In this system, virtual addresses are 52 bits long, and physical addresses are 40 bits long.

(a) What is the smallest page size that will still allow a PTE to fit into a 4 byte word? HINT: remember that the PTE only needs to store the physical frame number, not a full address.

(b) How big (number of entries) would a single level page table for this system be? From this point onward, assume 8 KB pages.

(c) From Problem 2b, its clear that we need multi-level page tables. If each top-level entry covered 1 GB, how big would the top-level table be? How many entries would be in each second-level page table?

(d) Instead, we use a three-level page table where top-level entries each refer to 256 GB and a level 2 page table has 8192 entries. How much memory does a single entry in each of the three levels map, and how many entries are in a page table in each of the three levels? (Yes, the answers to some of these values are already provided as part of the question.)

(e) AssumeaprogramusingthepagingsysteminProblem2dhasthreevalidregions:0x10000x8fffffff, 0xf000000000x1000007fff, and 0xfff90000000000xfffffffffffff. How much space (in KB) is required for the page tables for this program? Assume that a page table in a given level may not be truncatedif you need part of a particular page table, you need space for all of it.