A$=32,$ B$=2048$ C$=5,$ D$=5,$ E$=20,$ F$=3,$ G$=15$

$($Design of a multi$-$level page table$)$ Assume that we have an A$-$bit virtual address space, B$-$byte pages

and a page table entry $($PTE$)$ of C$-$bytes.

a$)$ Construct a multi$-$level page table so that each page table fits within a single page. Show all your

calculations and the details of your final design in a visual similar to the one below. $(20$ points$)$

b$)$ Suppose we have only one valid page in our address space. With our multi$-$level page table design,

calculate the memory saving as compared to a single level page table? $(10$ points$)$

c$)$ What is the overhead associated with this multi$-$level design $($again as compared to a single level$)?$

Provide a numerical comparison. $(10$ points$)$