Consider the following two processors P1 and P2 executing the same instruction s

Question

Consider the following two processors P1 and P2 executing the same instruction set with the clock rates and CPIs specified in the following table: a. Which processor has the better performance? How much faster? b. If the processors each execute a program in 75 seconds, find the number of cycles and the number of instructions for each processor. c. For processor P1, we are trying to reduce the time by 40% but this leads to an increase of 20% in CPI, what clock rate should we have to achieve this time reduction?

Explanation / Answer

a.

P1: 2.0 GHz/2.0 = 1.0 * 10^9 instructions per second . //(Formula=Clock rate/CPI)

P2:2.5 GHz/3.0 = 0.833 * 10^9 instructions per second.

So from above scenario, we can deduct that P1 is faster than the P2

b.

Cycles:

P1: 2GHz * 75 = 150 * 10^10 cycles //Formula (Clock Rate * Time to execute the Program by processor)

P2: 2.5GHz * 75 = 187.5 * 10^10 cycles

Num of instructions:

P1: 2GHz * 75 / 2 = 1 * 10^10 instructions

P2: 2.5GHz * 75/ 3 = 0.8333 * 10^10 instructions

c)

Execution time = (Num of instructions * CPI) / (Clock rate) So if we want to reduce the execution time by 40%, and CPI increases by 20%, we have:

Execution time * 0.6 = (Num of instructions * CPI * 1.2) / (New Clock rate) // 0.6 is 40 % less of 1

New Clock rate = Clock rate * 1.2 / 0.6 = 2 * Clock rate

Hence deducing the equation to below

P1: 2GHz * 2 = 4 GHz

P2: 2.5GHz * 2 = 5 GHz

Thanks for the question, Please let me know if your facing any issue to understand, will be glad to clarify.

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