uppose we have a cache /memory system with the following parameters: L1 cache wi

Question

uppose we have a cache /memory system with the following parameters: L1 cache with-a 5% miss rate cache hits require 1 clock cycle . Clock rate of 1 GHz(1 clock cycle 1 nanosecond) Memory system accesses require 20 nanoseconds Answer the following questions: 1 What is the average memory access time for a system with only a L1 cache? 2. We decide to add a second L2 cache that will be accessed only when accesses miss the L1 cache. If the L2 cache has a miss rate of 1%, what percentage of memory accesses will miss both caches and actually access memory?

Explanation / Answer

We have been given the following data:
1 clock cycle = 1 nanosecond.
Memory access time = 20 nanoseconds.
Cache access time = 1 nanosecond(given: 1 clock cycle)
Cache miss rate = 5% => cache hit rate = 95%

(a) So, the avg memory access time = (cache hit rate* cache access time + cache miss rate * memory access time)

=> avg memory access time= (0.95 * 1 + 0.05 * 20)ns = 1.95 nanoseconds

(b) Now we added another cache L2. But we will only access it when we will miss L1.
So speaking according to the data, we will access L2 only 5% of the times (L1 miss rate).
Miss rate of L2 = 1%.
To miss both the caches one has to be in 1% of the 5% of the total.
Therefore, the new miss rate will be: 1% of 5% = 0.01*0.05 = 0.0005 = 0.05%

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