Question

3. (4 pts) Calculate the time necessary to perform a multiply using the approach given in Figures 3.3 and 3.4 in textbook if an integer is 8 bits wide and each step of the operation takes four time-units. Assume that in step la an addition is always performed-either the multiplicand will be added, or a zero will be. Also assume that the registers have already been initialized (you are just counting how long it takes to do the multiplication loop itself). If this is being done in hardware, the shifts of the multiplicand and multiplier can be done simultaneously. If this is being done in software, they will have to be done one after the other. Solve for each case.

Answer 1

The steps for a computer multiplication operation are as follows:

1. Add multiplicand to product and place the result in Product register

2. Shift the Multiplicand register left 1 bit

3. Shift the Multiplier register right 1 bit

Hardware Case:

If the integer is 8-bits wide and there are 2 steps per operation (since the question says steps 2 and 3 are done simultaneously, requiring only one step), with each step taking 4 time units,

then the time it will take to complete the multiplication = 8 * 2 * 4 = 64

Therefore, the time to complete the multiplication in hardware case = 64 time units

Software Case:

Here, it is having 4 steps per operation since the question says that shifts of the multiplicand and multiplier must be done one after the other (thus requiring 2 steps).

Then the time it will take to complete the multiplication = 8 * 3 * 4 = 96

Therefore, the time to complete the multiplication in software case = 96 time units