Comparison%20of%20Various%20Multipliers%20for%20Performance%20Issues

1
Comparison of Various Multipliers for Performance
Issues
By Manto Kwan
High Speed Low Power ASIC 97.575
24 March 2003. Depart. Of Electronics
2
Contents

• Introduction
• Twin-Piped Serial-Parallel Multiplier
• Array Multiplier
• Wallace Tree Multiplier
• Modified Booth Multiplier
• Combined Modified Booth-Wallace Tree Multiplier
• Conclusion

24 March 2003. Depart. Of Electronics, Page 2
3
Introduction

• Multiplier plays an very important role in
  today's digital circuits. The design of high
  speed, low power consumption, less area, and low
  irregularity in layout are very important.
• There are various types of multipliers
• Twin-Piped Serial-Parallel Multiplier,
• Array Multiplier, Wallace Tree Multiplier,
• Modified Booth Multiplier, and
• Combined Modified Booth-Wallace Tree Multiplier.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 3
4
Twin-Piped Serial-Parallel Multiplier

• Odd-indexed data bits and even-indexed data bits
  are processed in different clock phase and
  different circuits.
• Results in double throughput.
• The multiplier consists of 4 units.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 4
5
Twin-Piped Serial-Parallel Multiplier

• The multiplicand is fed in parallel. The
  multiplier is fed in serial.
• The product is shifted out in series.
• Use where area and power consumption is
  restricted and speed is not important.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 5
6
Array Multiplier

• Regular structure.
• Partial products are added and then shifted.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 6
7
Wallace Tree Multiplier

• Partial Sum adders can be re-arranged in a
  tree-like fashion, reducing the critical path and
  the number of cells needed.
• Fig. (a) Only column 3 has to add 4 bits. All
  others are less complex.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 7
8
Wallace Tree Multiplier

• Fig. (b) Half Adders (HA) in column 3 4.
• Fig.(c) Full Adders (FA) in column 3, 4, and 5
  HA in column 2.
• Fig. (d) Finally, HA from column 1 to 6.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 8
9
Wallace Tree Multiplier

• Wallace Tree multiplier implementation.
• Substantial saving on larger multiplier.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 9
10
Modified Booth Multiplier

• Reduction on number of partial product by one
  half on average.
• Great savings on silicon area and increase in
  speed as the number of stage reduced by half.

11
Modified Booth Multiplier
24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 11
12
Combined Modified Booth-Wallace Tree Multiplier

• Better area performance due to Modified Booth
  Algorithm and reduced delay due to Wallace Tree.
• However, building a regular structure becomes a
  challenge.

13
Comparison of 5 different multipliers

• Wallace tree multiplier and Combined
  Booth-Wallace tree multiplier have the least
  delay.
• Serial Parallel multiplier requires the least
  area and power when speed is not important.

14
Conclusion

• Each multiplier has its own advantage and
  disadvantage.
• Choice of a specific multiplier depends on
  application and constraint on area, power, delay.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 14
15
Design Project

• Design an 8 bit Array Multiplier
• Using Logical Effort and Logical Balance.
• Compare the power consumption and delay.

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 15
16
Tentative Schedule

• Background Research
• First half of April
• Designing
• Third week of April onward
• Simulations
• 21-30 April 2003
• Presentation
• 26-28 April 2003
• Report
• 1-5 May 2003

24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 16
17
The End
24 March 2003. Depart. Of Electronics
24 March 2003. Depart. Of Electronics, Page 17