Question

Consider the following page reference string :

1 2 3 4 2 1 5 6 2 1 2 3 7 6 3 2 1 2 3 6
i) For LRU page replacement algorithm with 4 frames, the number of page faults is :
a) 10
b) 14
c) 8
d) 11

Answer 1

The student's question involves calculating the number of page faults using the Least Recently Used page replacement algorithm given 4 frames and a specific page reference string. By simulating the LRU algorithm step by step and tracking page faults, it's determined that there are 10 page faults. Thus, the correct answer is option (a) 10.

Step-by-step explanation:

The student is asking about the Least Recently Used (LRU) page replacement algorithm in the context of operating systems. When a page needs to be replaced, LRU chooses the page that has not been used for the longest period of time. Given a page reference string and a fixed number of frames, one must count how often a new page needs to be loaded into one of the frames, which is not already loaded, indicating a page fault.

Considering the page reference string '1 2 3 4 2 1 5 6 2 1 2 3 7 6 3 2 1 2 3' and 4 frames, let's perform LRU page replacement step by step:

1. Load 1 into a frame: page fault
2. Load 2 into a frame: page fault
3. Load 3 into a frame: page fault
4. Load 4 into a frame: page fault
5. Page 2 is already in a frame: no page fault
6. Page 1 is already in a frame: no page fault
7. Load 5 into a frame, replace 4 (LRU): page fault
8. Load 6 into a frame, replace 3 (LRU): page fault
9. Page 2 is already in a frame: no page fault
10. Page 1 is already in a frame: no page fault
11. Page 2 is already in a frame: no page fault
12. Page 3 needs to be loaded, replace 5 (LRU): page fault
13. Load 7 into a frame, replace 6 (LRU): page fault
14. Page 6 needs to be loaded, replace 2 (LRU): page fault
15. Page 3 is already in a frame: no page fault
16. Page 2 needs to be loaded, replace 7 (LRU): page fault
17. Page 1 needs to be loaded, replace 6 (LRU): page fault
18. Page 2 is already in a frame: no page fault
19. Page 3 needs to be loaded, replace 1 (LRU): page fault
20. Page 6 needs to be loaded, replace 2 (LRU): page fault

Counting the page faults, we get a total of 10 page faults. Therefore, the correct answer is option (a) 10.

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