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    <div class="header">Paging and Page Replacement Algorithms</div>
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          <li>
            <a href="#Paging">Paging</a>
          </li>
          <li>
            <a href="#algos">Page Replacement Algorithms</a>
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          <li>
            <a href="#FIFO">&emsp;First In First Out</a>
          </li>
          <li>
            <a href="#LRU">&emsp;Least Recently Used</a>
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          <li>
            <a href="#Optimal">&emsp;Optimal Page Replacement</a>
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            <a href="./simulation.php">Try Simulation</a>
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        <div class="section">
          <h1 id="Paging">Paging</h1>
          <p>
            Paging is a function of memory management where a computer will
            store and retrieve data from a device's secondary storage (hard
            disk, SSD) to the primary storage (RAM). Memory management is a
            crucial aspect of any computing device, and paging specifically is
            important to the implementation of virtual memory.
          </p>
          <p>
            Virtual memory, what paging is used for often, is a memory
            management technique where secondary memory can be used as if it
            were a part of the main memory. Paging acts as an important part of
            virtual memory, as it allows programs in secondary storage to exceed
            the available size of the physical storage.
          </p>
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        <div class="section">
          <h1 id="algos">Page Replacement Algorithms in Operating Systems</h1>
          <p>
            In an operating system that uses paging for memory management, a
            page replacement algorithm is needed to decide which page needs to
            be replaced when new page comes in.
          </p>
          <p>
            <span>Page Fault-</span>A page fault happens when a running program
            accesses a memory page that is mapped into the virtual address
            space, but not loaded in physical memory.
          </p>
          <p>
            Since actual physical memory is much smaller than virtual memory,
            page faults happen. In case of page fault, Operating System might
            have to replace one of the existing pages with the newly needed
            page. Different page replacement algorithms suggest different ways
            to decide which page to replace. The target for all algorithms is to
            reduce the number of page faults.
          </p>
        </div>
        <div class="section">
          <h3>Page Replacement Algorithms:</h3>
          <h4 id="FIFO">1. First In First Out</h4>
          <p>
            This is the simplest page replacement algorithm. In this algorithm,
            the operating system keeps track of all pages in the memory in a
            queue, the oldest page is in the front of the queue. When a page
            needs to be replaced page in the front of the queue is selected for
            removal.
          </p>
          <p>
            <span>Example:</span>Consider page reference string 1, 3, 0, 3, 5,
            6, 3 with 3 page frames.Find number of page faults.
          </p>
          <img src="./assets/fifo.png" alt="First In First Out Replacement" />
          <p>
            Initially all slots are empty, so when 1, 3, 0 came they are
            allocated to the empty slots —><span> 3 Page Faults.</span><br />
            when 3 comes, it is already in memory so —><span>
              0 Page Faults.</span
            ><br />
            Then 5 comes, it is not available in memory so it replaces the
            oldest page slot i.e 1. —><span> 1 Page Fault.</span><br />
            6 comes, it is also not available in memory so it replaces the
            oldest page slot i.e 3 —><span>1 Page Fault.</span><br />
            Finally when 3 come it is not available so it replaces 0—><span
              >1 Page Fault.</span
            ><br />
          </p>
        </div>
        <div class="section">
          <h3 id="LRU">2. Least Recently Used</h3>
          <p>
            In this algorithm page will be replaced which is least recently
            used.
          </p>
          <p>
            <span>Example:</span>Consider the page references 7, 0, 1, 2, 0, 3,
            0, 4, 2, 3, 0, 2, 3 with 4 page frame. Find number of page fault.
          </p>
          <img src="./assets/lru.png" alt="Least Recently Used Replacement" />
          <p>
            Initially all slots are empty, so when 7 0 1 2 are allocated to the
            empty slots —><span>4 Page faults</span><br />
            0 is already there so —> <span>0 Page fault.</span><br />
            when 3 came it will take the place of 7 because it is least recently
            used —><span>1 Page fault</span><br />
            When 4 comes in it will take place of 1 because it is least recently
            used —><span>1 Page fault</span><br />Now for the further page
            reference string —> <span>0 Page fault</span><br />because they are
            already available in the memory. <br />
          </p>
        </div>
        <div class="section">
          <h3 id="Optimal">3. Optimal Page Replacement</h3>
          <p>
            In this algorithm, pages are replaced which would not be used for
            the longest duration of time in the future.
          </p>
          <p>
            <span>Example:</span>Consider the page references 7, 0, 1, 2, 0, 3,
            0, 4, 2, 3, 0, 2, 3 with 4 page frame. Find number of page fault.
          </p>
          <img src="./assets/optimal.png" alt="Optimal Page Replacement" />
          <p>
            Initially all slots are empty, so when 7 0 1 2 are allocated to the
            empty slots —><span>4 Page faults</span><br />
            0 is already there so —> <span>0 Page fault.</span><br />
            when 3 came it will take the place of 7 because it is not used for
            the longest duration of time in the future. —><span
              >1 Page fault</span
            ><br />
            0 is already there so —> <span>0 Page fault</span><br />
            4 will takes place of 1 —> <span>1 Page Fault.</span><br />
            Now for the further page reference string —>
            <span>0 Page fault</span><br />
            because they are already available in the memory. <br />
          </p>
          <p>
            Optimal page replacement is perfect, but not possible in practice as
            the operating system cannot know future requests. The use of Optimal
            Page replacement is to set up a benchmark so that other replacement
            algorithms can be analyzed against it.
          </p>
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