Homework SourseShow the multiplication process for the numbers A 21 and B
Show the multiplication process for the numbers A = 21 and B = 10 for each of the following cases. Use a width of 6 bits:
a. Modified Booth’s algorithm with shifting-over 0s/1s
b. Modified Booth’s algorithm with multi-bit scanning where m=2
Solution
A = 21 convert into binary = 010101 (6 bit width)
B = -10 convert into binary = 001010 (6 bit width)
10 = 1010 in 6 bit width 001010
-10 = 110101
If we multiply 010101 * 110101 =
A
0
1
0
1
0
1
21
X
x
1
1
0
1
0
1
-11
Y
0
-1
1
-1
1
-1
recoded multiplier
Add -A
+
1
0
1
0
1
1
Shift
1
1
0
1
0
1
1
Add A
+
0
1
0
1
0
1
0
0
1
0
1
0
1
Shift
0
0
0
1
0
1
0
1
Add -A
+
1
0
1
0
1
1
1
1
0
0
0
0
0
1
Shift
1
1
1
0
0
0
0
0
1
Add A
+
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
Shift
0
0
0
1
1
0
1
0
0
1
Add -A
+
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
Shift
1
1
1
0
0
0
1
1
0
0
1
Shift Only
1
1
1
1
0
0
0
1
1
0
0
1
-210
| A | 0 | 1 | 0 | 1 | 0 | 1 | 21 | |||||||
| X | x | 1 | 1 | 0 | 1 | 0 | 1 | -11 | ||||||
| Y | 0 | -1 | 1 | -1 | 1 | -1 | recoded multiplier | |||||||
| Add -A | + | 1 | 0 | 1 | 0 | 1 | 1 | |||||||
| Shift | 1 | 1 | 0 | 1 | 0 | 1 | 1 | |||||||
| Add A | + | 0 | 1 | 0 | 1 | 0 | 1 | |||||||
| 0 | 0 | 1 | 0 | 1 | 0 | 1 | ||||||||
| Shift | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | ||||||
| Add -A | + | 1 | 0 | 1 | 0 | 1 | 1 | |||||||
| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | |||||||
| Shift | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | |||||
| Add A | + | 0 | 1 | 0 | 1 | 0 | 1 | |||||||
| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | ||||||
| Shift | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | ||||
| Add -A | + | 1 | 0 | 1 | 0 | 1 | 1 | |||||||
| 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | |||||
| Shift | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | |||
| Shift Only | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | -210 |
