A demand paged virtual memory system uses $$16$$ bit virtual address, page size of $$256$$ bytes, and has $$1$$ Kbyte of main memory. $$LRU$$ page replacement is implemented using a list, whose current status (page numbers in decimal ) is
$$\eqalign{ & \,\, \uparrow \cr & LRU\,Page \cr} $$
For each hexa decimal address in the address sequence given below,
$$00FF,$$ $$010D,$$ $$10FF,$$ $$11B0$$
Indicate,
i) The new status of the list
ii) Page faults, if any, and
iii) Page replacements, if any

A computer installation has 1000K of main memory. The jobs arrive and finish in the following sequence.
Job 1 requiring 200k arrives
Job 2 requiring 350k arrives
Job 3 requiring 300k arrives
Job 1 finishes
Job 4 requiring 120k arrives
Job 5 requiring 150k arrives
Job 6 requiring 80k arrives

(a) Draw the memory allocation table using Best Fit and First fit algorithm.
(b) Which algorithm performs better for this sequence?

The following page addresses, in the given sequence, were generated by a program:
1 2 3 4 1 3 5 2 1 5 4 3 2 3

This program is run on a demand paged virtual memory system, with main memory size equal to $$4$$ pages. Indicate the page references for which page faults occurs for the following page replacement algorithms.
(a) $$LRU$$
(b) $$FIFO$$

Assume that the main memory is empty initially.

Let the page reference and the working set window be c c d b c e c e a d and 4, respectively. The initial working set at time $$t = 0$$ contains the pages {a, d, e}, where a was referenced at time $$t = 0, d$$ was referenced at time $$t = -1,$$ and $$e$$ was referenced at time $$t = -2.$$ Determine the total number of page faults and the average number of page frames used by computing the working set at each reference.