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Suppose that you wish to design a virtual memory system with the following characteristics:

i. The size of a page table entry is 4 bytes.

ii. Each page table must fit into a single physical frame.

iii. The system must be able to support virtual address spaces as large as $2^{38}$ bytes (256 GB)

Suppose that you decide to use a multi-level paging scheme with no more than two levels of page tables. What is the minimum page size that your system must have?

  1. 8KB
  2. 16KB
  3. 32KB
  4. none
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$\text{Hope it’s clear}$

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VA = 38 bits

Let page size as $2^{x}$ Byte 

Page table fits in one page means size of PT = Size of page. Also Division of page number bits will be equal as we have to consider the general case. 

Important point here is that "to have minimum page size we must do 2  level paging" as it has asked to do upto 2 level paging. 

See the answer for further explanation. 

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