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GATE CSE 2020 Q31: Average access time of a direct-mapped cache with word-wise refill

Question

A direct mapped cache memory of 1 MB has a block size of 256 bytes. The cache has an access time of 3 ns and a hit rate of 94%. During a cache miss, it takes 20 ns to bring the first word of a block from the main memory, while each subsequent word takes 5 ns. The word size is 64 bits. The average memory access time in ns (round off to 1 decimal place) is _______.

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 13.3 (or 13.5) (official GATE 2020 final answer key)

Concept used: Average access time = hit time weighted by hit rate plus miss time weighted by miss rate; the miss penalty is the time to load the whole block.

First step: A block holds 256/8=32256/8 = 32 words, so the miss penalty is 20+31×5=17520 + 31 \times 5 = 175 ns. The official key accepts 13.3 or 13.5, depending on whether the 3 ns cache access is added on a miss.

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Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key

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