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# Understanding Amdahl's Law calculation

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Problem Detail:

I have a homework problem: Calculate the overall speedup of a system that spends 40% of its time in calculations with a processor upgrade that provides for 100% greater throughput.

Which is a pretty straightforward calculation with Amdahl's Law

$S = \frac{1}{(1-f)+(\frac{f}{k})}$

$f$ = fraction of work performed by component = .40

$k$ = the speedup of new component = 1.00

$S$ = overall system speedup

Plugging in my values I get

$S = \frac{1}{(1-.4)+(\frac{.4}{1})}$

$S = 1$

Which from my understanding mean's there is no speed up in the system. I am unsure if my calculation is wrong or my understanding of Amdahl's Law because I would think this processor upgrade would've provided at least some system speedup.

My book gives an example where $S = 1.22$ means a $22\%$ increase in speed so I think I am interpreting the answer correctly, which implies I did my calculation wrong, but that also seems correct.

"100% greater throughput" means a (local) speed-up by factor $k=2$.