Question

Consider a page reference string as: 7, 0, 1, 2, 0, 3, 0, 4, 2, 3, 0, 3, 2. Assume that there are 3-page frames available. Calculate the total number of page faults for the above reference string if LRU policy is used for page replacement.

• A. 10
• B. 8
• C. 9
• D. 11

Hint:

LRU replaces the least recently used page. Track the order of page references and replace the least accessed page when a new one is needed.

Answer 1

The Correct Option is C

Step 1: LRU (Least Recently Used) Page Replacement.
In LRU, the page that has not been used for the longest time is replaced.

Step 2: Process the page reference string.
We process the reference string one page at a time, replacing the least recently used page when necessary. The sequence of frames is updated after each reference. - Reference 7 → Page fault, frames: [7] - Reference 0 → Page fault, frames: [7, 0] - Reference 1 → Page fault, frames: [7, 0, 1] - Reference 2 → Page fault, replace 7 (LRU), frames: [0, 1, 2] - Reference 0 → No page fault, frames: [0, 1, 2] - Reference 3 → Page fault, replace 1 (LRU), frames: [0, 2, 3] - Reference 0 → No page fault, frames: [0, 2, 3] - Reference 4 → Page fault, replace 2 (LRU), frames: [0, 3, 4] - Reference 2 → Page fault, replace 3 (LRU), frames: [0, 4, 2] - Reference 3 → Page fault, replace 0 (LRU), frames: [3, 4, 2] - Reference 0 → Page fault, replace 4 (LRU), frames: [3, 0, 2] - Reference 3 → No page fault, frames: [3, 0, 2] - Reference 2 → No page fault, frames: [3, 0, 2]

Step 3: Count the total number of page faults.
Total page faults = 9.