1. Module IV
Memory Organization

2. LFU Page Replacement Algorithm
It involves keeping track of the number of times a page is referenced in memory. 
Implementation:
Assign a counter to every block that is loaded into the cache.
Each time a reference is made the counter is incremented
When the cache reaches capacity, system will search for the page with lowest counter and remove it from the cache

3. LFU Page Replacement Example Consider the reference string :
7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
for a memory with three frames.

4. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)

5. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1)

6. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1)

7. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)

8. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2)

9. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)

10. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3)

11. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)

12. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)

13. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)

14. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)

15. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)

16. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1

17. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)

18. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)

19. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)
0(5)

20. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)
0(5)
1(2)

21. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)
0(5)
1(2) 7
7(1)

22. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)
0(5)
1(2) 7
7(1)
0(6)

23. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)
0(5)
1(2) 7
7(1)
0(6)
Hit Ratio = 9/20
No. of Page Faults = 11

24. 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1, 7, 0, 1
Page
Frame
Hit -1 7
7(1)
0(1) 1
1(1) 2
2(1)
0(2) 3
3(1)
0(3) 4
4(1)
0(4)
3(2)
Page
Frame
Hit -1 2
3(2)
0(4)
2(2) 1
1(1)
2(3)
0(5)
1(2) 7
7(1)
0(6)
Hit Ratio = 9/20
No. of Page Faults = 11