Question

Given a system where a specific task occupies 80% of execution time, what is the theoretical maximum speedup according to Amdahl’s Law if that task is made 4 times faster?

Accepted Answer

Amdahl&#x27;s Law is a formula used to calculate the maximum theoretical speedup of a system when only a part of it is improved. The formula is Speedup = 1 / ((1 - f) + (f / s)), where f is the fraction of time the task takes in the original system, and s is the speedup factor applied to that specific task. In this scenario, the task occupies 80 percent of the time, so f equals 0.80. The remaining 20 percent of the system, which is not improved, is represented by (1 - 0.80), which equals 0.20. The task is made 4 times faster, so s equals 4. To calculate the new execution time, you divide the improved portion by the speedup factor: 0.80 divided by 4 equals 0.20. You then add this result to the portion that was not improved: 0.20 plus 0.20 equals 0.40. This means the system now takes 40 percent of its original time to complete the same work. Finally, to find the total speedup, you divide 1 by the new total time of 0.40, resulting in 2.5. Therefore, the theoretical maximum speedup is 2.5 times the original speed.

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Given a system where a specific task occupies 80% of execution time, what is the theoretical maximum speedup according to Amdahl’s Law if that task is made 4 times faster?