$2.$ Consider the following sequence of virtual memory references $($in decimal$)$ generated by a single program in a pure paging system:

$100,110,1400,1700,703,3090,1850,2405,4304,4580,3640$

a$)$ Derive the corresponding reference string of pages $($i$.$e$.$ the pages the virtual addresses are located on$)$ assuming a page size of $1024$ bytes. Assume that page numbering starts at page $0.($In other words, what page numbers are referenced. Convert address to a page number$).$

b$)$ For the page sequence derived in part $($a$),$ determine the number of page faults for each of the following page replacement strategies, assuming that $2$ page frames are available to the program. $($Assume no TLB$)$

$1)$ LRU

$2)$ FIFO

$3)$ OPT $($Optimal$)$