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Consider an instruction which has a speed up factor 12 while operating with a 70% efficiency. What could be the number of stages in the pipeline?

What will be its answer 17 or 18? And why?

Efficiency= SpeedUp/MaxSpeedUp

MaxSpeedUp is also a SpeedUp so let us denote it as NewSpeedUp as for now.

NewSpeedUp=SpeedUp/Effieciency

=12/0.7=17.1 .......... (1)

For ideal case we know MaxSpeedUp=K  .............(2)

If we take K=17 then result (1) violates result (2) as 17.1>17 i.e NewSpeedUp >K , which cannot happen . The speedup anyhow should be less than or equal to K.

If we take K=18,

Then 17.1<18 , does not violate the condition that NewSpeedUp<K.

You can think it in another way.

If K=17

Calculate the efficiency with SpeedUp=17.1

Efficiency =17.1/17 = 1.005

ie Efficiency>100% , which is not possible.