Design and Implementation of High Speed and Low Power Multiplier using Urdhwa Tiryagbhyam Sutra

DOI : 10.17577/IJERTV3IS031919

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Design and Implementation of High Speed and Low Power Multiplier using Urdhwa Tiryagbhyam Sutra

  1. Padmaja1,M.Tech

    Department of ECE,K.G.R.C.E.T, Moinabad,Hyderabad,AP

    1. Saida2,M.Tech

Department ofECE, K.G.R.C.E.T , Moinabad, Hyderabad ,AP

Anuradha Shankar 3,

Student, Department of ECE,K.G.R.C.E.T, Moinabad,Hyderabad,AP

Arjun Singh4,Student, Department of ECE,K.G.R.C.E.T, Moinabad,Hyderabad,AP

AbstractA processing unit devotes considerable amount of its processing time in performing arithmetic operations and multiplication operation plays a vital role in this . As a multiplier unit is required in most real time processing applications , so higher throughput multiplication operations are important to achieve desired performance . An efficient multiplier design is proposed using vedic mathematics sutra :- Urdhwa Tiryagb-hyam , 3:2 compressors[1][2] and a 4 bit novel adder that reduces delay and power .

KEYWORDS :Multiplication , Urdhwa Tiryagbhyam , 3:2 compressors , 4 bit novel adder .


Multipliers are an integral part of most processing units hence the performance of processors greatly depend upon the functioning of their multiplication units .

Multiplication is the process of adding a number of partial products. Multiplication algorithms differ in terms of partial product generation and partial product addition to produce the final result . Higher throughput arithmetic operations are important to achieve the desired performance in many real time signal and image processing applications .

Several new architectures have been proposed for improving the functioning of multiplier units to meet the constraints of reducing the delay , power consumption ,regularity of layout and hence less area or even combination of them in one , thus making them suitable for various high speed, low power and compact VLSI implementations . Though ,an efficient multiplier design is yet to come.In order to address the disadvantages associated with multiplier architectures , vedic mathematic approach was proposed . Multipliers were designed using Urdhwa Tiryagbhyam

[3].Inthis paper, an even more efficient approach to improve multiplier units compared to the vedic multipliers is being proposed.


    1. Array Multiplier

      Array multiplier is well known due to its regular structure. Itis an efficient layout of a combinational multiplier.

      Multiplier circuit is based on add andshift algorithm. Each partial product is generated by the multiplication of the multiplicand withone multiplier bit. The partial product are shifted according to their bit orders and then added.

      FIGURE 1: A 4 bit array multiplier

      Consider an array multiplierfor two binary numbers A and B, of n bits each as shown in figure 1 below. There are n2summands that are produced in parallel by a set of n2 andgates. An × n multiplier requires n(n-1) full adders and

      n2andgates.Although the method is simple as it can be seen from this example, the addition is done seriallyas well as in parallel.

      Array multipliershavehigh power consumption as well as number of components required. Delay is the time taken by the signals to propagate through the gates and in array multiplier, the worst case delay would be (2n+1) tddue to the gates that forms the multiplication array.

      Thus array multipliersare less economical with more hardware complexity.

    2. Vedic Multipliers:using Urdhwa Tiryagbhyam sutra and 4 bit novel adder

    Vedic multiplierdesigned using Urdhwa Tiryagbhyam sutra and 4 bit novel adder [4] is as shownbelow in figure 2. The novel 4 bitadder performs the addition of 4 bits at a time and produces three output bits .These three output bits comprise of one sum bit and two carry bits.

    The 4 bit adder adds the four input bits at a time

    and the speed of the multiplication increases.

    FIGURE 2: 4 bit novel adder based multiplier

    By using this 4×4 multiplier we can design the architecture for 8×8 multiplier also . Though the multiplier reduces the design complexity and power drastically the delay can still be reduced further .

  2. Proposed multiplier

    In this proposed multiplier design, we are introducing compressors in the existing vedic multiplier using novel adder .A compressor is a device that reduces the combination of input bits at the output. Shown below in figure 3, is a 3:2 adder compressor that functions similar to a full adder .

    FIGURE 3: 3:2 compressor

    It takes 3 inputs A, B, C to generate 2 outputs, the sum and the carry bits. Equations for sum and carry bits are governed by 1 and 2 as:-

    Sum = (AB) C + () C (1) Carry = (AB) C + ( ) A (2)

    This compressor is built using xor-xnor and

    multiplexer modules. We are replacing the full adders in the vedic multiplier design using novel 4 bit adder by 3:2 compressor. Even though a 3:2 compressor works same as full adder, the difference lies in propagation delay. A full adder needs 2 half adders which are in turn built using

    xor and and gates . The delay produced by a full adder is 0.027ns whereas a 3:2 compressor adder produces a delay of only 0.019 ns

    FIGURE 4: 4 bit Multiplier using 3:2 compressor adder and

    4 bit novel adder

    FIGURE 5:8 bit Multiplier using 3:2 compressor adder and 4 bit novel adder

    Hence we are improving the delay and power consumption very efficiently in the above

    Technology in nm




    Array multiplier

    0.160 ns

    0.339 ns

    Vedic multiplier

    0.103 ns

    0.219 ns

    Proposed Vedic


    0.092 ns

    0.199 ns

    multiplier architecture though the area constraint can still be improved further using other techniques

  3. Results

  1. Simulation Results

    Using the Xilinx 12.2 version and Spartan 3 FPGA kit , the simulation results were found as shown below

    1. For 4 bit proposed multiplier

      FIGURE 6: Simulation output for 5×12,3×5 , 12×2 , 15×15

    2. For 8 bit proposed multiplier

    FIGURE 7 : Simulation output for 204 x 204 ,204 x 239 ,204 x

    236 ,239 x 255

  2. Delay Tables and Graphs

    1. For 4 bit proposed multiplier

      FIGURE 8: Delay table, graph for 4 bit

    2. For 8 bit proposed multiplier

    Technology in nm




    Array multiplier

    0.264 ns

    0.569 ns

    Vedic multiplier

    0.166 ns

    0.370 ns


    Vedic multiplier

    0.149 ns

    0.340 ns

    FIGURE 8 : Delay table , graph for 8 bit

  3. RTL and Technology Schematics

    1. For 4 bit proposed multiplier

      FIGURE 9: Schematics for 4 bit

    2. For 8 bit prposed multiplier

    FIGURE 10: Schematics for 8 bit


    Power in (mw)





    Proposed Vedic


  4. Power comparison table and graph



power in(mw)










  1. Sushma R. Huddar and SudhirRao

  2. Rupanagudi, Kalpana M., Surabhi Mohan, Novel High Speed Vedic Mathematics Multiplier using Compressors, 978-1-4673-5090-7/13/$31.00 ©2013 IEEE

  3. Hsiao, Shen-Fu, Ming-Roun Jiang, and Jia-SienYeh, "Design of high speed

  4. low-power 3-2 counter and 4-2 compressor for fast

    multipliers, IEEE Electronics Letters, vol. 34, no.4, pp. 341-343, Feb. 1998.

  5. MD. Belal Rashid, Balaji B.S. and Prof. M.B. Anandaraju

    , VLSI Design and Implementation of Binary Number Multiplier based on Urdhva Tiryagbhyam Sutra with reduced Delay and Area , International Journal of Engineering Research and Technology,ISSN 0974-3154 Volume 6, Number 2 (2013), pp. 269-278

  6. Rajasekhar. N, Shanmuganatham. T, A Novel 4 Bit Adder Based Urdhwa TiryakbhyamMultiplier, IJCSMC, Vol. 2, Issue. 10, October 2013, pg.219 225

array vedic proposed vedic


FIGURE 10 : Power comparison in different multipliers


    The proposed vedic multiplier using 4 bit novel adder and 3:2 compressor has produced an improved performance compared to its predeccesors by reducing the delay and power consumption. These multipliers can improve the performances of applications in which they are used .


Though hardware area has reduced by only small percent, it can be further improved . The same can be implemented for higher bits also .

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