Implementation of 8 Bit and 12 Bit Mulitpliers using 4-2 and 5-2 Compressors

Implementation of 8 Bit and 12 Bit Mulitpliers using 4-2 and 5-2 Compressors

Anushka Pothukuchi1; Disha Agarwal2 ; Ankita Keshari3

School of Electrical Engineering Vellore Institute of Technology Vellore, India

Abstract–This paper aims to compare different structures of 8×8 and 12×12 binary multipliers. One structure uses full adders and half adders to add the partial products. The other (modified) structure explores the use of 4-2 and 5-2 compressors. The multipliers are implemented using Xilinx ISE Design Suite 12.3 and the timing, cell area and power are compared using Cadence RTL Compiler. It is shown that the modified method has better performance parameters.

Keywordscompressor; multiplier; Wallace tree; cell area; power; timing

1. INTRODUCTION

   Multiplication forms the basis of Arithmetic Logic Units which are used in several microprocessors. It also finds use in implementation of Digital Signal Processing algorithms.

   [1] Reducing timing of the multiplier structures is essential because it contributes to the critical path delay of the above systems. At the same time, cell area and power consumption must also be considered.

   Multiplication of binary bits is done by accumulating partial products. This is conventionally done using full adders and half adders. Different algorithms like the Booth algorithm, Ripple Carry and Carry Save are used. The number of stages while adding the partial products determines the performance of the multiplier in terms of delay, power and area. [5]

   In this paper, the Wallace Tree structure is used to accumulate partial products. The structure employs carry save form. Here, the carries generated in the adders are passed on to the next stage, until the last stage. At the last stage, ripple carry form is used to generate the final product. The Wallace Tree implementation was preferred because it has less critical path, hence reducing delay.

2. 4-2 COMPRESSOR ARCHITECTURE

   A 4-2 compressor is used for the addition of four binary bits. It takes in four primary inputs, plus one input carry from the neighbouring cell. The outputs are Sum, Carry and an auxiliary carry that is taken as input to the next 4-2 compressor. [1]

   Here, four inputs are compressed to two outputs. Compression ratio is thus 4/2=2. This is higher than that of the full adder.

   When a 4-2 compressor is used, it involves less wiring compared to when two full adders are used separately.

   One implementation of 4-2 is as given below:

   A B C D

   FULL ADDER

   X_out X_in

   FULL ADDER

   z

   Carry Sum

   Fig. 1. Implementation of 4-2 Compressor using 3-2 Compressors

   Boolean Expressions Boolean Expressions

   (1)

   ( ) ( ) (2)

   ( ) (3)

3. 5-2 COMPRESSOR ARCHITECTURE

   A 5-2 compressor is used for the addition of five binary bits. It takes five primary inputs, and two additional carries from the neighbouring cell. It has two main outputs, Sum and Carry, and two auxiliary carries which are inputs to the next compressor. [1]

   Here five inputs are compressed to two outputs. Hence the

   compression ratio in this case is 5/2=2.5.

   Using a 5-2 compressor reduces wiring more than that done by a 4-2 compressor.

   One implementation of the 5-2 compressor is:

   D E

   A B C

   (4)

   ( ) ( )

   (5)

   ( ) (6)

   ( ) ( )

   (7)

4. 8X8 MULTIPLIER

   8 bit multiplication was implemented using the Wallace Tree structure. Wallace tree employs the carry save approach, where carries that are generated in a particular stage go to the next stage instead of going to the next cell in the same stage (ripple carry adder).

   1. Conventional Method

      First, full adders and half adders were used for partial product accumulation.

      The structure used (where dots represent adders) was:

      X1_out

      FULL ADDER

      X1_in

      FULL ADDER

      . . . . . . . . . . . . .

      . . . . . . . . . . . . .

      . . . . . . . . . . . .

      X2_out X2_in

      FULL ADDER

      Carry Sum

      . . . . . . . . . . . .

      . . . . . . . . . . .

      . . . . . . . . . .

      . . . . . . . . . .

      Fig. 3. Implementation of 8×8 multiplier by conventional method

      Fig. 2. Implementation of 5-2 Compressors using 3-2 Compressors

   2. Modified Method

   This method shows 8 bit multiplication using the 4-2 and 5-2 compressors to improve performance of the multiplier.

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   B. Modified Method

   This structure uses 4-2 and 5-2 compressors:

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   Fig. 4. Implementation of 8×8 multiplier using compressors

5. 12X12 MULTIPLIER

   12 bit multiplication was also implemented similarly, using Wallace tree.

   A. Conventional Structure

   The structure given below uses full adders and half adders for partial product generation. The dots represent these adders.

   Fig. 6. Implementation of 12×12 multipliers using compressors

6. SIMULATION AND RESULTS

   Xilinx ISE Design Suite 12.3 was used to implement and simulate the 8×8 multiplier and 12×12 multiplier structures in order to test their functionality.

   Cadence RTL Compiler was used to compare the different design parameters (power, cell area and delay) of the multipliers.

   The results are as follows:

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   Fig. 5. Implementation of 12×12 multiplier by conventional method

   TABLE I RESULTS

   	8×8 Multiplier			12×12 Multiplier
   Structure	Cell Area	Power (nW)	Timing (ps)	Cell Area	Power (nW)	Timing (ps)
   Conventional	1306.066	113129.504	2696	3164.616	348587.857	3902
   Using compressors	1238.32	112744.294	2693	2930.357	334162.882	4042

7. CONCLUSION

The aim of this paper was to compare the timing, power and cell area between multipliers designed by two different structures. The first structure employed was the conventional method using full adders and half adders. The modified structure used 4-2 and 5-2 compressors also.

As per the results, the modified structure showed improved performance in two out of three parameters (area and power), with a trade-off on timing.

ACKNOWLEDGMENT

We would like to thank Prof. Balamurugan S and Prof. Marimituhu R of VIT University for their guidance and support.

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