Suppose A 3 and B 5 both in base 10 Show the steps require

Suppose A = -3 and B = +5 (both in base 10). Show the steps required to compute the result Of C = A * B (A is multiplicand and B is multiplier) using Booth algorithm. Assume A and B are 4-bit 2\'s complement numbers and C is an 8-bit 2\'s complement number. b) Show the result of part (a) as a single precision floating point number using the IEEE 754 standard.

Solution

Step

Multiplicand

Action

Multiplier Upper 4 bit 0 , lower 4 bit multiplier

1 booth bit initially 0

0

1101

Initialization

0000 0101 0

1

1101

10 : Subtract Multiplicand

Shift Right Arithmetic

1101 0101 0

1110 1010 1

2

1101

01 : Add Multiplicand

Shift Right Arithmetic

1111 1010 1

1111 1101 0

3

1101

10 : Subtract Multiplicand

Shift Arithmetic Right

0010 1101 0

0001 0110 1

4

1101

01: Add Multiplicand

Shift Arithmetic right

1110 0110 1

1111 0011 0

5

1101

10 : Subtract Multiplicand

Shift Arithmetic Right

0010 0011 0

0001 0001 1

6

1101

11 : No operation

Shift Arithmetic Right

0000 1000 1

7

1101

01 : Add Multiplicand

Shift Arithmetic Right

1101 1000 1

1110 1100 0

8

1101

00 : No Operation

Shift Arithmetic Right

1110 1100 0

1111 0110 0

9

1101

00 : No Operation

Shift Arithmetic Right

1111 0110 0

1111 1011 0

Step	Multiplicand	Action	Multiplier Upper 4 bit 0 , lower 4 bit multiplier 1 booth bit initially 0
0	1101	Initialization	0000 0101 0
1	1101	10 : Subtract Multiplicand Shift Right Arithmetic	1101 0101 0 1110 1010 1
2	1101	01 : Add Multiplicand Shift Right Arithmetic	1111 1010 1 1111 1101 0
3	1101	10 : Subtract Multiplicand Shift Arithmetic Right	0010 1101 0 0001 0110 1
4	1101	01: Add Multiplicand Shift Arithmetic right	1110 0110 1 1111 0011 0
5	1101	10 : Subtract Multiplicand Shift Arithmetic Right	0010 0011 0 0001 0001 1
6	1101	11 : No operation Shift Arithmetic Right	0000 1000 1
7	1101	01 : Add Multiplicand Shift Arithmetic Right	1101 1000 1 1110 1100 0
8	1101	00 : No Operation Shift Arithmetic Right	1110 1100 0 1111 0110 0
9	1101	00 : No Operation Shift Arithmetic Right	1111 0110 0 1111 1011 0