Question

Consider three different processors P1, P2, and P3 executing the same instruction set. P1 has a 3 GHz clock rate and a CPI of 1.5.P2 has a 2.5 GHz clock rate and a CPI of 1.0. P3 has a 4.0 GHz clock rate and has a CPI of 2.2.

a. Which processor has the highest performance expressed in instructions per second?

b. f the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions.

c. We are trying to reduce the execution time by 30% but this leads to an increase of 20% in the CPI. What clock rate should we have to get this time reduction?

Short answer

a. P2 has the highest performance expressed in instructions per second is$2.5\times {10}^9$

b. Several cycles:$P1=30\times {10}^{9}s,P2=25\times {10}^{9}s,P3=40\times {10}^{9}s$

Several instructions:$P1=20\times {10}^9,P2=25\times {10}^9,P3=18.18\times {10}^9$

c. Clock rate to get time reduction:

$P1=5.14GHz,P2=4.28GHz,P3=6.75GHz$

Step-by-step solution

Measuring Performance and Formulae

The performance of the system is measured based on time. The computer that performs the work in the least time is considered as the fastest. CPU execution time is the time that the CPU takes to complete the execution of the process.

When considering the execution of the program, the average number of the clock cycles taken to execute each instruction is called Clock cycles Per Instruction (CPI).

Write the formula for Performance

$Performance=\frac{Clockrate}{CPI}$ ….. (1)

Write the formula for finding a number of cycles of processor:

$Numberofcycles=Executiontime\times Clockrate$ ….. (2)

Write the formula for finding a number of instructions of processor:

$Numberofinstructions=\frac{Numberofcyles}{CPI}$ ….. (3)

Write the formula to find the clock rate.

$Executiontime=\frac{Numberofinstruction\times CPI}{Clockrate}$ ….. (4)

$Clockrate=\frac{NumberofInstructions\times NewCPI}{Executiontime}$ ….. (5)

Determine the high-performing Processor.

a,

Given: The processors P1, P2, and P3 execute the same instruction set.

$$\begin{gathered} PerformanceofP1=\frac{Clockrate}{CPI} \\ =\frac{3\times {10}^9}{1.5} \\ =2\times {10}^9 \end{gathered}$$

$$\begin{gathered} PerformanceofP2=\frac{Clockrate}{CPI} \\ =\frac{2.5\times {10}^9}{1.0} \\ =2.5\times {10}^9 \end{gathered}$$

$$\begin{gathered} PerformanceofP3=\frac{Clockrate}{CPI} \\ =\frac{4\times {10}^9}{2.2} \\ =1.8\times {10}^9 \end{gathered}$$

From the performance measure of the Processors P1, P2, and P3 that are expressed in instruction per second. P2 is the highest performing processor.

Determine the number of cycles and number of instructions

b.

Given that each processor executes a program in 10 seconds.

The number of cycles required for each processor to execute a program in 10 seconds, is calculated as follows:

$$\begin{gathered} NumberofcyclesofP1=Executiontime\times Clockrate \\ =10\times 3\times {10}^9 \\ =30\times {10}^9 \end{gathered}$$

$$\begin{gathered} NumberofcyclesofP2=Executiontime\times Clockrate \\ =10\times 2.5\times {10}^9 \\ =25\times {10}^9 \end{gathered}$$

$$\begin{gathered} NumberofcyclesofP3=Executiontime\times Clockrate \\ =10\times 4\times {10}^9 \\ =40\times {10}^9 \end{gathered}$$

The number of instructions required to each processor to execute a program in 10 seconds, is calculated as follows:

role="math" localid="1650413443540" $$\begin{gathered} NumberofInstructions\left(PI\right)=\frac{Numberofcycles}{CPI} \\ =\frac{30\times {10}^9}{1.5} \\ =20\times {10}^9 \end{gathered}$$

$$\begin{gathered} NumberofInstructions\left(P2\right)=\frac{Numberofcycles}{CPI} \\ =\frac{25\times {10}^9}{1} \\ =25\times {10}^9 \end{gathered}$$

$$\begin{gathered} NumberofInstructions\left(P3\right)=\frac{Numberofcycles}{CPI} \\ =\frac{40\times {10}^9}{2.1} \\ =18.18\times {10}^9 \end{gathered}$$

Determine the clock rate to achieve the given reduced time

c.

It is given that they are trying to reduce the execution time by 30% but this increases the value of CPI by 20%.

The following formula can be modified to find the clock rate.

The new clock rate for the reduced CPI value is calculated as follows:

From the New CPI, The Clock rate for the processors can be calculated as follows: