Suppose that the virtual Address space has eight pages and physical memory…

Answer: 13 page faults.

Explanation: Simulate the Least Recently Used (LRU) page replacement with four physical frames, starting with empty frames. For each reference, note whether it causes a page fault and the resulting frame contents (ordered from least recently used to most recently used).

1. Reference 0 — fault. Frames: [0]

2. Reference 2 — fault. Frames: [0, 2]

3. Reference 1 — fault. Frames: [0, 2, 1]

4. Reference 3 — fault. Frames: [0, 2, 1, 3]

5. Reference 5 — fault (evict 0). Frames: [2, 1, 3, 5]

6. Reference 4 — fault (evict 2). Frames: [1, 3, 5, 4]

7. Reference 6 — fault (evict 1). Frames: [3, 5, 4, 6]

8. Reference 3 — hit. Frames recency updated: [5, 4, 6, 3]

9. Reference 7 — fault (evict 5). Frames: [4, 6, 3, 7]

10. Reference 4 — hit. Frames recency: [6, 3, 7, 4]

11. Reference 7 — hit. Frames recency: [6, 3, 4, 7]

12. Reference 3 — hit. Frames recency: [6, 4, 7, 3]

13. Reference 3 — hit. Frames remain: [6, 4, 7, 3]

14. Reference 5 — fault (evict 6). Frames: [4, 7, 3, 5]

15. Reference 5 — hit. Frames: [4, 7, 3, 5]

16. Reference 3 — hit. Frames recency: [4, 7, 5, 3]

17. Reference 1 — fault (evict 4). Frames: [7, 5, 3, 1]

18. Reference 1 — hit. Frames: [7, 5, 3, 1]

19. Reference 1 — hit. Frames: [7, 5, 3, 1]

20. Reference 7 — hit. Frames recency: [5, 3, 1, 7]

21. Reference 2 — fault (evict 5). Frames: [3, 1, 7, 2]

22. Reference 3 — hit. Frames recency: [1, 7, 2, 3]

23. Reference 4 — fault (evict 1). Frames: [7, 2, 3, 4]

24. Reference 1 — fault (evict 7). Frames: [2, 3, 4, 1]

Total page faults = 13