Describe the working of the LRU-K-8 (Least Recently Used with K and 8th Chance) page replacement algorithm.

The LRU-K-8 (Least Recently Used with K and 8th Chance) page replacement algorithm is an enhancement of the traditional LRU (Least Recently Used) algorithm. It aims to improve the efficiency of page replacement by considering both the recency and frequency of page accesses.

In the LRU-K-8 algorithm, each page in memory is associated with a counter that keeps track of the number of times the page has been accessed. Additionally, there is a reference bit associated with each page, which is set to 1 whenever the page is accessed.

When a page fault occurs, the algorithm first checks if there is an empty frame available in memory. If so, the page is simply loaded into the empty frame. Otherwise, the algorithm selects a victim page for replacement.

The selection of the victim page is done in two steps. First, it identifies the set of pages with the lowest counter value. From this set, it selects the page with the reference bit set to 0. If all pages in the set have their reference bit set to 1, it clears the reference bit of each page and repeats the process until a page with the reference bit set to 0 is found.

Once the victim page is selected, it is replaced with the new page, and the counter and reference bit of the new page are initialized accordingly.

The LRU-K-8 algorithm introduces the concept of K additional bits, which are used to track the recency of page accesses. These bits are shifted right by one position whenever a page is accessed. If the least significant bit of the K bits is 1, it means that the page has been accessed recently. Otherwise, it indicates that the page has not been accessed recently.

The 8th Chance component of the algorithm is related to the reference bit. Whenever a page is accessed, the reference bit is set to 1. However, after every 8th access, the reference bit is cleared to 0, indicating that the page has not been accessed recently.

By combining the recency information from the K bits and the reference bit, the LRU-K-8 algorithm can make more informed decisions about page replacement, considering both the recent and frequent accesses to pages. This helps in improving the overall efficiency of memory management in an operating system.