x86 Paging Tutorial Multi-level paging scheme numerical translation example by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Page 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. - 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
. Paging is done by the Memory Management Unit (MMU) part of the CPU.
It was later integrated into the CPU, but the term MMU still used.
It basically replaces a bunch of discrete digital components with a single chip. So you don't have to wire things manually.
Particularly fundamental if you would be putting those chips up a thousand cell towers for signal processing, and ever felt the need to reprogram them! Resoldering would be fun, would it? So you just do a over the wire update of everything.
Vs a microcontroller: same reason why you would want to use discrete components: speed. Especially when you want to do a bunch of things in parallel fast.
One limitation is that it only handles digital electronics: electronics.stackexchange.com/questions/25525/are-there-any-analog-fpgas There are some analog analogs, but they are much more restricted due to signal loss, which is exactly what digital electronics is very good at mitigating.
The History of the FPGA by Asianometry (2022)
Source. 
Google BigQuery alternative.
Mentioned at: aws.amazon.com/ec2/instance-types/g4/
TODO meaning of "nd"? "n" presumably means Nvidia, but what is the "d"? Compare it g4ad.xlarge which has AMD GPUs. aws.amazon.com/ec2/instance-types/g4/ mentions:
This feels good.
One problem though is that Heroku is very opinionated, a likely like other PaaSes. So if you are trying something that is slightly off the mos common use case, you might be fucked.
Another problem with Heroku is that it is extremely difficult to debug a build that is broken on Heroku but not locally. We needed a way to be able to drop into a shell in the middle of build in case of failure. Otherwise it is impossible.
Deployment:
git push heroku HEAD:masterView stdout logs:
heroku logs --tailPostgreSQL database, it seems to be delegated to AWS. How to browse database: stackoverflow.com/questions/20410873/how-can-i-browse-my-heroku-database
heroku pg:psqlDrop and recreate database:All tables are destroyed.
heroku pg:reset --confirm <app-name>Restart app:
heroku restart 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. 
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