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How many page faults occur in LRU page replacement algorithm for the given reference
string, with four-page frames
7, 0, 1, 2, 0, 3, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1
- a)6
- b)8
- c)9
- d)7
Correct answer is option 'D'. Can you explain this answer?
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Solution:
To understand why the least recently used (LRU) page will be 3, let's go through the page reference sequence and the page frames.
Page Reference Sequence:
0 2 1 3 2 1 0 1 2 1
Page Frames:
Page frames are the available slots to store pages in memory. In this case, we have four page frames.
Initially, all page frames are empty:
- Frame 1: Empty
- Frame 2: Empty
- Frame 3: Empty
- Frame 4: Empty
Page Reference 0:
Since the page frame is empty, we can directly allocate page 0 to the first frame.
- Frame 1: 0
- Frame 2: Empty
- Frame 3: Empty
- Frame 4: Empty
Page Reference 2:
Page 2 is not present in any of the frames, so we allocate it to the next available frame.
- Frame 1: 0
- Frame 2: 2
- Frame 3: Empty
- Frame 4: Empty
Page Reference 1:
Page 1 is not present in any of the frames, so we allocate it to the next available frame.
- Frame 1: 0
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 3:
Page 3 is not present in any of the frames, but all frames are already occupied. We need to replace a page using the LRU algorithm, which means we need to select the page that was least recently used.
The least recently used page is 0 because the page reference for 0 is the earliest among all the pages currently in the frames. So, we replace 0 with 3.
- Frame 1: 3
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 2:
Page 2 is already present in frame 2, so there is no need to make any changes.
- Frame 1: 3
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 1:
Page 1 is already present in frame 3, so there is no need to make any changes.
- Frame 1: 3
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 0:
Page 0 is not present in any of the frames, but all frames are already occupied. We need to replace a page using the LRU algorithm, which means we need to select the page that was least recently used.
The least recently used page is 3 because the page reference for 3 is the earliest among all the pages currently in the frames. So, we replace 3 with 0.
- Frame 1: 0
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 1:
Page 1 is already present in frame 3, so there is no need
To understand why the least recently used (LRU) page will be 3, let's go through the page reference sequence and the page frames.
Page Reference Sequence:
0 2 1 3 2 1 0 1 2 1
Page Frames:
Page frames are the available slots to store pages in memory. In this case, we have four page frames.
Initially, all page frames are empty:
- Frame 1: Empty
- Frame 2: Empty
- Frame 3: Empty
- Frame 4: Empty
Page Reference 0:
Since the page frame is empty, we can directly allocate page 0 to the first frame.
- Frame 1: 0
- Frame 2: Empty
- Frame 3: Empty
- Frame 4: Empty
Page Reference 2:
Page 2 is not present in any of the frames, so we allocate it to the next available frame.
- Frame 1: 0
- Frame 2: 2
- Frame 3: Empty
- Frame 4: Empty
Page Reference 1:
Page 1 is not present in any of the frames, so we allocate it to the next available frame.
- Frame 1: 0
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 3:
Page 3 is not present in any of the frames, but all frames are already occupied. We need to replace a page using the LRU algorithm, which means we need to select the page that was least recently used.
The least recently used page is 0 because the page reference for 0 is the earliest among all the pages currently in the frames. So, we replace 0 with 3.
- Frame 1: 3
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 2:
Page 2 is already present in frame 2, so there is no need to make any changes.
- Frame 1: 3
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 1:
Page 1 is already present in frame 3, so there is no need to make any changes.
- Frame 1: 3
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 0:
Page 0 is not present in any of the frames, but all frames are already occupied. We need to replace a page using the LRU algorithm, which means we need to select the page that was least recently used.
The least recently used page is 3 because the page reference for 3 is the earliest among all the pages currently in the frames. So, we replace 3 with 0.
- Frame 1: 0
- Frame 2: 2
- Frame 3: 1
- Frame 4: Empty
Page Reference 1:
Page 1 is already present in frame 3, so there is no need
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How many page faults occur in LRU page replacement algorithm for the given referencestring, with four-page frames7, 0, 1, 2, 0, 3, 4, 2, 3, 0, 3, 2, 1, 2, 0, 1a)6b)8c)9d)7Correct answer is option 'D'. Can you explain this answer?
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