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 For FIFO page replacement algorithms with 3 frames, the number of page faults is?a.15b.14c.11d.16

Sure, let's go through the FIFO (First-In-First-Out) page replacement algorithm step by step with the given page reference string and 3 frames.

Page reference string: 1 2 3 4 2 1 5 6 2 1 2 3 7 6 3 2 1 2 3 6

1. Start with an empty set of frames: [ - , - , - ]

2. Process each page in the reference string:

   • 1: [ 1 , - , - ] (Page fault)
   • 2: [ 1 , 2 , - ] (Page fault)
   • 3: [ 1 , 2 , 3 ] (Page fault)
   • 4: [ 4 , 2 , 3 ] (Page fault, 1 is replaced)
   • 2: [ 4 , 2 , 3 ] (No page fault, 2 is already in the frame)
   • 1: [ 4 , 1 , 3 ] (Page fault, 2 is replaced)
   • 5: [ 4 , 1 , 5 ] (Page fault, 3 is replaced)
   • 6: [ 6 , 1 , 5 ] (Page fault, 4 is replaced)
   • 2: [ 6 , 2 , 5 ] (Page fault, 1 is replaced)
   • 1: [ 6 , 2 , 1 ] (Page fault, 5 is replaced)
   • 2: [ 6 , 2 , 1 ] (No page fault, 2 is already in the frame)
   • 3: [ 3 , 2 , 1 ] (Page fault, 6 is replaced)
   • 7: [ 3 , 7 , 1 ] (Page fault, 2 is replaced)
   • 6: [ 3 , 7 , 6 ] (Page fault, 1 is replaced)
   • 3: [ 3 , 7 , 6 ] (No page fault, 3 is already in the frame)
   • 2: [ 2 , 7 , 6 ] (Page fault, 3 is replaced)
   • 1: [ 2 , 1 , 6 ] (Page fault, 7 is replaced)
   • 2: [ 2 , 1 , 6 ] (No page fault, 2 is already in the frame)
   • 3: [ 2 , 1 , 3 ] (Page fault, 6 is replaced)
   • 6: [ 2 , 6 , 3 ] (Page fault, 1 is replaced)

Now, let's count the number of page faults:

1. 1 (fault)
2. 2 (fault)
3. 3 (fault)
4. 4 (fault)
5. 1 (fault)
6. 5 (fault)
7. 6 (fault)
8. 2 (fault)
9. 1 (fault)
10. 3 (fault)
11. 7 (fault)
12. 6 (fault)
13. 2 (fault)
14. 1 (fault)
15. 3 (fault)
16. 6 (fault)

Total page faults = 16

So, the correct answer is: d. 16