Consider a processor executing a program consisting of 3 different instructions

Question

Consider a processor executing a program consisting of 3 different instructions classes (A,B,C), each with the same CPI, and with distributions A=40%, B=40%, C=20%. As currently implemented, the program executes in 500 milliseconds. How long would it take for the program to fully execute if we modify the processor such that the speed of class B instructions is doubled (i.e.,class B instructions take half as long after the improvement)? In this scenario, how much faster is the improved processor relative to the orginial?

Explanation / Answer

Initial distribution is A = 40%, B = 40% and C = 20%

Let time taken for execution be t seconds so

time for A = 0.4t, B = 0.4t, c = 0.2t

Now speed of execution of instruction B has doubled

So time for B has been halved = 0.4t/2 = 0.2t

So New total time = time for A + time for B (new) + time for C

= 0.4t + 0.2t + 0.2t

= 0.8t

Hence the improve processor takes 0.8t time which is 0.2t faster than previous one.

impovement = improvement in time / original time = 0.2t/t = 20%

So it is 20% faster

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