vedic Multiplier Based on Compressor Adder
Harshit Swaroop · International Journal for Research in Applied Science and Engineering Technology · 2018
This paper proposed the design of 16 bit Multiplier using the techniques of Ancient Indian Vedic Mathematics that have been modified to improve performance. Vedic Mathematics is the ancient system of mathematics which has a unique technique of calculations based on 16Sutras.The work has proved the efficiency of Urdhva tiryakbhyam -Vedic method for multiplication which strikes a difference in the actual process of multiplication itself.It enables parallel generation of intermediate products, eliminates unwanted multiplication steps with zeros and scaled to higher bit levels.So the design complexity gets reduced for inputs of larger no of bits and modularity gets increased.The adders used for partial product sum generation are the major power consuming elements.In our design we can optimize the adder design for minimizing the power consumption.We have proposed the low power adder design using compressor adders.The proposed Vedic multiplier is coded in VHDL (Very High Speed Integrated Circuits Hardware Description Language), synthesized and simulated using EDA (Electronic Design Automation) tool -Xilinx9.1.Keywords: Vedic Multiplier, VHDL, sutras, Urdhva tiryakbhyam, multiplication, compressor adders characteristics, Vedic maths has already crossed the boundaries of India and has become an interesting topic of research abroad.Vedic maths deals with several basic as well as complex mathematical operations.Especially, methods of basic arithmetic are extremely simple and powerful.The word "Vedic" is derived from the word "Veda" which means the store-house of all knowledge.Vedic mathematics is mainly based on 16 Sutras (or aphorisms) dealing with various branches of mathematics like arithmetic, algebra, geometry etc.These Sutras along with their brief meanings are enlisted below alphabetically.A. (Anurupye) Shunyamanyat -If one is in ratio, the other is zero.B. Chalana-Kalanabyham -Differences and Similarities.C. Ekadhikina Purvena -By one more than the previous One.D. Ekanyunena Purvena -By one less than the previous one.E. Gunakasamuchyah -The factors of the sum is equal to the sum of the factors.F. Gunitasamuchyah -The product of the sum is equal to the sum of the product.G. Nikhilam Navatashcaramam Dashatah -All from 9 and last from 10. H. Paraavartya Yojayet -Transpose and adjust.I. Puranapuranabyham -By the completion or noncompletion.J. Sankalana-vyavakalanabhyam -By addition and by subtraction.K. Shesanyankena Charamena -The remainders by the last digit.L. Shunyam Saamyasamuccaye -When the sum is the same that sum is zero.M. .Urdhva-tiryagbhyam -Vertically and crosswise.N. Vyashtisamanstih -Part and Whole.O. Yaavadunam -Whatever the extent of its Deficiency. III. CONVENTIONAL ADDERS DESIGN A. Ripple Carry Adder