Exercise $\backslash$#$1[20$ pts$]$

Consider the following page table, in which $"\backslash ($ x $\backslash )"$ means an invalid entry.

Assume a $\backslash (\backslash$mathbf$\{8$ K i B$\}\backslash )$ page size. For convenience, in this exercise all physical and logical addresses are decimal values.

Give the physical address corresponding to the following logical addresses, or state that an error occurs $($your answer should thus be decimal values and should include the details of how you performed the computation$)$:

a$.[5$ pts$]20$

b$.[5$ pts$]9100$

c$.[5$ pts$]50321$

$-$ d$.[5$ pts$]81589$

Exercise $\backslash$#$2[6$ pts$]$

Consider a logical address space of $32$ pages with $2,048$ bytes per page, mapped onto a physical memory of $8$ frames.

$-$ a$.[3$ pts$]$ How many bits are required in the logical address? $($show your work$)$

$-$ b$.[3$ pts$]$ How many bits are required in the physical address? $($show your work$)$

Exercise $\backslash$#$3[8$ pts$]$

Consider a computer system with a $32-$bit logical address and $\backslash (8-\backslash$mathrm$\{$KiB$\}\backslash )$ page size. The system supports up to $2$ GiB of physical memory.

$-$ a$.[4$ pts$]$ How many entries are there in a conventional single$-$level page table? $($show your work$)$

$-$ b$.[4$ pts$]$ How many entries are there in an inverted page table? $($show your work$)$

Exercise $\backslash$#$4[16$ pts $+5$ pts$]$

Suppose we have a computer system with a $38-$bit logical address, page size of $32$ KiB $,$ and $8$ bytes per page table entry.

$-$ a$.[8$ pts$]$ How many pages are in the logical address space? $($show your work$)$

$-$ b$.[8$ pts$]$ Suppose we use two$-$level paging and arrange for all page table pages to fit into a single page frame. How will the bits of the address be divided up$?($show your work$)$

$-$ c$.[5$ pts EXTRA CREDIT$]$ Suppose we have a program with a $8$ GiB address space. Using the two$-$level page table scheme from the previous question, How much memory, in number of page frames, is used counting the process's pages and the page table? $($show your work, and the result should be a sum of three terms$)$