A page table is a data structure used in virtual memory systems to map virtual addresses to physical addresses. Common techniques for structuring page tables include hierarchical paging, hashed page tables, and inverted page tables. Hierarchical paging breaks up the logical address space into multiple page tables, such as a two-level or three-level structure. Hashed page tables use hashing to map virtual page numbers to chained elements in a page table. Inverted page tables combine a page table and frame table into one structure with an entry for each virtual and physical page mapping.

1. STRUCTURE OF THE PAGE
TABLE
PRESENTATION
BY
D.Madhuri

2. PAGE TABLE :
• A PAGE TABLE is the data structure used by a virtual
memory system in a computer operating system to store
the mapping between virtual addresses and physical
addresses.

4. Common Techniques used for structuring the
page table are :
• Hierarchical paging
• Hashed page tables
• Inverted page tables

5. HIERARCHICAL PAGING:
• It is also known as multilevel paging.
• The page table might be too big to fit in a contiguous space , so
we may have a hierarchy with several levels.
• So , we break up the logical address space into multiple page
tables.
• For this a simple techniques we can use are:
Two level page table
Three level page table

6. TWO LEVEL PAGING:
• A logical address (on 32-bit machine with 4k page size) is divided
into:
A page number consisting of 20 bits.
A page offset consisting of 12 bits.
• Since the page table is paged , the page number is further divided
into:
A 10-bit page number.
A 10-bit page offset.
• Thus a logical address is as follows:
page number | page offset
pi p2 d

7. Address translation scheme for the two level
paging is as follows:

8. THREE LEVEL PAGING:
• A logical address(on 64-bit machine with 4k page size)
is divided into:
outer page inner page offset
42 10 12
2nd outer page outer page inner page offset
32 10 10 12
Pi P2 d
Pi P2 P3 d

9. HASHED PAGE TABLES:
• It is a common approach used when address space is
>32 bits.
• The virtual page number is hashed into a page table .
This page table contains a chain of elements hashing to
the same location.
• Each element consists of three fields:
1. The virtual page number
2. The value of the mapped page frame
3. A pointer to the next element in the linked list.

10. Address translation scheme for the hashed
page table is as follows:

11. INVERTED PAGE TABLES:
• The inverted page table combines A page table and A frame table
into one data structure.
• One entry for each virtual page number & real page of memory.
• Entry consists of the virtual address of the page stored in that real
memory location , with information about the process that owns
that page.
• Decreases memory needed to store each page table , but increases
time needed to search the table when a page reference occurs.

12. Address translation scheme for the Inverted
page table is as follows: