Computer Organization and Design MIPS Edition, Fifth Edition: The Hardware/Software Interface (The Morgan Kaufmann Series in Computer Architecture and Design)
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Chapter 1, Problem 1.5E

a.

Explanation of Solution

Given,

The clock rate and the Cycles Per Instruction (CPI) of the processor P1 is 3 GHz and 1.5 respectively.

The clock rate and the CPI of the processor P2 is 2.5 GHz and 1.0 respectively.

The clock rate and the CPI of the processor P3 is 4 GHz and 2.2 respectively.

The performance of the processor in terms of instructions per second can be calculated using the following formula is given below:

Performance=ClockrateCPI

Substitute, “3×109” for “Clock rate” and “1.5” for “CPI” is given below:

Thus, the performance of the processor P1 is 3×1091.5=2×109 instructions/second.

Substitute, “2.5×109” for “Clock rate” and “1.0” for “CPI” is given below:

Thus, the performance of the processor P1 is 2.5×1091.0=2.5×109 instructions/second.

Substitute, “4×109” for “Clock rate” and “2.2” for “CPI” is given below:

Thus, the performance of the processor P1 is 4×1092.2=1.8×109 instructions/second.

By comparing the above performances of the processors, it is concluded that the processor P1 is having highest performance.

b.

Explanation of Solution

Given,

The clock rate and the Cycles Per Instruction (CPI) of the processor P1 is 3 GHz and 1.5 respectively.

The clock rate and the CPI of the processor P2 is 2.5 GHz and 1.0 respectively.

The clock rate and the CPI of the processor P3 is 4 GHz and 2.2 respectively.

Time taken by each processor to execute the required program is 10 seconds.

The number of cycles of the processor per 10 seconds can be calculated using the following formula is given below:

Numberofcycles=Numberofseconds×Clockrateoftheprocessor

Substitute, “3×109” for “Clock rate” and “10” for “Number of seconds” is given below:

Thus, the number of cycles of the processor P1 per 10 seconds is 10×3×109=30×109.

Substitute, “2.5×109” for “Clock rate” and “10” for “Number of seconds” is given below:

Thus, the number of cycles of the processor P2 per 10 seconds is 10×2.5×109=25×109.

Substitute, “4×109” for “Clock rate” and “10” for “Number of seconds” is given below:

Thus, the number of cycles of the processor P3 per 10 seconds is 10×4×109=40×109.

The number of instructions of the processor per 10 seconds can be calculated using the following formula is given below:

Numberofinstructions=NumberofcyclesCPI

Substitute, “30×109” for “Number of cycles” and “1.5” for “CPI” is given below:

Thus, the number of instructions of the processor P1 per 10 seconds is 30×1091.5=20×109.

Substitute, “25×109” for “Number of cycles” and “1.0” for “CPI” is given below:

Thus, the number of instructions of the processor P2 per 10 seconds is 25×1091.0=25×109.

Substitute, “40×109” for “Number of cycles” and “2.2” for “CPI” is given below:

Thus, the number of instructions of the processor P3 per 10 seconds is 40×1092.2=40×109.

c.

Explanation of Solution

Given,

The clock rate and the Cycles Per Instruction (CPI) of the processor P1 is 3 GHz and 1.5 respectively.

The clock rate and the CPI of the processor P2 is 2.5 GHz and 1.0 respectively.

The clock rate and the CPI of the processor P3 is 4 GHz and 2.2 respectively.

The number of instructions of the processor per 10 seconds can be calculated using the following formula is given below:

Numberofinstructions=NumberofcyclesCPI

Substitute, “30×109” for “Number of cycles” and “1.5” for “CPI” is given below:

Thus, the number of instructions of the processor P1 per 10 seconds is 30×1091.5=20×109.

Substitute, “25×109” for “Number of cycles” and “1.0” for “CPI” is given below:

Thus, the number of instructions of the processor P2 per 10 seconds is 25×1091.0=25×109.

Substitute, “40×109” for “Number of cycles” and “2.2” for “CPI” is given below:

Thus, the number of instructions of the processor P3 per 10 seconds is 40×1092.2=18.18×109.

The CPInew is calculated using the formula CPInew=CPIold×1.2

Substitute, “1.5” for “CPIold” is given below:

Thus, the CPInew of the processor P1 is 1.5×1.2=1.8.

Substitute, “1.0” for “CPIold” is given below:

Thus, the CPInew of the processor P2 is 1.0×1.2=1.2.

Substitute, “4.0” for “CPIold” is given below:

Thus, the CPInew of the processor P3 is 2.2×1.2=2.6.

The required clock rate cam be calculated using a function f and the required formula is as follows:

f=Numberofinstructions×CPInewtime

Substitute, “20×109” for “Number of instructions”, “1.8” for “CPInew” and “7” for “time” is given below:

Thus, the required function of the processor P1 is f(P1)=20×109×1.87=5.14GHz.

Substitute, “25×109” for “Number of instructions”, “1.2” for “CPInew” and “7” for “time” is given below:

Thus, the required function of the processor P2 is f(P2)=25×109×1.27=4.28GHz.

Substitute, “40×109” for “Number of instructions”, “2.6” for “CPInew” and “7” for “time” is given below:

Thus, the required function of the processor P3 is f(P3)=40×109×2.67=6.75GHz.

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