Question $3.[3$ marks$]$

Considering a virtual memory system with paging:

Assume that the page size is bytes$),$ and each physical and virtual address is

represented by a $16-$bit binary or equivalently a $4-$digit hexadecimal number. So$,$ the

relationship between virtual memory address and virtual page number should be as follows:

A process was assigned $3$ physical frames with frame numbers $5,8,$ and $10$ by the system. This

means that no matter how many virtual pages the process has, all its virtual pages must be

mapped into only the three frames assigned above.

Now it is time spot $100($a larger time value indicates a later point in time$).$ The current content

of the page table is shown below with Table $1,$ in which the "Access time" column shows the

time of the most recent visit to the virtual page in the corresponding row $($e$.$g$,80$ indicates that

virtual page $2$ is visited most recently at time spot $80).$

Page numbers are given in decimal format. The $"-"$ symbol in the virtual page column indicates

that no virtual page has been mapped to the frame that is listed in the same row as the virtual

page. The $"-"$ symbol in the "Access time" column indicates that this physical page is not visited

yet.

Assume that LRU replacement is used for page replacement. This means if all the $3$ physical

pages have been mapped with $3$ virtual pages, and a $4^{th}$ different virtual page is accessed, among

the $3$ mapped virtual pages, the one with the oldest $($smallest$)$ "access time" will be replaced by

the $4^{th}$ new virtual page.

From now on$,$ the following virtual addresses will be accessed sequentially:

$0$x$2198,0$x$33$F$6,0$x$4769,0$x$5$AB$6,0$x$084$D at time $120,150,200,220$ and $300$ respectively.

Please complete the page table after the above four accesses, by filling in the blanks in Table $2.$

Note that you are required to input the page numbers in decimal format.

Table $1$: The original page table

Virtual page number Physical page number Access time

$2580$

$5860$

$-10-$

Answer:

Table $2$: The page table after the five accesses

Virtual page number Physical page number Access time

$\_\_\_\_\_\_\_\_5\_\_\_\_\_\_\_\_$

$\_\_\_\_\_\_\_\_8\_\_\_\_\_\_\_\_$

$\_\_\_\_\_\_\_\_10\_\_\_\_\_\_\_\_$