Problem $4(20$ Points$)$

A page$-$based virtual memory is using a linear page table

where its:

Virtual address space size $=128$ bytes

Physical memory size $=1024$ bytes

Page size $=16$ bytes

The leftmost bit in each PTE is the VALID bit. If this bit is $1,$ the

rest of the entry is the PFN$.$ If the bit is $0,$ the page is not valid.

Assume the shown contents of the page table $($in hexadecimal$).$

a$)$ In front of each of the following virtual addresses, write its

corresponding physical address as a $3-$digit hexadecimal

number in the format Oxabc. For an invalid virtual address,

write FAULT for its physical address.

b$)$ Explain how a multi$-$level page table $($by utilizing a page directory$)$ helps in reducing the

memory needed compared to a linear page table.