Floating Point Visually Explained (2017)

See also:

* https://float.exposed/ (companion blog post: https://ciechanow.ski/exposing-floating-point/)

* http://www.toves.org/books/float/

(Reproducing from another discussion a month ago: https://news.ycombinator.com/item?id=18832155)

I think this explanation still makes it harder than it needs to be. Just imagine what a "floating point" number would mean in decimal: you get (say) 5 adjacent digits to play with, and you get to choose where you put the decimal place, within a limited range.

So you can represent 12345000 or 12.345 or 0.00012345.

But 12345600 rounds to 12346000, 12.3456 rounds to 12.346, and 0.000123456 rounds to 0.00012346.

This is an awesome explanation, thanks for sharing! I remember struggling mightily in college to understand Floating Point, and my professor never offered anything other than the mathematical formula explanation. That never really helped me understand how the computer is actually dealing with these numbers, but this step-by-step explanation really clicked.

Intel's floating point coprocessor may have been out of reach for most people in the early 90's, but there were clones available. My 386 had a Cyrix I believe.

I don't understand how the pictures help. The core formula is compact, but that doesn't make it bad. A few sentences of explanation is great for people who haven't learned standard high-school-level math notation or who want a walkthrough as a refresher (so thanks tonthr author for writing it down ), but refusing to learn math notation is going to make learning every math concept harder, penny wise and pound foolish. I don't see how this blog post/book chapter's explanation is novel as it claims to be, or why every other explanation of floating point is supposedly poor. I suspect it's just a matter of learning concepts requires thinking, so thrilled author jotted notes while he was thinking, and misattributed his progress to the specific visuals and no to the process of thinking about the formula.

The hard part of floating point isn't the representation of numbers, it's how to perform arithmetic with rounding/truncation in the specified way (and why the specified way is preferred). The blog post doesn't touch on that at all.

Discussed at the time: https://news.ycombinator.com/item?id=15359574

Some might be mistaken this post is from fabrice bellard just like me, it it not. The web address might be a little bit confusing. This is not a post by fabrice bellard the guy who initiated ffmpeg project among many others.

My son and I have been trying to understand floating point numbers with almost no success, since it's usually explained with arcane mathematical symbols that neither of us understand. This page is brilliant and I'm going to show this to him, after editing the hilarious image with the owl. Why is profanity necessary to convey intensity? It's 2019, surely we have better ways of doing so by now.