Question

Calculate the time necessary to perform a multiply using the approach given in Figure 3.7 if an integer is 8 bits wide and an adder takes 4 time units.

Short answer

Time units that is necessary to perform a multiplication:

12 time units

Step-by-step solution

Determine the Multiplication Using Adders

For each bit of multiplier, one 32-bit adder will be assigned. AND operation will be performed with the multiplier bit and the result will be the input to the adder.

The adders will be placed parallelly to organize 31 additions in a parallel manner. Instead of 31 repetitions, 31 additions will be performed simultaneously.

Determine the time units for multiplication in 31-adder setup

Given that the each step of the operation will take 4 time units.

The adders are arranged in a tree structure. It requires log₂ levels.

It is given that the integer is 8-bit wide which is “a”. For this case 7 adders will be added in 3 levels.

Therefore, the time units taken for hardware is as follows:

$$\begin{gathered} 3\times t=3\times 4 \\ =12timeunits \end{gathered}$$