A $32-$bit computer implements paging with page sizes of $8$Kbytes. The amount of physical memory

available is $64$ Mbytes. A fully$-$associative TLB with $16$ entries is available.

$($a$)$ What is the number of entries needed in the page table?

$($b$)$ If each page table entry contains the physical page number, valid bit, dirty bit, and four bits for

protection, what is the size of each entry in bits?

$($c$)$ How many bits is each TLB entry? $($Do not store PID in TLB$).$

$($d$)$ What is the maximum size of the swap space needed on the hard disk? $($Assume a dirty bit is

present$).$