given that main memory is composed of only three page frames for public use and that a program requests pages in the following order: a,c,b,d,a.c,e,a,c,b,d,e

There's a question here someplace?

LRU

To answer this question, we need to use the concept of page replacement algorithms, specifically the FIFO (First-In-First-Out) algorithm. FIFO works on the principle that the page which is brought into memory first will be the one that is replaced first when a page fault occurs. Let's step through the process using the given page reference sequence.

Initially, the main memory contains no pages. As the program starts requesting pages, we will track the sequence of page frames in memory.

1. a: Since there are no pages in memory, we bring page 'a' into the first frame.
Memory state: [a, -, -]

2. c: Page 'c' is not in memory, so it causes a page fault. We replace the oldest page in memory, which is 'a', with page 'c'.
Memory state: [c, -, -]

3. b: Page 'b' is not in memory, so another page fault occurs. Page 'a' is the oldest page in memory, so we replace it with page 'b'.
Memory state: [c, b, -]

4. d: Page 'd' is not in memory, causing a page fault. Again, the oldest page 'c' is replaced with 'd'.
Memory state: [d, b, -]

5. a: As page 'a' was accessed previously and is still in memory, no page fault occurs. Memory state remains the same.
Memory state: [d, b, -]

6. c: Page 'c' is already in memory, so no page fault occurs.
Memory state: [d, b, -]

7. e: Page 'e' is not in memory, resulting in a page fault. We replace the oldest page 'd' with 'e'.
Memory state: [e, b, -]

8. a: Although page 'a' is already in memory, it was the first page brought into memory, so we consider it the oldest. Thus, it is replaced with 'a'.
Memory state: [e, b, a]

9. c: Page 'c' is still in memory, so no page fault occurs.
Memory state: [e, b, a]

10. b: Page 'b' is already in memory, so no page fault.
Memory state: [e, b, a]

11. d: Page 'd' is not in memory, generating a page fault. The oldest page 'e' is replaced.
Memory state: [d, b, a]

12. e: Page 'e' is already in memory, so no page fault occurs.
Memory state: [d, b, a]

At the end of the page sequence, the final memory state is [d, b, a]. This means that pages 'd', 'b', and 'a' are in memory. The page replacement algorithm used here, FIFO, determines the order of replacement based on which page was brought into memory first.

Note: This example assumed there were no additional page references beyond the given sequence. In a real scenario, the memory state would continue to evolve based on the sequence and the page replacement algorithm used.