GATE CSE 2014 | Set 3 | Question: 20

Question

A system uses $3$ page frames for storing process pages in main memory. It uses the Least Recently Used (LRU) page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? 

$\text{4, 7, 6, 1, 7, 6, 1, 2, 7, 2}$

Comments

the only thing to take care is update your LRU array or whatever you use to keep track of LRU property , on $\underline{"Page\ hits"}$ aswell

Answer 1

Total page faults $=6.$

$\small\begin{array}{|c|c|c|c|} \hline \quad\bf{4}\quad& \quad\bf{7} \quad& \quad \bf{6}\quad & \quad\bf{1}\quad&\quad\bf{7}\quad&\quad \bf{6}\quad &\quad \bf{1}\quad &\quad \bf{2}\quad &\quad \bf{7}\quad &\quad \bf{2}\quad \\ \hline & & \underset{\boxed{F}}6&6&6&6&6&6&\underset{\boxed{F}}7&7\\ \hline \hline &\underset{\boxed{F}}7 &7 &7&7&7&7&\underset{\boxed{F}}2&2&2\\ \hline
\hline \underset{\boxed{F}}{4}&4 & 4&\underset{\boxed{F}}1&1&1&1&1&1&1\\ \hline
  \end{array} \implies 6\text{ faults}$

 

Another way of answering the same.

$\require{cancel} \begin{array}{|c|}\hline
\quad6\quad \\\hline 7\\\hline\quad\cancel {4} \quad 1\\ \hline
\end{array}$ $\require{cancel} \begin{array}{|c|}\hline
\quad6\quad \\\hline \cancel{7}{2}\\\hline 1\\ \hline
\end{array}$ $\require{cancel} \begin{array}{|c|}\hline
\quad\cancel {6}{7}\quad \\\hline{2}\\\hline1\\ \hline
\end{array}$$\require{cancel} \begin{array}{|c|}\hline
\quad7\quad \\\hline {2}\\\hline 1\\ \hline
\end{array}$ $\implies 3 \text{ faults}+3 \text{ initial access faults} = 6 \text{ page faults}$

OR

$\require{cancel} \begin{array}{|c|}\hline
\quad\cancel6 7\quad \\\hline\cancel {7}2\\\hline\cancel 4 1\\ \hline
\end{array} \implies 3 \text{ faults}+3 \text{ initial access faults} = 6 \text{ page faults}$

Comments

In the LRU technique go to the backward direction and delete the oldest pages.

Answer 2

answer will be 6 page fault

Comments

Image is wrong . Answer is 6

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as i have missed the hit by myself  as i have use shortcut while answering .... :)