Chapter 1, Problem 1.15E

Explanation of Solution

Processor number	Required time	Waiting time	Speedup	Ratio
1	100
2	50	54	1.85	0.93
4	25	29	3.44	0.86
8	12.5	16.5	6.06	0.75
16	6.25	10.25	9.76	0.61

The execution time of the processor can be calculated using the following formula

$\text{Required}\text{time}\text{=}\frac{\text{Execution}\text{time}}{\text{Processor}\text{number}}$

Substitute, “100” for “execution time” and “1” for “processor number” in the above formula is given below:

$\begin{array}{c}\text{Required}\text{time}\text{=}\frac{\text{100}}{\text{1}}\\ \text{=}\text{100}\end{array}$

Thus the time required by the first processor is 100 seconds.

Substitute, “100” for “execution time” and “2” for “processor number” in the above formula is given below:

$\begin{array}{c}\text{Required}\text{time}\text{=}\frac{\text{100}}{2}\\ \text{=}5\text{0}\end{array}$

Thus the time required by 2 processors is 50 seconds.

Substitute, “100” for “execution time” and “4” for “processor number” in the above formula is given below:

$\begin{array}{c}\text{Required}\text{time}\text{=}\frac{\text{100}}{4}\\ \text{=}25\end{array}$

Thus the time required by 4 processors is 25 seconds.

Substitute, “100” for “execution time” and “8” for “processor number” in the above formula is given below:

$\begin{array}{c}\text{Required}\text{time}\text{=}\frac{\text{100}}{8}\\ \text{=}\text{12}\text{.5}\end{array}$

Thus the time required by 8 processors is 12.5 seconds.

Substitute, “100” for “execution time” and “16” for “processor number” in the above formula is given below:

$\begin{array}{c}\text{Required}\text{time}\text{=}\frac{\text{100}}{\text{16}}\\ \text{=}6.25\end{array}$

Thus the execution time of 16 processors is 6.25 seconds.

The waiting time of the processor can be calculated using the formula $\text{Waiting}\text{time}\text{=}\text{Required}\text{time}\text{+}\text{Overhead}\text{time}$

The waiting time of the first processor is 0 because the processor itself starts the process on the requirement.

Substitute, “50” for “required time” and “4” for “overhead time” in the above formula is given below:

$\begin{array}{c}\text{Waiting}\text{time}\text{=}\text{50}\text{+}\text{4}\\ \text{=}\text{54}\end{array}$

Thus, the waiting time of 2 processors is 54 seconds.

Substitute, “25” for “required time” and “4” for “overhead time” in the above formula is given below:

$\begin{array}{c}\text{Waiting}\text{time}\text{=}25\text{+}\text{4}\\ \text{=}29\end{array}$

Thus, the waiting time of 4 processors is 29 seconds.

Substitute, “12.5” for “required time” and “4” for “overhead time” in the above formula is given below:

$\begin{array}{c}\text{Waiting}\text{time}\text{=}12.5\text{+}\text{4}\\ \text{=}16\end{array}$