Paging concept and page tables in Operating Systems - Step-by-Step Execution

Concept Flow - Paging concept and page tables

Process wants memory

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Divide memory into pages

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Divide physical memory into frames

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Page table maps pages to frames

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CPU uses page table to find frame

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Access physical memory frame

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Return data to process

The process memory is split into pages, physical memory into frames, and a page table maps pages to frames so the CPU can find data.

Execution Sample

Operating Systems

Virtual Address: 0x1234
Page Size: 1KB (1024 bytes)
Page Number = Virtual Address / Page Size
Offset = Virtual Address % Page Size
Use Page Number to find Frame in Page Table
Physical Address = Frame * Page Size + Offset

This shows how a virtual address is translated to a physical address using page number, offset, and the page table.

Analysis Table

Step	Virtual Address	Page Number	Offset	Frame Number (from Page Table)	Physical Address Calculation	Physical Address
1	0x1234 (4660 decimal)	4 (4660/1024=4)	4660 % 1024 = 564	7	7 * 1024 + 564	7168 + 564 = 7732 (0x1E34)
2	0x0A00 (2560 decimal)	2 (2560/1024=2)	2560 % 1024 = 512	3	3 * 1024 + 512	3072 + 512 = 3584 (0x0E00)
3	0x1FFF (8191 decimal)	7 (8191/1024=7)	8191 % 1024 = 1023	1	1 * 1024 + 1023	1024 + 1023 = 2047 (0x07FF)
4	0x2000 (8192 decimal)	8 (8192/1024=8)	8192 % 1024 = 0	5	5 * 1024 + 0	5120 + 0 = 5120 (0x1400)
5	0x3000 (12288 decimal)	12 (12288/1024=12)	12288 % 1024 = 0	Page not mapped	No frame found	Page fault - no physical address
6	N/A	N/A	N/A	N/A	N/A	Stop - address not mapped

💡 Execution stops when a virtual page is not mapped in the page table, causing a page fault.

State Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
Virtual Address	N/A	0x1234	0x0A00	0x1FFF	0x2000	0x3000	N/A
Page Number	N/A	4	2	7	8	12	N/A
Offset	N/A	564	512	1023	0	0	N/A
Frame Number	N/A	7	3	1	5	N/A	N/A
Physical Address	N/A	7732	3584	2047	5120	Page fault	N/A

Key Insights - 3 Insights

Why does the physical address sometimes not exist?

When the page number is not found in the page table (see step 5 in execution_table), it means the page is not loaded in physical memory, causing a page fault.

How is the offset calculated and why is it important?

Offset is the remainder after dividing the virtual address by page size (see execution_table column 'Offset'). It tells the exact byte inside the frame to access.

Why do we divide the virtual address by page size to get the page number?

Because memory is split into fixed-size pages, dividing gives which page the address belongs to (see execution_table column 'Page Number').

Visual Quiz - 3 Questions

Look at the execution_table at step 3. What is the physical address calculated?

A 7636 (0x1DBC)

B 2047 (0x07FF)

C 3584 (0x0E00)

D 5120 (0x1400)

💡 Hint

Check the 'Physical Address' column in execution_table row for step 3.

At which step does the page fault occur because the page is not mapped?

A Step 2

B Step 4

C Step 5

D Step 1

💡 Hint

Look for 'Page not mapped' or 'Page fault' in the execution_table rows.

If the page size was doubled, how would the page number for virtual address 0x1234 change?

A It would be half as large

B It would stay the same

C It would double

D It would become zero

💡 Hint

Page number = Virtual Address / Page Size; increasing page size decreases page number.

Concept Snapshot

Paging splits virtual memory into fixed-size pages.
Physical memory is split into frames of the same size.
Page table maps each virtual page to a physical frame.
Virtual address = page number + offset.
CPU uses page table to find frame for a page.
If page not mapped, page fault occurs.

Full Transcript

Paging is a memory management method where virtual memory is divided into pages and physical memory into frames. Each virtual page is mapped to a physical frame using a page table. To find the physical address from a virtual address, the CPU divides the virtual address by the page size to get the page number and offset. It then looks up the frame number for that page in the page table. The physical address is calculated by multiplying the frame number by the page size and adding the offset. If the page is not mapped in the page table, a page fault occurs, stopping the process until the page is loaded. This method helps efficiently use memory and isolate processes.