A computer has 64-bit virtual addresses, byte-addressed memory, 1 Kbyte page size, 16 M page frames in main memory, and has 8 bits of metadata about each page.

a) How many physical address bits are there in the address bus to main memory for this computer?

b) A program for this computer uses a total of 8 consecutive pages of virtual memory to hold all of its instructions and data. How many bytes of main memory will be consumed for the page table of this program if the page table is single level?

c) Same question as part (b) but now the page table is a two-level design, so give an upper bound. The second level table holds the page metadata, not the first-level table. However, all page table entries are aligned in memory as 32-bit integers.

d) Same question as part (b) but for a three-level table.