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Consider a system with $2$ level cache. Access times of Level $1$ cache, Level $2$ cache and main memory are $0.5$ ns, $5$ ns and $100$ ns respectively. The hit rates of Level $1$ and Level $2$ caches are $0.7$ and $0.8$, respectively. What is the average access time of the system ignoring the search time within the cache?





Solution

evel $1$ hit rate $=0.7$

Level $2$ hit rate $=0.8$

Level $1$ access time $=0.5$ ns

Level $2$ access time $=5$ ns

Main memory access time $=100$ ns

Average access time is

$0.7(0.5)+0.3[0.8(5)+0.2(100)]$

$=0.35+0.3[4+20]$

$=0.35+0.3(24)$

$=0.35+7.2$

$=7.55$ ns



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