$4\mathrm{.}2$ Finding data in cache using physical address. $(15$ pts$)4\mathrm{.}2\mathrm{.}1$ How many sets does the $256$KB cache consist of$?4\mathrm{.}2\mathrm{.}2$ Write down the physical address BA$9$E$78$H in binary and mark the WORD, SET Index, and TAG fields taking into account the cache parameters. $4\mathrm{.}2\mathrm{.}3$ Which set did the cache controller approach? State the set number in binary. $4\mathrm{.}2\mathrm{.}4$ Having approached a specific set, how many comparisons of what size $($include valid bit in your count$)$ were performed to see if the needed block was available in the cache? $4\mathrm{.}2\mathrm{.}5$ If you wish to have $$wide$$ memory to facilitate fast moving of a block from the main memory to the cache, how wide do you wish to organize the main memory? Explain why do you make this choice? $($a$)256$ bits $($b$)128$ bits $($c$)64$ bits $($d$)16$ bits $($e$)8$ bits