Multiplication is a fundamental operationing most signal processing algorithms. Multipliers have large area, long latency and consume considerable power. Fast multipliers are essential parts of digital signal processing systems. The speed of multiplier operation is of great importance in digital signal processing as well as in the general purpose processors today. one of the example are Radix 2 modified booth multiplier.
Radix 2 modified booth multiplier
Booth algorithm provides a procedure for multiplying binary integers in signed-2’s complement
representation Accor ding to the multiplication procedure, strings of 0’s in the multiplier
require no addition but just shifting and a string of 1’s in the multiplier from bit w eight 2 k to w eight 2m can be treated as 2k+ 1 - 2m.
Booth algorithm involves recoding the multiplier first. In the recoded format, each bit in the multiplier can take any of the three values: 0, 1 and -1.Suppose w e want to multiply a number by 01110 (in decimal 14). This number can be considered as the difference between 10000 (in decimal 16) and 00010 (in decimal 2). The multiplication by 01110 can be achieved by summing up the following products:
24 times the multiplicand(24 = 16)
2’s complement of 21 times the multiplicand (2 1 =2).
In a standard multiplication, three additions are required due to the string of three 1’s.This can b e replaced by one addition and one subtraction. The above requirement is identified by recoding of the multiplier 01110 using the following rules summarized in table 1.
Radix 2 modified booth multiplier
Booth algorithm provides a procedure for multiplying binary integers in signed-2’s complement
representation Accor ding to the multiplication procedure, strings of 0’s in the multiplier
require no addition but just shifting and a string of 1’s in the multiplier from bit w eight 2 k to w eight 2m can be treated as 2k+ 1 - 2m.
Booth algorithm involves recoding the multiplier first. In the recoded format, each bit in the multiplier can take any of the three values: 0, 1 and -1.Suppose w e want to multiply a number by 01110 (in decimal 14). This number can be considered as the difference between 10000 (in decimal 16) and 00010 (in decimal 2). The multiplication by 01110 can be achieved by summing up the following products:
24 times the multiplicand(24 = 16)
2’s complement of 21 times the multiplicand (2 1 =2).
In a standard multiplication, three additions are required due to the string of three 1’s.This can b e replaced by one addition and one subtraction. The above requirement is identified by recoding of the multiplier 01110 using the following rules summarized in table 1.
| Qn | Qn+1 | Re coded bits | Operation performed |
| 0 | 0 | 0 | Shift |
| 0 | 1 | +1 | Add M |
| 1 | 0 | -1 | Subtr act M |
| 1 | 1 | 0 | Shift |
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Deepti K
Assistant Professor
ECE Department
Sphoorthy Engineering College
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| Sphoorthy Engineering College |
