A system implements a paged virtual address space for each process using a one$-$level page table. The maximum size of virtual address space is $64$KB$.$ The page table for the running process includes the following valid entries $($ the $->$ notation indicates that a virtual page maps to the given page frame, that is$,$ it is located in that frame$)$:

Virtual page $1->$ Page frame $0$

Virtual page $2->$ Page frame $4$

Virtual page $8->$ Page frame $1$

Virtual page $7->$ Page frame $2$

Virtual page $10->$ Page frame $5$

Virtual page $20->$ Page frame $6$

The page size is $1$K bytes and the maximum physical memory size of the machine is $8$KB$.$

$20.$ How many bits are required for each virtual address?

$2$

$4$

$8$

$9$

$11$

$13$

$16$

$24$