$.(6$ points$)$ Suppose we have a system with $9$ bit sized virtual addresses, $8$ bit sized physical addresses,

and a page size of $16$ bytes.

$($a$)$ How many bytes of data can virtual memory support?

$($b$)$ How many bytes of data can physical memory support?

$($c$)$ How many bits is the offset address?

$($d$)$ How many virtual pages are there?

$($e$)$ How many physical pages are there?

$($f$)$ How many entries will the page table have?