CPE 315
Professor Stearns
Booth's Algorithm - Conceptual Examples


Note: these examples assume 4 bit multipler/multiplicand and 8 bit product.

Example 1

  0010
×
0110
 

Using Booth's algorithm, the product is calculated with 2 arithmetic operations.
  0010  
×
0110  
 
- 00000100   sub (first 1 in multiplier) = 0010 × 2 1
+ 00010000   add (prior step had last 1) = 0010 × 2 3
 
 
  00001100

Example 2

  0011
×
0110
 

Using Booth's algorithm:
  0011  
×
0110  
 
- 00000110   sub (first 1 in multiplier) = 0011 × 2 1
+ 00011000   add (prior step had last 1) = 0011 × 2 3
 
 
  00010010

Example 3

  0011
×
0111
 

Using Booth's algorithm:
  0011  
×
0111  
 
- 00000011   sub (first 1 in multiplier) = 0011 × 2 0
+ 00011000   add (prior step had last 1) = 0011 × 2 3
 
 
  00010101

Example 4 (6 bit multiply)

  011010
×
100110
 

Using Booth's algorithm:
  011010  
×
100110  
 
- 000000110100   sub (first 1 in multiplier) = 011010 × 2 1
+ 000011010000   add (prior step had last 1) = 011010 × 2 3
- 001101000000   sub (first 1 in multiplier) = 011010 × 2 5
+ 011010000000   add (prior step has last 1) = 011010 × 2 6
 
 
  001111011100
Last updated 12/11/02