x86 Paging Tutorial Single level paging scheme numerical translation example by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Suppose 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 Multiple addresses translate to a single physical address by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16The same linear address can translate to different physical addresses for different processes, depending only on the value inside
cr3.Both linear addresses
00002 000 from process 1 and 00004 000 from process 2 point to the same physical address 00003 000. This is completely allowed by the hardware, and it is up to the operating system to handle such cases.This often in normal operation because of Copy-on-write (COW), which be explained elsewhere.
Such mappings are sometime called "aliases".
esolangs.org/wiki/Y86 mentions:
One specification at: web.cse.ohio-state.edu/~reeves.92/CSE2421sp13/PracticeProblemsY86.pdf
Our definition of fog computing: a system that uses the computational resources of individuals who volunteer their own devices, in which you give each of the volunteers part of a computational problem that you want to solve.
"De novo" means "starting from scratch", that is: you type the desired sequence into a computer, and the synthesize it.
The "de novo" part is important, because it distinguishes this from the already well solved problem of duplicating DNA from an existing DNA template, which is what all our cells do daily, and which can already be done very efficiently in vitro with polymerase chain reaction.
Notably, the dream of most of those companies is to have a machine that sits on a lab bench, which synthesises whatever you want.
The initial main applications are likely going to be:but the real pipe dream is building and bootstraping entire artificial chromosomes
- polymerase chain reaction primers (determine which region will be amplified
- creating a custom sequence to be inserted in a plasmid, i.e. artificial gene synthesis
News coverage:
Nuclera eDNA enzymatic de novo DNA synthesis explanatory animation (2021)
Source. The video shows nicely how Nuclera's enzymatic DNA synthesis works:- they provide blocked nucleotides of a single type
- add them with the enzyme. They use a werid DNA polymerase called terminal deoxynucleotidyl transferase that adds a base at a time to a single stranded DNA strand rather than copying from a template
- wash everything
- do deblocking reaction
- and then repeat until done
This is Ciro Santilli's favorite laptop brand. He's been on it since the early 2010's after he saw his then-girlfriend-later-wife using it.
Ciro doesn't know how to explain it, but ThinkPads just feel... right. The screen, the keyboard, the lid, the touchpad are all exactly what Ciro likes.
The only problem with ThinkPad is that it is owned by Lenovo which is a Chinese company, and that makes Ciro feel bad. But he likes it too much to quit... what to do?
Ciro is also reassured to see that in every enterprise he's been so far as of 2020, ThinkPads are very dominant. And the same when you see internal videos from other big tech enterprises, all those nerds are running... Ubuntu on ThinkPads! And the ISS.
Those nerds like their ThinkPads so much, that Ciro has seen some acquaintances with crazy old ThinkPad machines, missing keyboard buttons or the like. They just like their machines that much.
ThinkPads are are also designed for repairability, and it is easy to buy replacement parts, and there are OEM part replacement video tutorials: www.youtube.com/watch?v=vseFzFFz8lY No visible planned obsolescence here! With the caveat that the official online part stores can be shit as mentioned at Section "Lenovo".
Further more, in 2020 Lenovo is announced full certification for Ubuntu www.forbes.com/sites/jasonevangelho/2020/06/03/lenovos-massive-ubuntu-and-red-hat-announcement-levels-up-linux-in-2020/#28a8fd397ae0 which fantastic news!
The only thing Ciro never understood is the trackpoint: superuser.com/questions/225059/how-to-get-used-of-trackpoint-on-a-thinkpad Why would you use that with such an amazing touchpad? And vimium.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact