$1.$ Consider the following page reference string:

$1,2,3,4,1,5,2,3,1,2,4,3,2,5,2.$

Assuming demand paging with THREE and FOUR frames, how many page faults would occur

and what is the page fault ratio of each for the following replacement algorithms?

a$)$ First In First Out $($FIFO$)$ replacement

b$)$ Optimal replacement

c$)$ Least Recently Used $($LRU$)$ replacement

d$)$ LRU replacement $-$ Stack implementation

e$)$ LRU replacement $-$ Counter implementation

$2.$ Suppose a disk drive has $100$ cylinders, numbered $0$ through $99.$ Suppose that the drive is

currently servicing a request at cylinder $20$ and moving in the direction of increasing cylinder

numbers. The order of request in the request queue is as follows:

$10,22,20,2,40,6$ and $38$

Starting from the current head position, identify the total distance, in cylinders, that the arm

moves to satisfy all pending requests for the following disk scheduling algorithms. Show all

workings.

a$)$ First Come First Serve $($FCFS$)$

b$)$ Shortest Seek Time First $($SSTF$)$

c$)$ SCAN

d$)$ C$-$SCAN

$3.$ Assume a computer with a memory size of $256K,$ initially empty. Requests are received for

blocks of memory of $5K,25K,35K$ and $20K.$ Show how the buddy system would deal with

each request, showing the memory layout at each stage and the status of the lists at the end.

After allocating all the processes, what would be the effect of the $25K$ process terminating and

returning its memory?