Question $8[2$x $3=6\%]$

Suppose that a system has $32-$bit physical addresses, $48-$bit virtual addresses and page size is $8$KB$.$ Let us also assume that accessing a page directly from main memory takes $100$ns$,$ while having to retrieve the page from the disk takes $2$ms$.$ Answer the following:

a$)$ What is the maximum required page fault rate in order to ensure average memory access time does not increase more than $25\%$ of the direct memory access time?

b$)$ A Translation Lookaside Buffer $($TLB$)$ is added to the system. In case of a TLB hit, memory access is reduced to $30$ns$.$ The TLB hit rate is $95\%.$ What is the average access time if we assume a page fault rate of $0\mathrm{.}005\%?$