Suppose that a machine has $48-$bit virtual addresses and $32-$bit physical addresses.

$($a$)$ If pages are $4KB,$ how many entries are in the page table if it has only a single level? Explain.

$($b$)$ Suppose this same system has a TLB $($Translation Lookaside Buffer$)$ with $32$ entries. Furthermore, suppose that a program contains instructions that fit into one page and it sequentially reads long integer elements from an array that spans thousands of pages. How effective will the TLB be for this case?