x86 Paging Tutorial Single level paging scheme numerical translation example by 
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01Suppose that the OS has setup the following page tables for process 1:and for process 2:
entry index entry address page address present
----------- ------------------ ------------ -------
0 CR3_1 + 0 * 4 0x00001 1
1 CR3_1 + 1 * 4 0x00000 1
2 CR3_1 + 2 * 4 0x00003 1
3 CR3_1 + 3 * 4 0
...
2^20-1 CR3_1 + 2^20-1 * 4 0x00005 1entry index entry address page address present
----------- ----------------- ------------ -------
0 CR3_2 + 0 * 4 0x0000A 1
1 CR3_2 + 1 * 4 0x12345 1
2 CR3_2 + 2 * 4 0
3 CR3_2 + 3 * 4 0x00003 1
...
2^20-1 CR3_2 + 2^20-1 * 4 0xFFFFF 1When process 1 tries to access a linear address, this is the physical addresses that will be actually accessed:
linear physical
--------- ---------
00000 001 00001 001
00000 002 00001 002
00000 003 00001 003
00000 FFF 00001 FFF
00001 000 00000 000
00001 001 00000 001
00001 FFF 00000 FFF
00002 000 00003 000
FFFFF 000 00005 000To switch to process 2, the OS simply sets
cr3 to CR3_2, and now the following translations would happen:linear physical
--------- ---------
00000 002 0000A 002
00000 003 0000A 003
00000 FFF 0000A FFF
00001 000 12345 000
00001 001 12345 001
00001 FFF 12345 FFF
00004 000 00003 000
FFFFF 000 FFFFF 000Step-by-step translation for process 1 of logical address
0x00000001 to physical address 0x00001001:- split the linear address into two parts:
| page (20 bits) | offset (12 bits) | - look into Page table 1 because
cr3points to it. - The hardware knows that this entry is located at RAM address
CR3 + 0x00000 * 4 = CR3:
*0x00000because the page part of the logical address is0x00000
*4because that is the fixed size in bytes of every page table entry - since it is present, the access is valid
- by the page table, the location of page number
0x00000is at0x00001 * 4K = 0x00001000. - to find the final physical address we just need to add the offset:
00001 000 + 00000 001 --------- 00001 001because00001is the physical address of the page looked up on the table and001is the offset.The offset is always simply added the physical address of the page. - the hardware then gets the memory at that physical location and puts it in a register.
Another example: for logical address
0x00001001:- the page part is
00001, and the offset part is001 - the hardware knows that its page table entry is located at RAM address:
CR3 + 1 * 4(1because of the page part), and that is where it will look for it - it finds the page address
0x00000there - so the final address is
0x00000 * 4k + 0x001 = 0x00000001
x86 Paging Tutorial The problem with single-level paging by Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01The problem with a single-level paging scheme is that it would take up too much RAM: 4G / 4K = 1M entries per process.
If each entry is 4 bytes long, that would make 4M per process, which is too much even for a desktop computer:
ps -A | wc -l says that I am running 244 processes right now, so that would take around 1GB of my RAM!The Quantum Story by Jim Baggott (2011) page 2 mentions how newton's support for the corpuscular theory of light led it to be held for a very long time, even when evidence of the wave theory of light was becoming overwhelming.
Kavli Institute for Theoretical Physics by Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01 How to teach Projects with global impact by Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01 Human mitochondrial molecular clock by Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-16 +Created 1970-01-01Databases and projects:
- www.ncbi.nlm.nih.gov/pmc/articles/PMC2716027/ The Knockout Mouse Project (2004)
Exciting... sometimes cruel. But too exciting not to do:
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