$$

$0$:$46$:$270$

$$

$23$

Possible transitions $($that is$,$ possible next states$)$ for a process in the Ready state are

Running $.a0$

Blocked $.b$

New $.c$

Ready $.d$

$$

Consider the following string of page references: $7,0,1,2,0,3,0,4,2,3,0,3,2.$

Given an empty main memory with $3$ page frames, find out the total number of page faults for the OPTIMAL page replacement algorithm. Count page faults only after all frames have been initialized.

Note: Assume the page reference string continues with $1,2,0,1,7,0,1$

$7.$a $$

$6.$b $$

$3.0$

$5.$ d $0.$