Describe following in brief i) Tools compliment representation ii) LRU algorithm निम्नलिखित को संक्षेप में वर्णन करें: i) टूल्स कॉम्प्लीमेंट रिप्रेजेंटेशन ii) LRU एल्गोरिथ्म

i) Tools Compliment Representation:

In Tools Compliment Representation, the negative value of a number is calculated using the following formula:

Negative of a Number = (2^n) - Decimal Value

This method is widely used to represent negative integers in computers and offers the benefits of easy subtraction and a compact representation. The range of decimal numbers that can be represented using n bits in 2's complement is from -(2^(n-1)) to (2^(n-1))-1, providing a balanced range of positive and negative values.

Advantages:

• Allows for quick subtraction of integers.
• Minimizes the need for specialized hardware instructions for addition and subtraction.
• Offers a compact representation for negative numbers, making it easy to implement in computers.

Disadvantages:

• Requires additional overhead to handle negative values, such as sign extension in some operations.
• Can be confusing for beginners who are not familiar with the concept of 2's complement representation.

ii) LRU Algorithm (Least Recently Used):

The LRU algorithm is an efficient page replacement algorithm used in operating systems to manage memory allocation. It operates on the principle of replacing the least recently used page from memory when a new page needs to be loaded. The main idea behind LRU is that pages that have not been accessed for a longer period of time are less likely to be needed in the near future compared to pages that have been recently used.

Working:

• The pages are maintained in a queue, with the most recently used page at the head of the queue.
• When a new page needs to be loaded and there is no free space in memory, the page at the tail of the queue (which is the least recently used page) is removed to make space for the new page.
• If the removed page has been modified, it is written back to the backing store before it is removed.

Advantages:

• Simple to implement and efficient in practice.
• Aims to keep the most frequently used pages in memory, leading to improved memory utilization and reduced page faults.
• Provides good performance for a wide variety of applications.

Disadvantages:

• Does not consider the size of pages, which can lead to thrashing if large pages are frequently accessed and replaced.
• Relies on the assumption that past usage patterns will continue in the future, which may not always be accurate.