Suppose a processor has access to three levels of cache memory. Level $1$ and $2$ are

exclusive to the processor and level $3$ is shared with other processors. The processor

also has access to the computer main memory. Level $1$ has an access time of $10$

microseconds, level $2$ has an access time of $25$ microseconds and level $3$ has an access

time of $80$ microseconds. Main memory has an access time of $250$ microseconds. Level

$1$ contains a subset of the bytes contained in level $2,$ and level $2$ contains a subset

of the bytes contained in level $3.$ Level $3$ contains a subset of the bytes contained in

main memory. It is estimated that $15\%$ of all requested bytes are contained in level

$1,30\%$ of all requested bytes are contained in level $2$ and $60\%$ of all requested bytes

are contained in level $3.100\%$ of all requested bytes are contained in main memory.

If a byte to be accessed is in level $1,$ then the processor will directly access it from

level $1.$ If a byte to be accessed is not in level $1$ but in level $2,$ then the processor

will directly access it from level $2.$ If a byte to be accessed is not in level $1$ and not

in level $2,$ but in level $3,$ then the processor will first transfer the block containing

the byte from level $3$ to level $1$ and then access the byte from level $1.$ If a byte to be

accessed is not in cache memory at all, then the processor will first transfer the block

containing the byte from main memory to level $2$ and then access it from level $2.$

For simplicity, ignore the time it takes to transfer bytes between the memory levels.

Moreover, ignore the time that is required for the processor to determine whether a

byte can be found in cache or main memory.

$2\mathrm{.}1(21/2$ What is the average access time of this system? Write down all intermediate $)$

steps.

$2\mathrm{.}2($

$1/2$ What is the hit ratio of level $3?$