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Problem 1: A Two-Level Table
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Assume we are putting together a 2-level page table (as discussed in class).

Given: 
- a 128 KB virtual address space
- 1 MB of physical memory (max)
- page size of 128 bytes

How much space do you need in a page-table entry? (PTE)

How much space do you need in a page-directory entry?

Describe what a 2-level page table would look like. 
- How many bits of a virtual address are needed to index
  into a page of a page table?
- How many bits of a virtual address are needed to index
  into the page directory?

What happens to the size of the page directory as we add more bits
to the virtual address (i.e., increase the size of the address space) ?



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Problem 2: Beyond Two Levels
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Assume we have a 32-bit virtual address space with 1KB pages. Assuming a
4-byte PTE size, how many levels of page table would we need to ensure
that no page directory is ever longer than the size of a single page?