Any help would be great, thank you in advance! Assume you just purchased your fa

Question

Any help would be great, thank you in advance!

Assume you just purchased your favorite laptop that contains a quad-core CPU, with the clock speed (each core) of 2.0 GHz (G = 2 30). Assume you would like to execute a program with 1000 instructions on the laptop distributed among the cores. Furthermore, assume that each core is capable of executing 2 instructions in each clock cycle. What is the clock cycle time (each core) in nanoseconds? What is the execution time of the program? In a perfect situation, what is the theoretical speedup of the CPU in comparison to a single-core CPU with the same architectural design? In reality, a multi-core CPU rarely archieves the linear (full) speedup expected. What is the execution time of the program if the quad-core CPU can achieve only 70% of its theoretical speed (obtained in part c)?

Explanation / Answer

a). This part requires to just find the clock cycle time of each core.Since clock speed is given it is the inverse of 2*(2^30) ,that is 1/2^31 seconds.Convert it into nanoseconds by multiplying by 10^9.It comes out to be 0.465 nanoseconds.

b).It is a quad core processor => 4 cores.

so 1000 instructions split over 4 cores.

effectively 250 instructions by each core for calculation of execution time.

It is given that 2 instructions per clock cycle.

So 250/2=125 clock cycles needed.

we found out each clock cycle to be 0.465 ns in the (a) part.

So execution time is 125*0.465 ns = 58.125 ns.

c). The theoretical speed up would be simply 4 as we are able to execute 4 instructions on 4 cores in parallel.

d).Now the non-ideal case is 70 % speed up compared to ideal case.

=> that the execution time is (100/70)*(time found out in part c).

The reason is speed is inverse of the time required so speed becomes 70% means that execution time increases and the value of new execution time is

(100/70)*58.125 ns = 83.07 ns.

Really sorry for the error in calculations and also the statement in D) just indicates reduction in speed and no value is needed from part C.Now the answer seems right.

I hope I am clear and could help you .I would be glad if you rate me.

Thanks and Cheers.

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