Suppose the page size is $8$ bytes, the first$-$level page table has $4$ entries and the second$-$

level page table has $8$ entries. You need to answer the following questions:

Calculation $(20$ marks$)$

What is the size of the virtual address space?

How many bits does a virtual address have?

How many bits should be reserved for the first$-$level page table index, the second$-$level page

table index and the offset respectively?

Address Translation $(50$ marks$)$

For the virtual address space defined by the two$-$level page tables as shown in Figure $1,$ given the

following virtual addresses: $51,72,172,200.$

Which virtual addresses are mapped?

If a virtual address is mapped, what is its corresponding physical address?

Figure $1.$ The two$-$level page mapping table. The numbers in entries are physical

page frame numbers. Entries in gray color are not mapped.