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					  VLSI Arithmetic

         Lecture 9:
         Multipliers

Prof. Vojin G. Oklobdzija
 University of California
http://www.ece.ucdavis.edu/acsel
    Multiplication Algorithm*




                           *from Parhami
2                                11 May 2004
    Multiplication Algorithm*




                           *from Parhami
3                                11 May 2004
    Multiplication Algorithm*




                                *from Parhami

4                                11 May 2004
    *from Parhami
5       11 May 2004
    Multiplication*




                      *from Parhami
6                         11 May 2004
    Multiplication*




                      *from Parhami
7                         11 May 2004
    *from Parhami

8     11 May 2004
    *from Parhami

9     11 May 2004
     Multiplier Recoding*
                            *from Parhami




10                              11 May 2004
     *from Parhami

11    11 May 2004
     Multiplication by Constants




                                   *from Parhami

12                                  11 May 2004
     Multiplication by Constants




                             *from Parhami
13                                 11 May 2004
     Fast Multipliers




                        *from Parhami
14                           11 May 2004
     Using Higher Radix Multiplier




                              *from Parhami
15                                   11 May 2004
     Using Higher Radix Multiplier




                                *from Parhami
16                                   11 May 2004
     Higher Radix Multiplier




                               *from Parhami
17                                  11 May 2004
     *from Parhami

18    11 May 2004
     Booth’s Recoding




                        *from Parhami
19                          11 May 2004
     Booth’s Recoding




                        *from Parhami
20                          11 May 2004
     Booth’s Recoding




                        *from Parhami
21                          11 May 2004
     *from Parhami

22         11 May 2004
                  Modified Booth Recording Implementation
                                    Multiplicand Y




                              -2Y   -Y     0    Y    2Y
  Multiplier




               Encoding                  Selectors




11 May 2004                 Multiplier Design               23
     Higher Radix Multipliers




                                *from Parhami

24                              11 May 2004
     Tree and Array Multipliers




                              *from Parhami
25                                11 May 2004
     Tree and Array Multipliers




                              *from Parhami
26                                11 May 2004
                Tree Multipliers




*from Parhami

        27                         11 May 2004
     Tree Multipliers




                        *from Parhami
28                          11 May 2004
     Generating Partial Products




29                    *from G. Bewick   11 May 2004
          Generating Partial Products
*from G. Bewick




   30                                   11 May 2004
Generating Partial Products using Booth’s
                Recoding




                                 *from G. Bewick
31                                     11 May 2004
Generating Partial Products using Booth’s
                Recoding




                                 *from G. Bewick
32                                     11 May 2004
Booth Partial Product Selector Logic




                             *from G. Bewick
33                                 11 May 2004
     Radix-2 Booth Recoded Multiplier
      with Negative Partial Products




                                 *from G. Bewick
34                                      11 May 2004
     Radix-2 Booth Recoded Multiplier
       with Summed Sign Extension




                                 *from G. Bewick
35                                      11 May 2004
     Radix-2 Booth Recoded Multiplier
       with Summed Sign Extension




                                 *from G. Bewick
36                                      11 May 2004
     Radix-2 Booth Recoded Multiplier
with Summed Sign Extension and Reduced
               Logic Depth




                    *from G. Bewick


 37                                   11 May 2004
     Complete Signed Radix-2 Booth
          Recoded Multiplier




                             *from G. Bewick
38                                 11 May 2004
     Tree Multipliers




                        *from Parhami
39                          11 May 2004
     Reduction using 4:2 Compressors




                                 *from G. Bewick


40                                     11 May 2004
     Tree Multipliers




                        *from Parhami
41                          11 May 2004
Multiplier Placement in a Standard Grid Topology




                                    *from G. Bewick
   42                                     11 May 2004
     Floor Plan of a Multiplier




                              *from G. Bewick
43                                  11 May 2004
     Delay Components of a Booth Recoded
              Parallel Multiplier




                                  *from G. Bewick
44                                      11 May 2004
Hollywood
                    THE
                                  END




11 May 2004   Multiplier Design         46

				
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