Question

Assume A = 47, B = 9 Using a table similar to that shown in Figure 3.6, calculate the product of unsigned 6-bit A and B, i.e., A * B, using the first version multiplication hardware described in Figure 3.4.

Answer 1

So before we should know that:

• We need 6bits for multiplier
• We need 12bits for multiplicand and product
• We must iterate for 6 cycles

Therefore we have the following table:

Step	Action	Multiplier	Multiplicand	Product
0	initialize	101111	000000 001001	000000 000000
1	Add multiplier and multiplicand	101111	000000 001001	000000 001001
1	L.Shift multiplicand	101111	000000 010010	000000 001001
1	R.Shift multiplier	010111	000000 010010	000000 001001
2	Add multiplier and multiplicand	010111	000000 010010	000000 011011
2	L.Shift multiplicand	010111	000000 100100	000000 011011
2	R.Shift multiplier	001011	000000 100100	000000 011011
3	Add multiplier and multiplicand	001011	000000 100100	000000 111111
3	L.Shift multiplicand	001011	000001 001000	000000 111111
3	R.Shift multiplier	000101	000001 001000	000000 111111
4	Add multiplier and multiplicand	000101	000001 001000	000010 000111
4	L.Shift multiplicand	000101	000010 010000	000010 000111
4	R.Shift multiplier	000010	000010 010000	000010 000111
5	NO CHANGE	000010	000010 010000	000010 000111
5	L.Shift multiplicand	000010	000100 100000	000010 000111
5	R.Shift multiplier	000001	000100 100000	000010 000111
6	Add multiplier and multiplicand	000001	000100 100000	000110 100111
6	L.Shift multiplicand	000001	001001 000000	000110 100111
6	R.Shift multiplier	000000	001001 000000	000110 100111

If you follow the algorithm, you can easily figure out the working of the algorithm. If incase you are facing problems with the algorithm, and have queries on filling the table, feel free to comment below. I shall be glad to help you with the algo.