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.
There's more to floating point! In this video, we missed out on Denormal numbers, which is a special case for small numbers. For more, watch the video here → • Denormal Numbers - Mor...
Try it out and see how it works → resources.nerdfirst.net/float
= 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 =
0612 TV, a sub-project of NERDfirst.net, is an educational KZbin channel. Started in 2008, we have now covered a wide range of topics, from areas such as Programming, Algorithms and Computing Theories, Computer Graphics, Photography, and Specialized Guides for using software such as FFMPEG, Deshaker, GIMP and more!
Enjoy your stay, and don't hesitate to drop me a comment or a personal message to my inbox =) If you like my work, don't forget to subscribe!
Like what you see? Buy me a coffee → www.nerdfirst.net/donate/
0612 TV Official Writeup: nerdfirst.net/0612tv
More about me: about.me/lcc0612
Official Twitter: / 0612tv
= NERDfirst =
NERDfirst is a project allowing me to go above and beyond KZbin videos into areas like app and game development. It will also contain the official 0612 TV blog and other resources.
Watch this space, and keep your eyes peeled on this channel for more updates! nerdfirst.net/
-----
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* 1. There is an edge case called "Denormal Numbers" that has not been accounted for in this video. Thanks to @PRANAnomaly for sharing! I have made a new video to discuss this concept: kzbin.info/www/bejne/mGOpmHloqLqiiZo Another set of special cases, namely Infinity and NaN, are also not covered in this video. For more details, please watch this other video I made: kzbin.info/www/bejne/emivg52Amrd-gNk 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! 3. ERRATA: At 15:47, note that the bits from the decimal portion were read off incorrectly. Thank you to spinakker for sharing! This is the version corrected by them: i.imgur.com/ufOeklR.png

[@intoeleven]

Somehow this comment is not pinnted to the top...You can add it to your subtitles.

[@NERDfirst]

Hello and thank you for your comment! Thanks for the heads up! I found that the pinned comment on quite a few of my videos had gotten unpinned somehow. I put them back whenever I come across them.

[@intoeleven]

@@NERDfirst Thanks for the reply. Your videos help me a lot!

[@hilaryyang3821]

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!

[@NERDfirst]

Hello and thank you very much for your comment! Glad to be of help =)

[@ladell5101]

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

[@NERDfirst]

Hello and thank you for your comment! All the best for your test =)

[@okboing]

How did u do

[@ladell5101]

@@okboing Super late, but I passed with a B+.

[@markus6056]

@@ladell5101YES!

[@ivanilanic9712]

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

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@msgabbana14]

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

[@NERDfirst]

Hello and thank you for your comment! Very happy to be of help =) Glad you got over that hurdle!

[@madhureshminoshi4272]

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

[@NERDfirst]

Hello and thank you very much for your comment! Glad you found the video useful =)

[@nouhamataoui8836]

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

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@vitzal3691]

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?

[@NERDfirst]

Hello and thank you very much for your comment and support! If you're looking for the smallest possible number (ie. a negative number) all the way up to the largest positive number, then yes - Just make the largest possible exponent and mantissa with both positive and negative signs and you'll get both. If you want to find the smallest positive number though, that's a bit harder. For that you'll need to look into Denormal numbers, which I did not cover in this video. A denormal number allows you to get an even smaller exponent than the exponent actually allows, by using zeroes in the mantissa. For more: kzbin.info/www/bejne/mGOpmHloqLqiiZo

[@lechi_2002]

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

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@daylyght3654]

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

[@NERDfirst]

Hello and thank you very much for your comment! Yeah, this particular video was months in the making, heh. Honestly, quite relieved it's up. Glad you liked it =)

[@bhagyaanuragith8414]

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

[@NERDfirst]

Hello and thank you for your comment! Glad to be of help =)

[@ThierryPBeaulieu]

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

[@NERDfirst]

Hello and thank you very much for your comment! Very happy to be of help =)

[@mullademir4589]

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!

[@NERDfirst]

Hello and thank you very much for your comment! Very happy to be of help :)

[@Hersonrock12]

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!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@brennan5618]

Absolutely excellent video. The website you created is a fantastic learning companion to the concept as well. Thank you!

[@NERDfirst]

You're welcome! Very happy to be of help :)

[@zekfad]

Thank's so much for a such quick video with a such huge impact on knowledge!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@albertomadalin2209]

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.

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@kdbin101-1]

Such a clean and intuitive explanation, thank you!! 🙏

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@CODPRICEGHOST]

Great explanation, best video I found so far for floating point

[@NERDfirst]

Hello and thank you very much for your comment! Glad you liked the video =)

[@mx6you]

Great Explanation. Thanks so much!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@janiceay5051]

Amazing tutorial. Easy to understand than others on youtube.

[@NERDfirst]

Hello and thank you for your comment! Very happy to be of help =)

[@tylercollins8075]

Very clearly explained! Thank you for this video

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@jiahganara7173]

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

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@redmoon8965]

i see a lot of simplicity in this video , Best WAY to explain stuff , thank you so much buddy !

[@NERDfirst]

You're welcome! Very happy to have been of help =)

[@51anirudh]

Loved your way of explanation. Crisp and Clean :) Thank you :)

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@dzungdoan6774]

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

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@riccardosola8326]

This was perfectly clear man! Thank you, really!

[@NERDfirst]

Hello and thank you very much for your comment! Very happy to be of help =)

[@arrogantermistkerl4579]

Great stuff. I really dont miss going to university with videos like this

[@NERDfirst]

Hello and thank you very much for your comment! Glad you liked the video =)

[@vaz5926]

Thank you, man! Super helpful!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@YRBYD]

One of the few videos on KZbin regarding floats where IEEE-754 is respected. Good job!

[@NERDfirst]

Hello and thank you very much for your comment! Do note that I do make some mistakes, please refer to the pinned comment for more =)

[@cokelight12]

Hats of to you sir, everything is crystal clear now :)

[@NERDfirst]

Hello and thank you very much for your comment! Happy to be of help =)

[@deinemudda2325]

what a legend. I really enjoyed the video. Thank you :)

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@junkmail4613]

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)

[@NERDfirst]

Hello and thank you very much for your comment! Very happy to be of help =)

[@hafsaahadbutt4529]

tysmmm u saved me....ur hardwork is much appreciated.

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@rastkostajic5525]

Thank you, great explanation!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@doug9000]

i try to watch other videos but only on this one i got it, great explanation, thanks!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@ugandaknuckle6649]

You are a life saver! Subbed!

[@NERDfirst]

Hello and thank you for your comment! Happy to be of help =)

[@pratyaymandal5031]

After 2 -3 videos I found this video and it cleared all my doubts and I just want to tell you that I am in love with your explanation .Loveeeeeeee Youuuuuu bro

[@NERDfirst]

Hello and thank you very much for your comment! Very happy to be of help =)

[@apall2764]

Gee I delved the whole Internet for a simple clear explanation like this Many thanks Bro!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@aeebeecee3737]

Very thanks to you for your clear information

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@Kevin-tx6gw]

king i learnt more from you in 19 minutes than in my university lecture

[@NERDfirst]

Hello and thank you for your comment! Glad to be of help =)

[@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!

[@NERDfirst]

You're welcome! Very happy to be of help =) For a more complete understanding, you might want to watch the follow up videos about Denormal numbers, and do take note of the errata in the comments as well.

[@maherhanna2432]

Thank you very clear explanation

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@rekxspein]

Damn, so clearly explained, man when I read in books I didn't understand at all 🤣🤣🤣

[@NERDfirst]

Hello and thank you for your comment! Glad to be of help =)

[@aeebeecee3737]

Your channel deserve more subscribers

[@lucasrodriguesdelima8697]

This video is amazing !!!! Thank you so much .. :)

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@TheTariqibnziyad]

Love your video man !!!

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@Gnomfresser1]

awesome description mate

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@georgebenjamin6632]

This is excellent!

[@NERDfirst]

Hello and thank you very much for your comment! Glad you liked the video =)

[@hongkyulee9724]

Wow ... I feel like fall in love with floating point numbers... Your video is awsome Thank you :D

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@jackchan2557]

great explanation!

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@heeseok7792]

Man.... u r the first one to make me have clear picture on this 👍👍

[@NERDfirst]

Hello and thank you very much for your comment! Glad to be of help =)

[@cyrilemeka6987]

Amazing explanation ❤

[@NERDfirst]

Hello and thank you very much for your comment! Glad you liked the video =)

thank you very much, great explanation! :-) Cheers from Czech republic.

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@RossMcgowanMaths]

14.25 -' if it was a zero we could stop it at a different place and express with a different exponent' ? What different place and what different exponent. I have used this video to code the floating point in VBA.It works with everything other than say 0.5. Very good video !

[@NERDfirst]

Hello and thank you for your comment! What I mean is, if you don't have the rule that the mantissa starts with 1, then all of the below are valid representations of 0.25: 0.25 × 2^1 0.5 × 2^-1 1 × 2^-2 2 × 2^-3 So to make the numbers consistent, the rules say the mantissa has an implied "1." in front.

[@hardiksen9722]

loved it. really helped me. It was the only thing I did not know for my exam. It is in 2 hours.

[@NERDfirst]

Hello and thank you for your comment! All the best for your exam!

[@Tubeytime]

My gratitude... is endless.

[@NERDfirst]

You're welcome! Glad to be of help =)

[@NS-te8jx]

very good explanation.

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@ryanzkp]

Thank you sooooooooo much! I finally got it!

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@totem1997]

Thanks…..I will revisit this video couple of times in order to fully understand floating point.😊

[@NERDfirst]

Hello and thank you for your comment! Feel free to do so, and to clarify any doubts in the comments if you need :)

[@pareeksharao6524]

thats amazing video finally after 4 days i got some easy and interesting video to learn floating point representation thakuu sir

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@aswinramachandran7103]

dude you are amazing keep making videos like this it is so damn helpful

[@NERDfirst]

Hello and thank you very much for your comment! Very happy to be of help =)

[@yousefelsayed4203]

Thank you very much this helped me a lot ❤

[@NERDfirst]

You're welcome! Glad to be of help =)

[@keskim]

Great video!

[@NERDfirst]

Hello and thank you for your comment! Very happy to be of help =)

[@user-ff1km4wp5d]

very helpful thanks

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@_AmHam_]

Thank you sooo much !!!

[@NERDfirst]

You're welcome! Happy to be of help =)

[@muhammadtaimourafzal5285]

Great explanation

[@NERDfirst]

Hello and thank you for your comment! Glad to be of help =)

[@qwerty_____146]

Thank you dear Bro. Thant's great. Nice. good job. 🙏

[@NERDfirst]

You're welcome! Glad to be of help =)

[@PCHerc]

Excellent!

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@xer_t3661]

amazing explanation

[@NERDfirst]

Hello and thank you very much for your comment! Glad you liked the video :)

[@ltahoe9257]

Omg do you have any idea how many videos I have watched, reread my CPE textbook to try to figure out why we add 1 to the mantissa. My textbook literally says, there's a one but it can be omitted and that bothered me so much that I didn't know. But now it makes sense, technically there is a 2 to the power of zero which is where the 1 comes from. Thank you!!!!!!!

[@NERDfirst]

Hello and thank you very much for your comment! Glad to be of help =)

[@konstantinrebrov675]

Great stuff! This video was in fact published just before we were going to cover it in class. Coincidence?

[@NERDfirst]

Hello and thank you for your comment! Heh, as much as I'd like to say I carefully calculated the timing to coincide with the uni semester, I'm afraid it's complete coincidence =P

[@hafsaahadbutt4529]

this was freakingggg helpful...

[@louiseghemmam8056]

thank youuu !!

[@NERDfirst]

You're welcome! Glad to be of help =)

[@CodingJesus]

Amazing video.

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@alexmay7250]

this video was amazing, you would be a great professor

[@NERDfirst]

Hello and thank you very much for your comment! I do teach in physical classes, so it's good to hear the vote of confidence =)

[@alexmay7250]

@@NERDfirst came back to review for my finial exam, your students are very lucky

[@feezasikandar2863]

Hi ! Thank you so much for explaining it so well and in a much simplified way. I just want to ask that in the number to binary conversion for the decimal bit I.e 0.125 didn’t u reversed the direction I.e went from top to bottom instead of going bottom to top. And then in the slide where u summed up all the discussion it is again bottom to top. If you could please explain it to me or was it just a mistake ?

[@NERDfirst]

Hello and thank you for your comment! If you are referring to 15:47, then yes, there was a mistake there. Please see the following image for correction by KZbin user spinakker: i.imgur.com/ufOeklR.png There are other errata in the video. Please refer to pinned comment for more.

[@feezasikandar2863]

@@NERDfirst okay,thanks a lot :)

[@jojisamuel6765]

Thank you so much.

[@NERDfirst]

You're welcome! Glad to be of help =)

[@anniesue1]

Nice explanation/narration. Nice animations and graphical illustrations. Clear and concise while being thorough enough. The light reflections in your glasses are somewhat distracting tho...

[@NERDfirst]

Hello and thank you very much for your comment! The reflections are hard to avoid when you want to light someone face-on, unfortunately! I've been experimenting with other placements to see the effect.

[@saikrishnapechetti8382]

Hello, have you created any playlist regarding these kinda topics ,cause i can't find one in your playlists

[@NERDfirst]

Hello and thank you for your comment! It depends on what you mean by "these kinda topics" - Floating point numbers is at the intersection of a few broad categories, and you could be referring to any of them. Alternatively you may also want to sort my channel by most popular. Barring a few product reviews which might be less interesting to you, I think you'll find most of the others to at least be relevant.

[@MaulCenter]

Hello and thank you for your video, bro...

[@NERDfirst]

You're welcome! Glad you liked the video =)

[@animeabsolute7130]

thank you! this video really helpfully for newbie as me T^T

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@aryafala949]

thank you so much

[@NERDfirst]

You're welcome! Happy to be of help :)

[@fortamx]

Hey man, great video! Could you explain why the exponent is represented with an offset and not another representation such as 2-complement? Thanks for the video!

[@NERDfirst]

Hello and thank you for your comment! The short answer would be "That is how it's designed", but naturally I was curious also as to why it was designed this way. Some people suggest that this helps with comparing two numbers - With the offset representation you could simply compare the bit strings of two floating point numbers as if they were integers and the answer would be correct. I wasn't able to find an official source to say that this is the reason why it was designed like that but it does seem to make a lot of sense. Some sources where this is discussed: employees.oneonta.edu/zhangs/csci201/IEEE%20Floating%20Point%20Format.htm stackoverflow.com/questions/2835278/what-is-a-bias-value-of-floating-point-numbers

[@olivier306]

Legendary guy!!!!

[@NERDfirst]

Hello and thank you very much for your comment! Glad you liked the video =)

[@Abon963]

Thanks!

[@NERDfirst]

You're welcome! Glad to be of help :)

[@eliosgreek8028]

great video.

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video =)

[@harinduchira2268]

THANKS MAN..

[@NERDfirst]

You're welcome! Glad to be of help =)

[@kpriemko]

Thx, bro, you get the job done. There is no misunderstanding here now.

[@NERDfirst]

You're welcome! Very happy to be of help =)

[@PopcornBunni]

My question is how large is the range of values able to be represented with this system, and what solutions/alternatives are used to represent larger or smaller numbers outside the range. Obviously floating point rounding will make some stuff imprecise, but I mean what is the largest and smallest absolute value for this?

[@NERDfirst]

Hello and thank you for your comment! To derive the largest and possible floating point values, the technique is to go for the largest possible exponent and mantissa. Then, flip the sign - The positive version is the largest possible value and the negative version is the smallest. Usually we also want to consider the smallest magnitude number (ie. The smallest positive number). For that, you'll need to go for the smallest denormal number (in which all exponent bits are zero), and only the least significant bit of the mantissa is 1. These have been worked out for 32-bit floats here but you technically do this for any bit length: stackoverflow.com/questions/32193791/single-precision-floating-point-format-range The simple solution to getting a larger range is to either use more bits, or to simply not use floats at all. Using strings or BigDecimal strategies are possible alternatives.

[@thisrandomdude_]

Fantastic video! Very interesting stuff. One question though, why subtract 127 in the exponent section? What led to that being the number to offset by? I'm guessing it's somehow related to 2^7 (128) but why is it 1 less than 128 and not just the entire thing?

[@NERDfirst]

Hello and thank you for your comment! This is a very interesting point. Of course, we know it's got to be between 127 and 128, since that's halfway in between the given 8-bit space, and we ideally want to have an equal number of positive and negative numbers. But as to why 127 has been chosen, I haven't been able to find an official reasoning for it. The best explanation I've found so far is that this makes it easy to compare two floating point numbers with each other using integer representations, and still be able to tell which is larger or smaller. But I'm not sure if there's any proof to say this is really the reason why IEEE chose excess-127 representation for the exponent. Some sources where this is discussed: employees.oneonta.edu/zhangs/csci201/IEEE%20Floating%20Point%20Format.htm stackoverflow.com/questions/2835278/what-is-a-bias-value-of-floating-point-numbers

[@thisrandomdude_]

@@NERDfirst Thank you so much for the reply, even several years after the making of this video! Your comment helped me understand a bit more about the way floating point numbers work, but I'm still not at the point where I know what integer representations are and all that. Much less whatever was being discussed on that stack overflow thread hahaha. Looking forward to be able to understand all that one day though! Your sheer knowledge and readiness to share it really shows your passion for the subject :) I'm really glad we have people like you to help us noobs out, you're really doing a service to the world!

[@NERDfirst]

No problem! All I want to do is to make learning more accessible, so I'm really glad I could be of help! "Integer representations" just refer to reading off the string of bits as a whole number, instead of breaking up the bits into sign, exponent and mantissa parts. So even if we just treated it (wrongly!) as a whole number, comparison operations would still make sense and give correct answers. If you're interested to find out more about bits I have another video here that you might like to look over: kzbin.info/www/bejne/aoLPpGash6aSfJY Again, thank you very much for your nice comment. Makes it all worth it =)

[@thisrandomdude_]

@@NERDfirst I can't believe how helpful that was! I can literally feel my brain expanding by the minute hahahaha. No matter how many times I thank you, it probably won't be enough, so here's a few cookies instead: 🍪🍪🍪🍪🍪🍪🍪🍪🍪🍪 enjoy! While you enjoy munching on them, I'm gonna go do myself a favour and check out your other stuff ;P see you!

[@NERDfirst]

Thank you very much! Yes, please do feel free to check out the other videos and if you have any other thoughts or questions, don't hesitate to comment on those too =)

[@rafaelmejia2000]

You're a legend

[@NERDfirst]

Cheers! Glad to be of help =)

[@farrukhabdukodirov4088]

awesome!!!!!

[@NERDfirst]

Hello and thank you for your comment! Happy to be of help =)

[@LinhNguyen-nh8oq]

Oh now I understand why we have to subtract 127: cause the exponent is 8 bit, so the max of it is 0-255. Inorder to represent smaller number(by multiply it with 2^-5 for ex), we have to represent the exponent in negative number => Split 255 in half = 127. And a second problem is why 2^ but not 10^ because by using base 2, we can convert bit to float and float to bit 😁

[@NERDfirst]

Hello and thank you for your comment! I would say simply that we use Base 2 because computers represent information in binary. Even when it's in bits (base 2), it already _is_ a floating point number,

[@batteryman2852]

well, finally i could work out my self after a very long time. because i couldn't understand way i always got incorrect result on my end., but i rather got the Big-endian correct, and when i tryed to swap the bytes i got a huge number. Turns out after a few hour, the HeX editor was telling in E notation... so my answer was correct for a long time, because i didn't see the "e"

[@NERDfirst]

Hello and thank you for your comment! What's important is that you figured it out =)

[@batteryman2852]

@@NERDfirst Yes indeed, i wrote a function 2 days ago that turned 8 bytes to float64 manually.., which then turned into a wall of text in code ...oh dear..., but anyway, the only weird thing, 4 decimal back, it rounded up. i guess that's a floating point quirk on my cpu or compiler

[@kellyprice882]

I LOVE YOU MAHN 😭😭

[@georgepalafox5967]

Hi. Great explanation. Quick question. In (11:57) u state one subtract from 0.5 is 0. Not clear. Can u explain again pls?

[@NERDfirst]

Hello and thank you for your comment! For each "layer", the answer comes from the previous number multiplied by two. For the final "layer", 0.5 × 2 gives 1. Since it is greater than or equal to one, we subtract one. This leave us with zero.

[@jritzeku]

Just curious...does your floating point representation fit the IEEE 754 floating-point standard?

[@NERDfirst]

Hello and thank you for your comment! This video covers a very small subset of the IEEE 754 standard. The standard also includes things like rounding rules, infinity, NaN (not a number) etc, which I have all left out. And of course, this is just the 32-bit format. According to wikipedia the standard specifies 8 formats with different bit lengths. So yeah, I think this is a good starting point, but not a substitute for actual material if you want to know the standard well!

[@dulmin_]

2:20 I'm confused here. I fairly remember that we were taught; 2^(1/2) = "Square root of 2" (which is not 0.5) But if 2^(-1) means "1 upon 2^1", then it's 1/2 = 0.5 as you are saying. I assume it's a screen error. Am I right? Or maybe I'm not understanding your tutorial property. Is that so ? 🤔

[@NERDfirst]

Hello and thank you for your comment! Sorry for the confusion, yes that is a typo on my part.

[@dulmin_]

@@NERDfirst Hi dear sir, I learnt a lot from your video!! Things I never understood before, are now very clear. I'm an audio producer, and I was curious to know why higher wav bit-depth(s) have the prefix "floating point". Thank you so much for this explanation, all your time spent on preparing these, and for your very quick reply to the initial comment above. (I asked it just bec I have weak confidence in maths, and I wasn't sure whether that's actually a typo, or perhaps something which I don't understand.)

[@JOURNEY-NEVER-ENDS]

nice video very good

[@NERDfirst]

Hello and thank you for your comment! Glad you liked the video :)