MULTIPLIER USING REGULAR PARTIAL PRODUCTS

By:

Bipin Likhar VLSI Design & CAD

(601161004)

Under The Guidance of: Ms SakshiECEDTU, Patiala

Applications of Multipliers

used commonly in processors like digital signal processes(DSPs) and microprocessors.

digital filter. Multiplication is an essential arithmetic

operation in DSP applications. multimedia applications such as 3D graphics signal processing systemsvideo processing

Classification of Multipliers

Steps for Multiplication

• Generating partial products.

• Summing up all partial products until only two rows remain.

• Adding the remaining two rows of partial products by using a carry propagation adder.

Methods for Partial Product Generation

• Radix – 2 booth multiplier

• Radix – 4 modified booth multiplier

• Higher radix booth multiplier

Comparison of radix 2, radix 4 and radix 8 algorithm

• Problem of isolated 1’s in radix-2 is overcome by radix– 4.

• In radix-8 more number of operations are required to generate {+1,+2, +3, +4, -1, -2, -3, -4}.

• Speed of Radix 8 is highest among Radix 2, 4 and 8 but the complexity increases.

Literature Review

Sr. No.

AUTHORS CONTRIBUTION YEAR

1. S.Sri Sakthi, N.Kayalvizhi Reconfigure the multiplier structure , required only n/4 clock cycle for multiplication.

2011

2. Manoj Sharma , Richa verma presented a new technique to compute the 2’s complement

2011

3. Shiann-Rong Kuang,, Jiun-Ping Wang

Proposed an approach to generate a regular partial product array .

2010

4. Zheng Li, Haimin Chen, Xianwen Yang

proposed new technique for the disposal of negative PP based on Radix-4 Booth algorithm.

2010

Contd….

Sr. No.

AUTHORS CONTRIBUTION YEAR

5. Jung-Yup Kang, Member, Jean-Luc Gaudiot,

Presented an algorithm to achieve fast multiplication in two’s complementrepresentation .

2006

6. Wen-Chang Yeh and Chein-Wei Jen

Developed an algorithm to generate regular partial product.

2000

7. Aamir A. Farooqui, Vojin G. Oklobdzija

Described the data-path and VLSI implementation of a 32x32 bit signed unsigned (MAC) unit.

1998

Radix-4 Multiplication

• Irregular structure.• Number of PP are n/2+1.

Contd….

Regular structure but still n/2+1 PP’s rows.

Contd….

• PP reduced to n/2 by 2’s complement technique.

• Irregular structure.

Contd….

• Taking both above technique , result will be regular PP with n/2 PP rows.

Gaps In The Study

• Focus on radix-2 and radix-4, not on higher radix.

• New methods for finding 2’s complement.• Recursive modified booth multiplier helps in

improving speed as compared to MBE but no emphasis has been given to reduce power dissipation.

Objectives of Proposed Studies

• To implement multiplication on higher order radix.

• Faster methods must be used to find 2’s complement.

• Some methods can be adopted to reduce power dissipation in recursive modified booth multiplier.

References

1. Wen-Chang Yeh and Chein-Wei Jen,” High-Speed Booth Encoded Parallel Multiplier Design”, IEEE, JULY 2000.2. Jung-Yup Kang, Jean-Luc Gaudiot “A Simple High-Speed Multiplier Design”. IEEE, OCTOBER 2006.3. Edwin de Angel and Earl E. Swartzlander, Jr. “Low Power Parallel Multipliers”. IEEE,1996.4. Aamir A. Farooqui, Vojin G. Oklobdzija “General Data-Path Organization of a MAC unit for VLSI Implementation of DSP

Processors”. IEEE,1998.

Contd….

5. Fayez Elguibaly ,“A Fast Parallel Multiplier-Accumulator Using the Modified Booth Algorithm”. IEEE ,Transactions on Circuits and System—II VOL. 47 September 2000. 6. Osman Hasan, Skander Kort “Automated Formal Synthesis of Wallace Tree Multipliers,”. IEEE Transactions on VLSI, 2007.7. S.Sri Sakthi, N.Kayalvizhi, “Power Aware and High Speed Reconfigurable Modified Booth Multiplier”. IEEE, February 2011.

Contd….

8. Shiann-Rong Kuang, Jiun-Ping Wang, and Cang-Yuan Guo “Modified Booth Multipliers With Regular Partial Product Array”. IEEE Transactions on Circuits and System—II, VOL. 56, NO. 5, MAY 2009.9. S.Saravanan, M.Madheswaran “Design of Hybrid Encoded Booth Multiplier with Reduced Switching Activity Technique and Low Power 0.13µm Adder for DSP Block in Wireless Sensor Node”. IEEE 2010. 10. Zheng Li, Haimin Chen, Xianwen Yang “Research on the disposal of negative partial product for booth algorithm”. Information Theory and Information Security (ICITIS), 2010.

Contd….

11. Manoj Sharma “Disposition (reduction) of (negative) partial product for Radix 4 Booth's Algorithm”. Information and Communication Technologies (WICT), 2011.12. Behrooz Parhami, Computer Arithmetic Algorithms and Hardware Design,2nd edition.

THANK YOU