x86 Paging Tutorial Multi-level paging scheme numerical translation example by 
Ciro Santilli 40 Updated 2026-10-19
Ciro Santilli 40 Updated 2026-10-19Page directory given to process by the OS:
entry index entry address page table address present
----------- ---------------- ------------------ --------
0 CR3 + 0 * 4 0x10000 1
1 CR3 + 1 * 4 0
2 CR3 + 2 * 4 0x80000 1
3 CR3 + 3 * 4 0
...
2^10-1 CR3 + 2^10-1 * 4 0Page tables given to process by the OS at
PT1 = 0x10000000 (0x10000 * 4K):entry index entry address page address present
----------- ---------------- ------------ -------
0 PT1 + 0 * 4 0x00001 1
1 PT1 + 1 * 4 0
2 PT1 + 2 * 4 0x0000D 1
... ...
2^10-1 PT1 + 2^10-1 * 4 0x00005 1Page tables given to process by the OS at where
PT2 = 0x80000000 (0x80000 * 4K):entry index entry address page address present
----------- --------------- ------------ ------------
0 PT2 + 0 * 4 0x0000A 1
1 PT2 + 1 * 4 0x0000C 1
2 PT2 + 2 * 4 0
...
2^10-1 PT2 + 0x3FF * 4 0x00003 1PT1 and PT2: initial position of page table 1 and page table 2 for process 1 on RAM.With that setup, the following translations would happen:
linear 10 10 12 split physical
-------- -------------- ----------
00000001 000 000 001 00001001
00001001 000 001 001 page fault
003FF001 000 3FF 001 00005001
00400000 001 000 000 page fault
00800001 002 000 001 0000A001
00801004 002 001 004 0000C004
00802004 002 002 004 page fault
00B00001 003 000 000 page faultLet's translate the linear address
0x00801004 step by step:- In binary the linear address is:
0 0 8 0 1 0 0 4 0000 0000 1000 0000 0001 0000 0000 0100 - Grouping as
10 | 10 | 12gives:which gives:0000000010 0000000001 000000000100 0x2 0x1 0x4So the hardware looks for entry 2 of the page directory.page directory entry = 0x2 page table entry = 0x1 offset = 0x4 - The page directory table says that the page table is located at
0x80000 * 4K = 0x80000000. This is the first RAM access of the process.Since the page table entry is0x1, the hardware looks at entry 1 of the page table at0x80000000, which tells it that the physical page is located at address0x0000C * 4K = 0x0000C000. This is the second RAM access of the process. - Finally, the paging hardware adds the offset, and the final address is
0x0000C004.
The Intel manual gives a picture of this translation process in the image "Linear-Address Translation to a 4-KByte Page using 32-Bit Paging": Figure 1. "x86 page translation process"
x86 page translation process
. 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.
Their crash system does not have an amazing user interface.
Tested on Ubuntu 21.10.
After something crashes, look under
/var/crash for a crash file, which helps to determine which package to report under on Launchpad.E.g. a file
/var/crash/_usr_sbin_gdm3.0.crash makes you want to file the bug under gdm at: bugs.launchpad.net/ubuntu/+source/gdm/+filebugThen, while reporting the bug, you want to give the developpers access to that Ubuntu's crash report system has already uploaded the
.crash file. But you can't publicly upload it because it contains memory dumps and could contain secret information. The way to do it is to look at the ID under:sudo cat /var/crash/_usr_sbin_gdm3.0.uploaded.crash for you, so you just have to confirm it and give the ID on the ticket.You can view a list of all your uploaded errors at:and each of those contain a link to:which you yourself cannot see.
xdg-open https://errors.ubuntu.com/user/$(sudo cat /var/lib/whoopsie/whoopsie-id)https://errors.ubuntu.com/oops/<.uloaded error id>askubuntu.com/questions/434431/how-can-i-read-a-crash-file-from-var-crash asks how to read the
.crash files.Running:splits it up into a few files, but does not make any major improvements.
sudo apport-unpack /var/crash/_usr_sbin_gdm3.0.crash /tmp/appapport-retracesudo apt install apport-retrace
sudo chmod 666 /var/crash/_usr_sbin_gdm3.0.crash
apport-retrace -g /var/crash/_usr_sbin_gdm3.0.crashTried:but then
echo "deb http://ddebs.ubuntu.com $(lsb_release -cs) main restricted universe multiverse" | sudo tee -a /etc/apt/sources.list.d/ddebs.list
echo -e "deb http://ddebs.ubuntu.com $(lsb_release -cs)-updates main restricted universe multiverse\ndeb http://ddebs.ubuntu.com $(lsb_release -cs)-proposed main restricted universe multiverse" | sudo tee -a /etc/apt/sources.list.d/ddebs.list
sudo apt install ubuntu-dbgsym-keyringsudo apt update fails with:E: The repository 'http://ddebs.ubuntu.com impish-security Release' does not have a Release file.
Some notable ones:
This is particularly important in SQL: Nested set model in SQL, as it is an efficient way to transverse trees there, since querying parents every time would require multiple disk accesses.
The ASCII art visualizations from stackoverflow.com/questions/192220/what-is-the-most-efficient-elegant-way-to-parse-a-flat-table-into-a-tree/194031#194031 are worth reproducing.
As the sets:
__________________________________________________________________________
| Root 1 |
| ________________________________ ________________________________ |
| | Child 1.1 | | Child 1.2 | |
| | ___________ ___________ | | ___________ ___________ | |
| | | C 1.1.1 | | C 1.1.2 | | | | C 1.2.1 | | C 1.2.2 | | |
1 2 3___________4 5___________6 7 8 9___________10 11__________12 13 14
| |________________________________| |________________________________| |
|__________________________________________________________________________|Consider the following nested set:
0, 8, root
1, 7, mathematics
2, 3, geometry
3, 6, calculus
4, 5, derivative
5, 6, integral
6, 7, algebra
7, 8, physics There are unlisted articles, also show them or only show them.