The computer processor has an L1 and L2 cache.
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The computer processor has an L1 and L2 cache. The hit rates of the L1 and the L2 caches are 0.85 and 0.66 respectively. What is the fraction of the memory accesses that miss in both the caches?
Show answer & explanation
To find the fraction of memory accesses that miss both caches, we calculate the miss rate for each cache and multiply them. L1 miss rate = 1 - 0.85 = 0.15. L2 miss rate = 1 - 0.66 = 0.34. An access misses both caches when it misses L1 AND then misses L2, so: 0.15 × 0.34 = 0.051.
Step-by-step Derivation:
Step 1: Calculate L1 cache miss rate.
Miss rate (L1) = 1 - Hit rate (L1) = 1 - 0.85 = 0.15
Step 2: Calculate L2 cache miss rate.
Miss rate (L2) = 1 - Hit rate (L2) = 1 - 0.66 = 0.34
Step 3: Determine probability of missing both caches.
An access misses both caches when it misses L1 (probability 0.15) AND then misses L2 (probability 0.34).
P(miss L1 AND miss L2) = 0.15 × 0.34 = 0.051
Answer: 0.051 or 5.1%