In this exercise, we will examine space$/$time optimizations for page tables. The following list provides parameters of a virtual memory system.

$[10]<5\mathrm{.}7>$ Using a multilevel page table can reduce the physical memory consumption of page tables, by only keeping active PTEs in physical memory. How many levels of page tables will be needed if the segment tables $($the upper$-$level page tables$)$ are allowed to be of unlimited size? And how many memory references are needed for address translation if missing in TLB$?$