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Consider a system with 2 level caches. Access times of Level 1 cache, Level 2 cache, and main memory are 1 ns, 10 ns, and 500 ns, respectively. The hit rates of Level 1 and Level 2 caches are 0.8 and 0.9, respectively. What is the average access time of the system ignoring the search time within the cache? 

Consider a system with 2 level caches. Access times of Level 1 cache, Level 2 cache, and main memory are 1 ns, 10 ns, and 500 ns, respectively. The hit rates of Level 1 and Level 2 caches are 0.8 and 0.9, respectively. What is the average access time of the system ignoring the search time within the cache?  Correct Answer 12.6 ns

Data:

T1 = 1 ns, T2 = 10 ns and T3 = 500 ns

H1 = 0.8, H2 = 0.9

Average access time = Tavg

Formula:

Tavg = H1T1 + (1 - H1) H2 (T1 + T2) + (1 - H1) (1 - H2) (T1 + T2 + T3)

Since search time within a cache is ignored

Tavg = H1T1 + (1 - H1) H2 (T2) + (1 - H1) (1 - H2) (T3)

Calculation:

Tavg =  0.8 × 1 + 0.2 × 0.9 × 10 + 0.2 × 0.1 × 500

Tavg = 0.8+ 0.18 +  10 = 12.6 ns

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