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
A memory access misses both L1 and L2 caches only if it first misses L1, and then subsequently misses L2. The miss rate of L1 is (1 - 0.85) = 0.15. Of those misses, the L2 cache is consulted, and its miss rate is (1 - 0.66) = 0.34. The combined miss probability is 0.15 × 0.34 = 0.051, representing accesses that bypass both cache levels and require main memory access.
Step-by-step Derivation:
Step 1: Calculate L1 miss rate = 1 - 0.85 = 0.15
Step 2: Calculate L2 miss rate = 1 - 0.66 = 0.34
Step 3: Accesses miss both caches only if they miss L1 AND miss L2. The L2 is only checked when L1 misses.
Step 4: Probability of missing both = P(L1 miss) × P(L2 miss | L1 miss) = 0.15 × 0.34 = 0.051