GATE CS 2024 Set 1 — Question 55
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Computer Organization & Architecture → Instruction Pipelining → Speedup & Efficiency
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Question
The baseline execution time of a program on a 2 GHz single core machine is 100 nanoseconds (ns). The code corresponding to 90% of the execution time can be fully parallelized. The overhead for using an additional core is 10 ns when running on a multicore system. Assume that all cores in the multicore system run their share of the parallelized code for an equal amount of time. The number of cores that minimize the execution time of the program is ________
Correct answer
3 to 3
Solution
To find the number of cores that minimize the execution time, we define the total execution time as a function of the number of cores .
1.Identify Sequential and Parallel Components:
- Total baseline time ns.
- Parallelizable part ns.
- Sequential part ns.
- When using cores, the parallel part is divided by .
- The overhead for using an additional core is 10 ns. For cores, there are additional cores, so the total overhead is ns.
- To find the minimum, take the derivative with respect to and set it to zero:
4.Verification with Discrete Values:
- ns (Baseline)
- ns
- ns
- ns
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