Question $1.(2$ points$)$ Consider the page table for a system with $12-$bit virtual and

physical addresses and $256-$byte pages.

The list of free frames is $DEF($that is$,D$ is at the head of the list, $E$ is second,

and $F$ is last$).$ A dash for a page frame indicates that the page is not in the memory.

Please convert the following hexadecimal virtual addresses to their equivalent

hexadecimal physical addresses.

a$.8EF$

b$.221$

c$.40A$

d$.7FD$

Hint: $256-$byte page $=>8-$bit page offset;$12-$bit virtual and physical addresses, $12-8$

$=4-$bit page numbers and frame numbers, so the first hexadecimal letter is the page

number in the hexadecimal virtual addresses; get the corresponding frame number

from the page table; if a page fault occurs $($the page is not in the memory and frame

number is $-),$ load the required page in the first free frame in the list; extract the

frame number, combine frame number and page offset to get physical address.