Floating Point Numbers

Floating point numbers are a huge part of any programmer's life - It's the way in which programming languages represent decimal numbers. We usually use them without second thought, but as it turns out, it's a fairly complex way to store a number! In this episode, we take a close look at how it works, as well as what concepts are relevant to it.

ERRATA: Please check the pinned comments for errors in this video and more information.

= CONTENTS =
0:00 Introduction
0:48 Recap on the basic bits of an integer
1:06 Fixed point numbers
1:39 Problems of Fixed point numbers
4:37 Fundamentals of Floating point numbers
6:12 Worked example of Bits → Float
→ 6:34 Sign
→ 6:44 Exponent
→ 7:55 Mantissa
→ 8:52 Putting everything together
9:49 Worked example of Float → Bits
→ 10:12 Creating a Fixed point representation
→ 13:29 Deriving the exponent & mantissa
→ 15:12 Putting everything together

= 0612 TV =

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= NERDfirst =
NERDfirst is a project allowing me to go above and beyond YouTube videos into areas like app and game development. It will also contain the official 0612 TV blog and other resources.

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Disclaimer: Please note that any information is provided on this channel in good faith, but I cannot guarantee 100% accuracy / correctness on all content. Contributors to this channel are not to be held responsible for any possible outcomes from your use of the information.

[NERDfirst]

*PLEASE READ THIS COMMENT IN ITS ENTIRETY FOR MORE INFO AND ERRORS IN THE VIDEO*



2. ERRATA: At 2:20, note that the number on the right should either be written as 1/2 or 2^-1, but not 2^(1/2)! Thanks 業夝王 for bringing this to my attention!

[hilaryyang]

This was so far the most helpful video on floating-point representation I've seen. I'm surprised it didn't get more views. Thanks man!

[ivanilanic]

Sir you have a natural talent to teach, thank you sooo much !!

[ladell]

Thanks, bro! This is appreciated. I literally have a test on this stuff in about 9 hours.

[lechi_]

It's much more clear for me how floating point representation works. Thanks!

[bhagyaanuragith]

you just saved my life. there is no other video explaining this stuff more clearly than you.

[msgabbana]

Thank you! I finally understand this after avoiding the subject for an entire semester..

[junkmail]

I'm 72. Real powerful presentation, and your "Floating Point Explorer" calculator gives a chance to verify my understanding. Thank you. 2021 10 04 (as 2 years after publishing)

[mullademir]

I was pretty lost when I started to study this topic, but thanks to you it's not a problem anymore. Keep up the good work!

[nouhamataoui]

I have been struggling with this chapter for days and you just explained it in 15 minutes ?? I wish I had found this video sooner. Thank you so so much, this was extremely helpful :D

[jiahganara]

this is way better than my module! finally get to understand :)

[ThierryPBeaulieu]

One of the best channels on YT for clarity of explanation! Hats down!

[vitzal]

You definitely earned this sub. This was an amazingly edited video and the information was thoroughly explained, much appreciated! If you want to find the range of this representation is it take all 1s for all the exponent bits for the largest possible exponent, take 1s for all the mantissa bits, add one to the mantissa and then complete the calculation from negative sign to positive sign?

[casual_gaming_]

thanks for putting in so much hard work in creating these videos . amazing explanation on floats .

[albertomadalin]

Thank you for making this video. You literally just helped me pass an exam i couldn't have studied on time for. You are the best. Keep up the good work.

[Hersonrock]

I appreciate so much having found this video, is not only greatly explained. But the page with the Floating point explorer is just beautiful. Thank you!

[daylyght]

I'm very sure it wasn't easy to put all of these great work together. I thank you for that.

[kaisolacegames]

THANK YOU. The way floating point numbers were explained in my textbook made absolutely no sense. This was easy to follow and actually helped me get my head around the concept. You're the best!

[dzungdoan]

There is no word that can describe how thankful to you . Thank you for the very helpful lesson.

[AudioBoi]

Very good video. Even though I didn't fully understand the process, it's still much easier to wrap my head around this concept overall.
Thank you 🙏🙏