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Multilevel Paging in Operating System

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  • Difficulty Level : Easy
  • Last Updated : 03 Nov, 2022
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Prerequisite – Paging 

Multilevel Paging is a paging scheme that consists of two or more levels of page tables in a hierarchical manner. It is also known as hierarchical paging. The entries of the level 1 page table are pointers to a level 2 page table and entries of the level 2 page tables are pointers to a level 3 page table and so on. The entries of the last level page table store actual frame information. Level 1 contains a single-page table and the address of that table is stored in PTBR (Page Table Base Register).

Why it is required?

Consider a 32-bit physical address space with page size = 4KB and let there are 2^{20} = 1M  total entries in the page table, page table entry size =  \frac{2^{32}}{2^{12}} = 2^{20}  and adding some protection bits and dirty bit in the page table entry. Now page table size = 2^{20}*24 \approx 3MB  which should be in the physical memory and since each process has its own page table there are so much memory wastage only for storing page tables.

One solution to the large memory requirements of page table is to use multilevel paging, only the outer most page table will reside in the main memory and other page tables will be brought to main memory as per the requirement because at a particular time we do not need complete page table, also we can save much memory space because outermost page table can fit in exactly one frame.


In multilevel paging whatever may be levels of paging, all the page tables will be stored in the main memory. So it requires more than one memory access to get the physical address of the page frame. One access for each level is needed. Each page table entry except the last level page table entry contains the base address of the next level page table. 

Reference to actual page frame: 

  • Reference to PTE in level 1 page table = PTBR value + Level 1 offset present in virtual address.
  • Reference to PTE in level 2 page table = Base address (present in Level 1 PTE) + Level 2 offset (present in VA). 
  • Reference to PTE in level 3 page table= Base address (present in Level 2 PTE) + Level 3 offset (present in VA). 
  • Actual page frame address = PTE (present in level 3). 
     

Generally, the page table size will be equal to the size of the page. 

Assumptions: 
Byte addressable memory and n is the number of bits used to represent virtual address. 

Important formula: 
 

Number of entries in page table: 
= (virtual address space size) / (page size) 
= Number of pages

Virtual address space size: 
= 2n B 

Size of page table: 
<>= (number of entries in page table)*(size of PTE) 

If page table size > desired size then create 1 more level. 

Disadvantage: 
Extra memory references to access address translation tables can slow programs down by a factor of two or more. Use translation look aside buffer (TLB) to speed up address translation by storing page table entries. 

Example: 
Q.Consider a virtual memory system with physical memory of 8GB, a page size of 8KB, and 46-bit virtual address. Assume every page table exactly fits into a single page. If page table entry size is 4B then how many levels of page tables would be required. 

Explanation: 

Page size = 8KB = 213 B
Virtual address space size = 246 B
PTE = 4B = 22 B

Number of pages or number of entries in page table, 
= (virtual address space size) / (page size) 
= 246B/213 B 
= 233 

Size of page table, 

= (number of entries in page table)*(size of PTE) 
= 233*22 B 
= 235 B 

To create one more level,  

Size of page table > page size

Number of page tables in last level, 
= 235 B / 213 B 
= 222 

The base address of these tables is stored in page table [second last level]. 

Size of page table [second last level] 
= 222*22B 
= 224B 

To create one more level, 
Size of page table [second last level] > page size  

Number of page tables in second last level 
= 224B/213 B 
= 211 

The base address of these tables are stored in page table [third last level]  

Size of page table [third last level] 
= 211*22 B 
= 213 B 
= page size 

∴ 3 levels are required. 

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