To skip this introduction, jump right to the Number Hall to start from square one. Just follow the Next buttons from there.
This site tells a story of computer arithmetic. There should be something of interest to anyone over the age of 5. Undergraduate students will find useful lore here rarely found in any college curriculum. Younger students might enjoy a computer's point of view on their everyday computation. Or they might get a sense of how the processors in game devices and graphics cards perform blazingly fast rendering and simulation.
Arithmazium tries to be engaging not encyclopedic. Even the most devoted experts should find something to enjoy.
You can always return to the home floor plan by clicking the blue Arithmazium banner.
In 2024, this site is very much under construction. So long as that is not a distraction, Arithmazium will remain open. What you see is what you get, and all the usual legal Latin applies: caveat emptor and tempis fugits, hopefully with a dash of compos mentis.
You need no more than enthusiasm to approach Arithmazium. The site presents many stories, not a tsunami of facts. Computer arithmetic is the subject. Elementary mathematics will get you a long way down the path.
When optional mathematical content arises to enrich the story, it is highlighted like this. But you need not pore over every fantastic formula like \[4/3 = 1 + 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 + \cdots\] to benefit from Arithmazium. Please feel free to skim or skip the math.
Of course, computer arithmetic is exploited through programming, but you won't need sophisticated programming knowledge to follow along. Literally, many of the code samples you'll see are variations on a simple theme:
new_value = old_value / TWO
If you're 5 and reading this, blaze on. You don't need my guidance. If you're with a young person or just wish to revel in the bits, head to the Number Hall to get started.
When you are ready to dig into floating point arithmetic and related topics, visit the Arithmetic Study. This is the heart of the matter.
If you are an expert interested in a dose of floating point lore, or if you're just feeling lucky, try the Paranoia Lab. You will find a semiliterate programming dissection of Prof. William Kahan's cult classic Paranoia code.
For something a bit off the beaten path, you can read a bit about continued fractions.
Arithmazium can't hope to tell the whole story. For that, you need the Library, where you will find a collection of supporting papers and technical manuals.
When all else fails, there's always the Mail Room. Read the FAQs. Leave a comment. Or learn a bit more about this site.
© 2024 Jerome Coonen