Virtual Memory & Page Replacement question bank (Operating Systems)

[Virtual Memory & Page Replacement Concept 5] A system uses 48-bit virtual addresses and 32-bit physical addresses with a page size of 8 KB ($2^{13}$ bytes). If each page table entry (PTE) takes 4 bytes, how many levels of hierarchical page tables are required if each page table must fit exactly within a single page frame?

[Virtual Memory & Page Replacement Concept 11] A system uses 48-bit virtual addresses and 32-bit physical addresses with a page size of 8 KB ($2^{13}$ bytes). If each page table entry (PTE) takes 4 bytes, how many levels of hierarchical page tables are required if each page table must fit exactly within a single page frame?