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26 April, 21:16

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.

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

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  1. 26 April, 22:31
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    P2 has the highest performance expressed in instructions per second i. e. 2.5 * 10^9

    Explanation:

    Given:

    Clock rate of P1 = 3 GHz

    Clock rate of P2 = 2.5 GHz

    Clock rate of P3 = 4.0 GHz

    Cycles Per Instruction CPI of P1 = 1.5

    Cycles Per Instruction CPI of P2 = 1.0

    Cycles Per Instruction CPI of P3 = 2.2

    To find:

    Highest Performance expressed in instruction per second.

    Solution:

    Performance = clock rate / CPI

    The performance of processor depends on instructions count and CPU time.

    As we know that

    CPU time = Instructions * Cycles Per Instruction / clock rate

    Instructions per second = Instruction count / CPU time

    As:

    CPU time = I * CPI / clock rate

    I/CPU time = clock rate/CPI

    So IPS = clock rate / CPI

    Hence

    Performance = Clock rate / Cycles per Instruction = clock rate CPI

    Performance for P1 = IPS = clock rate / CPI = 3 GHz / 1.5 = 2

    As we know that 1 GHz = 10 ^ 9 Hz. So:

    Performance of P1 expressed in instructions per second is 2 * 10^9

    Performance for P2 = IPS = clock rate / CPI = 2.5 / 1.0 = 2.5

    Performance of P2 expressed in instructions per second is 2.5 * 10^9

    Performance for P3 = IPS = clock rate / CPI = 4 GHz / 2.2 = 1.82

    Performance of P3 expressed in instructions per second is 1.82 * 10^9

    Hence P2 has the highest performance expressed in instructions per second.
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