Exercise $3.[30$ Marks$]$ We will explore the impact of cache capacity on performance, focusing

exclusively on the data cache and excluding instruction storage in the caches. Cache access time

is directly linked to its capacity. For the sake of simplicity, let's assume that accessing the main

memory takes $100$ns$,$ and in a specific program, $50\%$ of instructions involve data access.

Two distinct processors, denoted as P$1$ and P$2,$ are engaged in executing this program. Each

processor is equipped with its own L$1$ cache.

L$1$ size L$1$ Miss Rate L$1$ Hit Time

P$164$ KB $3\mathrm{.}6\%1\mathrm{.}26$ ns

P$2128$ KB $3\mathrm{.}1\%2\mathrm{.}17$ns

$($a$)$ What is the AMAT for P$1$ and P$2$ assuming no other levels of cache?

$($b$)$ Assuming an ideal CPI of $2\mathrm{.}0$ for both processors and where the L$1$ hit time determines the

cycle time, what is the CPIstall for P$1$ and P$2?$ Which processor is faster at executing this

particular program?

Now consider the addition of an L$2$ cache to P$1$ with the following characteristics. The data from

the previous table still holds.

L$2$ size L$2$ Miss Rate L$2$ Hit Time

$16$ MB $42\%21\mathrm{.}24$ s

$($c$)$ Determine the Average Memory Access Time $($AMAT$)$ for P$1$ with the introduction of an L$2$

cache. Does the inclusion of the L$2$ cache result in an improvement or degradation of the

AMAT?

$($d$)$ Given an ideal CPI of $2\mathrm{.}0,$ where the cycle time is dictated by the L$1$ hit time, calculate the

Cycle Per Instruction $($CPIstall$)$ for P$1$ with the incorporation of an L$2$ cache.

$($e$)$ Which processor demonstrates superior speed now that P$1$ is equipped with an L$2$ cache? If

P$1$ exhibits enhanced speed, what miss rate in its L$1$ cache would be required to match P$2\text{'}$s

performance? Alternatively, if P$2$ proves to be faster, what miss rate in its L$1$ cache would be

necessary to equal P$1\text{'}$s performance?