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?