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

$[15]<5\mathrm{.}7>$ An inverted page table can be used to further optimize space and time. How many PTEs are needed to store the page table? Assuming a hash table implementation, what are the common case and worst case numbers of memory references needed for servicing a TLB miss?