Booth multiplication
Booth Multiplication Algorithm
Abenet Getahun
Fall 2003 CSCI 401
Booth Multiplication Algorithm
Booth algorithm gives a procedure for multiplying binary integers in signed –2’s complement representation.
I will illustrate the booth algorithm with the following example:
Example, 2 ten x (- 4) ten
0010 two * 1100 two
Step 1: Making the Booth table
I. From the two numbers, pick the number with the smallest difference between a series of consecutive numbers, and make it a multiplier.
i.e., 0010 -- From 0 to 0 no change, 0 to 1 one change, 1 to 0 another change ,so there are two changes on this one
1100 -- From 1 to 1 no change, 1 to 0 one change, 0 to 0 no change, so there is only one change on this one.
Therefore, multiplication of 2 x (– 4), where 2 ten (0010 two) is the multiplicand and (– 4) ten (1100two) is the multiplier.
II. Let X = 1100 (multiplier)
Let Y = 0010 (multiplicand)
Take the 2’s complement of Y and call it –Y
–Y = 1110
III. Load the X value in the table.
IV. Load 0 for X-1 value it should be the previous first least significant bit of X
V. Load 0 in U and V rows which will have the product of X and Y at the end of operation. VI. Make four rows for each cycle; this is because we are multiplying four bits numbers. U
0000
V
0000
X
1100
X-1
0
Load the value
1st cycle
2nd cycle
3rd Cycle
4th Cycle
Step 2: Booth Algorithm
Booth algorithm requires examination of the multiplier bits, and shifting of the partial product. Prior to the shifting, the multiplicand may be added to partial product, subtracted from the partial product, or left unchanged according to the following rules:
Look at the first least significant bits of the multiplier “X”, and the previous least significant bits of the multiplier “X - 1”.
I
00
Shift only
11
Shift only.
01
Add Y to U, and shift
10
Subtract Y from U, and shift or add (-Y) to U and shift
II
Take U & V together and shift arithmetic right shift which
Abenet Getahun
Fall 2003 CSCI 401
Booth Multiplication Algorithm
Booth algorithm gives a procedure for multiplying binary integers in signed –2’s complement representation.
I will illustrate the booth algorithm with the following example:
Example, 2 ten x (- 4) ten
0010 two * 1100 two
Step 1: Making the Booth table
I. From the two numbers, pick the number with the smallest difference between a series of consecutive numbers, and make it a multiplier.
i.e., 0010 -- From 0 to 0 no change, 0 to 1 one change, 1 to 0 another change ,so there are two changes on this one
1100 -- From 1 to 1 no change, 1 to 0 one change, 0 to 0 no change, so there is only one change on this one.
Therefore, multiplication of 2 x (– 4), where 2 ten (0010 two) is the multiplicand and (– 4) ten (1100two) is the multiplier.
II. Let X = 1100 (multiplier)
Let Y = 0010 (multiplicand)
Take the 2’s complement of Y and call it –Y
–Y = 1110
III. Load the X value in the table.
IV. Load 0 for X-1 value it should be the previous first least significant bit of X
V. Load 0 in U and V rows which will have the product of X and Y at the end of operation. VI. Make four rows for each cycle; this is because we are multiplying four bits numbers. U
0000
V
0000
X
1100
X-1
0
Load the value
1st cycle
2nd cycle
3rd Cycle
4th Cycle
Step 2: Booth Algorithm
Booth algorithm requires examination of the multiplier bits, and shifting of the partial product. Prior to the shifting, the multiplicand may be added to partial product, subtracted from the partial product, or left unchanged according to the following rules:
Look at the first least significant bits of the multiplier “X”, and the previous least significant bits of the multiplier “X - 1”.
I
00
Shift only
11
Shift only.
01
Add Y to U, and shift
10
Subtract Y from U, and shift or add (-Y) to U and shift
II
Take U & V together and shift arithmetic right shift which