A multi processor system with 16 processors is used to execute a parallelizable task. If the serial portion of the task takes 200 clock cycles and the parallel portion take 800 clock cycles. When all 16 processor are used how many total clock cycles are required to complete the task ?
250
Amdahl's law models a task as a serial part, which only one processor can execute, and a parallel part, which can be divided equally among all processors. The total time with N processors is the serial time plus the parallel time divided by N.
Step 1 — Serial portion: 200 clock cycles, unchanged by the number of processors.
Step 2 — Parallel portion on 16 processors: \(\dfrac{800}{16} = 50\) clock cycles.
Step 3 — Total: \(200 + 50 = 250\) clock cycles. (On a single processor the task would take 1000 cycles, so the speedup is 4.)
A total of 300 would mean the parallel part ran on only 8 processors, 400 would mean only 4 processors, and 450 does not match an equal split of 800 cycles across the 16 processors.
250 option is correct.
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