Question

Another pitfall cited in Section 1.10 is expecting to improve the overall performance of a computer by improving only one aspect of the computer. Consider a computer running a program that requires 250 s, with 70 s spent executing FP instructions, 85 s executed L/S instructions, and 40 s spent executing branch instructions.

1.13.1 [5] <§1.10> By how much is the total time reduced if the time for FP operations is reduced by 20%?

1.13.2 [5] <§1.10> By how much is the time for INT operations reduced if the total time is reduced by 20%?

1.13.3 [5] <§1.10> Can the total time can be reduced by 20% by reducing only the time for branch instructions?

Short answer

1.13.1

236 seconds is reduced if the time for FP operations is reduced by 20%.

1.13.2

90% of the time for INT operation is reduced if the total time is reduced by 20%.

1.13.3

No, the total time can’t be reduced by 20% by only reducing the time for branch instructions.

Step-by-step solution

Define the concept.

1.13.1

If the previous time of running a program, the previous time for FP operations, the reducing percentage of the time for FP operations are known then it can be possible to calculate the time of running a program after reducing the specified percentage.

1.13.2

If the previous total time of running a program, the previous time of INT operation, the reducing percentage of the total time are known then it can be possible to calculate the time of INT operation after reducing the specified percentage by using.

The total time can be defined as,$Thetotaltime=ThetimeofexecutingFPinstruction+ThetimeofexecutingL/Sinstructions+thetimeofexecutingbranchinstructions+theexecutiontimeofINToperations.$

1.13.3

It is not possible to reduce the total time by 20% by only reducing the time for branch instructions.

The total time is the sum of the time of executing FP instruction, the time of executing L/S instructions, the time of executing branch instructions, and the execution time of INT operations.

Details of the calculation.

Given that, the time of running a program is 250 seconds.

The time of executing FP instructions is 70 seconds.

According to the question, the time for FP operations is reduced by 20%.

Hence, after reducing the time for FP operations, the required time of executing FP instructions = $0.8\times \text{70 = 56 seconds}$$$\begin{gathered} \text{Therefore, the required time of running the program =}\left(250-\left(70-56\right)\right)\text{seconds} \\ \text{=}\left(\text{250}-\text{14}\right)\text{seconds} \\ \text{=}236\text{seconds} \end{gathered}$$

1.13.2

Given that, the time of running a program is 250 seconds.

The time of executing FP instructions is 70 seconds.

The time of executing L/S instructions is 85 seconds.

And the time of executing branch instructions is 40 seconds.

According to the question, the total time is reduced by 20%.

Hence, after reducing the total time, the required total time is $\left(0.8\times \text{250}\right)\text{seconds = 200 seconds}$

Let, only the execution time of INT operations is changed.

Hence, after reducing the total time, the execution time of INT operations is

$$\begin{gathered} \left(\text{the required new total time - the time of executing FP instructions} \\ \text{- the time of executing L/S instructions - the time of executing branch instructions}\right)\text{seconds} \\ \text{=}\left(200-70-85-40\right)\text{seconds} \\ \text{= 5 seconds} \end{gathered}$$

Before reducing the total time, the execution time of INT operations was

$$\begin{gathered} \left(\text{the required total time - the time of executing FP instructions}\backslash \mathrm{hfill} \\ \text{- the time of executing L/S instructions - the time of executing branch instructions}\right)\text{seconds} \\ \text{=}\left(250-70-85-40\right)\text{seconds} \\ \text{= 55 seconds} \end{gathered}$$

$$\begin{gathered} \text{Hence,}\frac{\text{After reducing the total time, the execution time of INT operations}}{\text{Before reducing the total time, the execution time of INT operations}} \\ =\frac{5}{55} \\ =0.09 \end{gathered}$$

So, the time for INT operations is reduced by 91%.

1.13.3

Given, the time of running a program is 250 seconds.

The time of executing FP instructions is 70 seconds.

The time of executing L/S instructions is 85 seconds.

And the time of executing branch instructions is 40 seconds.

role="math" localid="1655190561140" $$\begin{gathered} \text{The total time of execution =}\left(55+70+85\right)\text{seconds}\left[\text{By ignoring the executing time of} \\ \text{branch instructions}\right] \\ \text{= 205 seconds} \\ \text{Hence,}\frac{\text{The new total time of execution}}{\text{The new total time of execution}} \\ =\frac{205}{250} \\ =0.82 \end{gathered}$$

The total time of execution is reduced by 18%.

So, the total time can’t be reduced by 20% by only reducing the time for branch instructions.