$1.$ Calculate the total number of page table entries $($PTE$)$required for a $1-$level page table to cover a virtual address space of $64$ GB with a page size of $4$ KB$.$

$2.$ Calculate the total number of entries required for a $2-$level page table to cover the same virtual address space mentioned in question $1,$ where the first$-$level page table has $1024$ entries and the second$-$level page table has $512$ entries, with a page size of $4$ KB$.$

$3.$ Based on the calculations from questions $1$ and $2,$ determine how much memory is saved $($in terms of the number of entries$)$ by using a $2-$level page table instead of a $1-$level page table for the given virtual address space.