A computer has a memory hierarchy consisting of two-level cache (L1 and L2) and a main memory. If the processor needs to access data from memory, it first looks into L1 cache. If the data is not found in L1 cache, it goes to L2 cache. If it fails to get the data from L2 cache, it goes to main memory, where the data is definitely available. Hit rates and access times of various memory units are shown in the figure. The average memory access time in nanoseconds (ns) is ________. (rounded off to two decimal places)
The average memory access time (AMAT) can be calculated using the formula:
AMAT = (Hit RateL1 × TimeL1) + (Miss RateL1 × Hit RateL2 × TimeL2) + (Miss RateL1 × Miss RateL2 × TimeMain)
Step 1: Identify Parameters
Hit RateL1 = 0.95, TimeL1 = 10 ns
Hit RateL2 = 0.85, TimeL2 = 20 ns
TimeMain = 200 ns
Step 2: Calculate Miss Rates
Miss RateL1 = 1 - Hit RateL1 = 0.05
Miss RateL2 = 1 - Hit RateL2 = 0.15
Step 3: Apply the Formula
AMAT = (0.95 × 10) + (0.05 × 0.85 × 20) + (0.05 × 0.15 × 200)
Step 4: Compute Each Term
(0.95 × 10) = 9.5
(0.05 × 0.85 × 20) = 0.85
(0.05 × 0.15 × 200) = 1.5
Step 5: Sum the Terms
AMAT = 9.5 + 0.85 + 1.5 = 11.85 ns
The average memory access time is 11.85 ns, which is within the range of [11.83, 11.87].
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