Question

I need this as soon as possible, please. It is due two hours and I need to check my answers.

Problem-1

Calculate the Product of the following using refined multiplication method (show all steps in table)

                                                                6 X 3

Problem-2

Calculate the Product of the following using Booth’s Multiplication Algorithm (show all steps in table)

1. 5 X (-4)
2. (-3) X (-6)

Answer 1

Problem 1:- The flow chart of refined multiplication method is as follows:-

Using above algorithm, the multiplication is done as follows:-

Multiplicand = 6 =0110, Multiplier = 0011

Iteration	Step	Product
0	initial values	0000 0011
1	Add multiplicand to left half of product	0110 0011
	Shift Product right	0011 0001
2	Add multiplicand to left half of product	1001 0001
	Shift Product right	0100 1000
3	Shift Product right	0010 0100
4	Shift Product right	0001 0010

Since we iterate the loop 4 times (number of bits in multiplicand) therefore we stop the iteration, and hence get the result 00010010 which is decimal equivalent to 18 which is correct as 6*3 = 18.

Problem 2:- The flow chart of Booth's multiplication is as follows:-

Using above algorithm, the multiplication is done as follows:-

(a.) 5*(-4)

M = 5 = 0101, M'+1 = 1011

Q = -4 = 1100

Q0Q-1	Operation	A	Q	Q-1	Count
		0000	1100	0	100
00	ASHR A,Q,Q-1	0000	0110	0	011
00	ASHR A,Q,Q-1	0000	0011	0	010
10	A = A-M ASHR A,Q,Q-1	1011 1101	1001	1	001
11	ASHR A,Q,Q-1	1110	1100	1	000

Since the value of Count become 0, therefore the iteration will stop and we get the result R = AQ = 11101100 which is 2's complement of 00010100 that is 20, therefore R = -20 which is correct.

(b.) -3*(-6)

M = -3 = 1101, M'+1 = 0011

Q = -6 = 1010

Q0Q-1	Operation	A	Q	Q-1	Count
		0000	1010	0	100
00	ASHR A,Q,Q-1	0000	0101	0	011
10	A = A-M ASHR A,Q,Q-1	0011 0001	1010	1	010
01	A=A+M ASHR A,Q,Q-1	1110 1111	0101	0	001
10	A=A-M ASHR A,Q,Q-1	0010 0001	0010	1	000

Since the value of Count become 0, therefore the iteration will stop and we get the result R = AQ = 00010010 which is equivalent to 18, which is correct.