Floating Point Number Representation - Conversion Example

[@michaelmonh962]

Final in a couple of hours... thank you so freaking much!

[@zacharykentner6765]

Update on how the test went? lol

[@Yourmom-er4vg]

we need the update

[@Borzacchinni]

@@Yourmom-er4vg seems like it didnt go that well :(

[@TareqB_]

What happened to the test?? 🙂🙂

[@michaelmonh962]

Update: I graduated 😂😂😂

[@hrajatverma]

Thank you so much. I watched many videos but you cleared my all doubts. Thank you again.

[@ShivamMiglani]

Sign bit is not mantissa but the fraction is. :/

[@NJSxPSYOP]

Man I just wanna say thanks for this video. Really helped me out a lot!

[@nathanporter2001]

The sign bit is not called the mantissa. That refers to the fractional component of the floating-point number.

[@a7med3bbady]

clear, fast and simple. just perfect thank you

[@eusebiuebi]

You sir, are my saviour. Thank you so much for fast and exact explanation

[@terraint3697]

Thank you! Your videos are so handy! Quick and precise info!

[@sigururbaldursson8118]

Should say this is only for normalized. When you do denormalized you would not have the 1. at the left of the dot but 0.1 etc. like he is doing it the normalized way at minute 01:00

[@frezertesfaye9055]

pleas how to get a number 127?

[@AfroDanceWithZeAmazingBreezy]

what if the number after the radix wasnt repetitive.... should we fill the other bits with zeros till we get 23bits for the mantissa?

[@vishakhadixit4318]

Why adding with 127??

[@vincentdanna3689]

From what I understand, it is the "bias", which is a constant that is added. I believe it is added to make sure the represented value is non- negative.

[@alibarma6650]

how the heck mantissa became the first part of the particular stuff???

[@waleedabbasi7030]

hi Daniel can you help ..... about (for example) how to represent 182.74 as afloating point number

[@danielgnz5483]

Great explanation ! Thank you, Daniel

[@БеглиСапаров-м3т]

Why do you replicate the mantissa? After recording : 0100110011 will be filled with zeros. If I am wrong then please explain why.

[@bustergaa]

is x the 2 to the decimal number needed? I know it is to get the full 23 bits on the Mantissa but my test paper says that we only need to use the number from when the decimal is moved.

[@eclypze_]

Thanks, I was having trouble with this

[@princedewangan1346]

good job my friend

[@majeste07]

thank you for clear explanation

[@GabrielWehrle]

Thanks for your help!

[@muhamedsamy895]

Thank you so much, Daniel.

[@bradleymarshall1996]

where did you get the A from?

[@kayodeoladipupo5378]

I reverse my statement. But that multiple of that radix point or decimal or real point is not properly explain. Please elucidate on another video thanks.

[@walidhnaidy6059]

you are the best 💓

[@damxx1827]

Why did you move the decimal point to the right two places?

[@marcelchelo2]

its called normalizing, you move it how many times needed untill there is only one number to left of the dot.

[@ziadmh4590]

why we add 127 to exponent ?

[@sachins117]

Ziad Mh 127 actually....is the constant .....exponent can vary between -128 to +127.....

[@silentsnow996]

finally found a video that explains my homework

[@raggyrags590]

How can we take the value of E as 127 and also how did the expression turned up to be E+2 could you please explain

[@zawad11]

As far as i can understand, E+2 is the same as 10 to the power 2. And I don't think he's taking the value of E as 127. The value of E is +2 in this case. He's just adding the integer bias of floating point with the value of E. As the exponent is 8 bits here, thus the integer bias is {(2^8-1)-1}=127. At last he's converting the outcome into binary..hope that helps.. :)

[@Kumamon-1230]

This made the whole process much more easy and understandable But it would be better if there more explanation for the structure of the floating point standard But yet, this saved my ass for the exam

[@LegendaryZappyBoy007]

how do u know its a pattern of just zeros

[@basictechs6634]

thank you for the explanation

[@rvijay7348]

why 127+2

[@thejunks3597]

I find it's just adding a 1 on the front of the characteristic so the characteristic is basically just the exponent in binary.. so if it was 6-bit for the characteristic and the exponent was 3 it should be 100011 for an 8-bit characteristic it would be 10000011 I find the bias is just the number needed to add a 1 to the front of the start of the characteristic

[@sonulohani]

Exponent bias

[@alihankayhan7841]

cuz he shifted left 2 times.

[@IIxINTENSAxII]

Fast and clear thank you !

[@twistedsab]

Excellent work, thank you

[@oamost]

Excellent explanation technique, many thanks!

[@james106810]

Thanks very much! helped a bunch

[@shorttuts]

Can I use this same process if I am asked to represent the same number but with a mantissa of 16bits, an exponent of 8bits and of course the sign bit of 1bit? Do you have a video which show how to take that binary representation and change it to decimal again?

[@awn-exotic8439]

I know this is an old question, but i'm replying for the sake of others with the same question. You do it in a very *Similar* way, but not exactly the same. The 2 differences are: 1) with the 8-bit exponent: You don't add 127 to the exponent, you keep the exponent the same as you calculated. 2a) When calculating the mantissa: You make the mantissa Zero-point-something not One-point-something i.e He got it as *1.*0100110011... but with a 16-bit mantissa, you would get *0.1*0100110011.... (your exponent is gonna be E^3 not instead of E^2 as you are deceasing your mantissa by an additional power) 2b) Your mantissa will thus start 101001100... not 0100110011... as you now include the *1.* in your mantissa.

[@Saadx71]

Thank you very much man

[@dalerichardson7236]

You are the man!

[@Zerpentile93]

I'm just going to ignore why that biased thing is added. Thanks for explaining.

[@javairclarke5745]

Thanks a lot, Your tutorial was of great help.

[@thomasleong3510]

Daniel how you know the rest of number is "0011001100110011... instead of 000000000000....?

[@madzharavusaniandy2199]

Thanks I found your explanation helpful

[@ranliao3827]

Why 127?

[@ayushjaiswalawesome]

+廖然 floating-point-gui.de/formats/fp/

[@manthanchauhan6954]

what's that

[@sonulohani]

Exponent bias

[@alihankayhan7841]

Cuz he shitfted left 2 times.

[@kalyaninutopia]

That is called bias, added to the number so that it doesn't have to explicitly store a sign bit. So, 0 becomes 127, -127 is stored as 0.

[@nasirhayat7168]

why .2 x2

[@alihankayhan7841]

Its just rule. If u want to find binary value of float part need to multiply by 2.

[@reecedeyoung6595]

Because it's base two. You can think of 0.1 in binary as 1/2 or .5 in decimal 0.01 is 1/4 or .25

[@bradleymarshall1996]

Thank you! Exam tomorrow. You saved me. What happens if the exponent is larger than 8 bits though? for example if the decimal place is shifted 129 places which would make 127+129 = 2^8, which is 100000000, larger than 8 bits. Perhaps this is an unrealistic case as 129 shifts is a really small number.

[@ishanmadhusankaamarathunga3930]

Good Explanation

[@johnpartridge6490]

Very well done! Is 64 bit representation any different or are there simply more positions that are used in pretty much the same way?

[@e_a_at]

You might visit his blog at the end of the video.

[@htnguvon8693]

Thank you very much for this video

[@ScientistRenzo]

Thank you!!❗️

[@elenawilson2271]

How to convert -0.0125 to binary

[@JiJi-jn7pr]

why 1.01 0011? not 0.101 0011?

[@prasadkishorpanchakshari1503]

Thank you so much bro ! Many thanks ! :)

[@salut730]

Thank you, great explanation 👍

[@virgiliodirks]

Thanks. You helped alot.

[@زهرةاحمد-و7غ]

شكرا جزيلا لك استاذ

[@instaminox]

The access 127 is not a trick it’s for the ieee754

[@GRYDE2000]

Thank you!

[@catulusinferni8612]

Thanks alot. But I guess I didn't fully understand it, because I can't calculate other numbers... What do you do if there is more then 1 digit after the . ? Like 5.25 Because if you multiply 25 with 2 you have a number bigger then 1 to mark as the binary expression, would you multiply the 5 again with 2 and would note 01 for that? What do you do if you have .75 or .898 ans so on? :/

[@maihuongnguyen3767]

thank u vr much !

[@iskenderbayndr4442]

Thank you bro. For exam.

[@markdioneeb8997]

NICE!!!

[@Florrrra]

Thanks a lot !!!

[@3washoka]

thank you

[@ghulamhaider2540]

simply.. wowwww

[@Angel-vb5mu]

why 0.8 times 2 is 0.6? Anyway, this video is great! simple and got the point!

[@johnpaulomusic4766]

Angel Ho cause 0.8x2 is 1.6 so we take 1 and then we are left with 0.6

[@Angel-vb5mu]

great, thanks

[@ashasharma7829]

nice help for exam

[@bphanikrishna1]

101.00110011.... 1.0100110011...E+2 upto this ok. But how they write 127 127+2 please explain me

[@sonulohani]

127 is Exponent bias

[@alihankayhan7841]

Cuz he shifted left 2 times.

[@ghettomusic132]

127 because excess-127

[@thivankasaranga9804]

Great. .. :)

[@webad8770]

your solution not for any lead zero numbers

[@edeny591]

Gal Kaminka brought me here

[@OxFLIP]

not clear enough..

[@mddilshadislam6617]

God bless you

[@maldoesfitness]

129 has to be like 10000010 correct?

[@DanielSodkiewicz]

129 is 10000001 Try using some online calculators to confirm your numbers. Example: www.mathsisfun.com/binary-decimal-hexadecimal-converter.html

[@МаксимКолядин-с8г]

You could've taken time and washed the dirt off your nails before shooting the video

[@aizatrahim8437]

final in a couple of seconds , sure come out meh !

[@kayodeoladipupo5378]

Why would you say a trick of adding range of 127bits of 64byte functions. It kind of wickedness. Don't waste time on this video, the floating point units is not fully explain in a lame man's knowledge. It's for the expert like us.

[@laracroft0075]

Thank you so much

[@ScopeZDragon]

Why .2 * 2

[@JamesWilson-jw6kh]

THANK YOU!

[@eibyangeles]

Thank you !

[@billal2731]

Thank you!