You have a system with 512MB physical memory and are trying to support 512MB virtual address space. You task is to design a two-level page table scheme to manage virtual-to-physical page mappings. Your page size is 8KB and each page table/directory entry is 8B.

(1) How many bits do you need to address the 512MB address space (2 pt)?

(2) How many page table entries do you need in total (2 pt)?

(3) How many page table entries should each page table hold (2 pt)?

(4) How many page tables do you need (2 pt)?

(5) How many bits of an address do you need for the page directory index (2 pt)?

(6) How many bits of an address do you need for the page table index (2 pt)?

(7) How many bits of an address do you need to address the offset within a page (2 pt)?

(8) Assume that a process uses exactly three virtual pages and all three pages are indexed by different page tables under your two-level page table design. How many physical pages will be utilized by your two-level page table scheme for this process (2 pt)?

(9) If you used a single-level page table instead of two-level page tables for the process in (8), then how many physical pages would be used by this single-level page table (2 pt)?