GATE CS 2025 Set 2 — Question 55
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Computer Organization & Architecture → Memory Hierarchy & Cache → Cache Numericals
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Question
Given a computing system with two levels of cache (L1 and L2) and a main memory. The first level (L1) cache access time is 1 nanosecond (ns) and the “hit rate” for L1 cache is 90% while the processor is accessing the data from L1 cache. Whereas, for the second level (L2) cache, the “hit rate” is 80% and the “miss penalty” for transferring data from L2 cache to L1 cache is 10 ns. The “miss penalty” for the data to be transferred from main memory to L2 cache is 100 ns.Then the average memory access time in this system in nanoseconds is ___________. (rounded off to one decimal place)
Correct answer
4 to 4
Solution
The average memory access time () for a multi-level cache system with hierarchical access is calculated as follows:Where the is the time taken to resolve a request when it is not found in L1. This involves checking L2 and, if it misses there, fetching from main memory:Given the values from the question:
- ns
- (given as miss penalty from L2 to L1) ns
- (given as miss penalty from main memory to L2) ns
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