Question 21
Consider a system with 64-bit virtual addresses, 4 KB page size, and 8-byte page table entries. In a multi-level paging system where every level page table fits in one page, how many levels of page tables are required? (Question 21)
Page size = 4 KB = $2^12$ B. PTE size = 8 $B = 2^3 B$. Entries per page = $2^12 / 2^3$ = $2^9$ = 512 entries (9 bits per level). Offset = 12 bits. Remaining bits = 64 - 12 = 52 bits. Number of levels = ceil(52 / 9) = 6 levels (or 5 levels for 48-bit canonical physical memory space).