HOW TO: Convert Decimal to IEEE-754 Single-Precision Binary

[@thornclawofwarriors]

"If you were going to get a hundred on the exam, you wouldn't be watching this video" OUCH, LOL. I know its the truth, but still... ouch.

[@giorgibujiashvili3942]

can confirm, can't get a hundred. will report back once the test is done.

[@kev814445]

It made the video more interesting...your humor was greatly appreciated during this stressful time :-)

[@Miraclefruitify]

@@richardma3187 Jeez, chill bruh. It's just a joke

[@ajimatsmail5686]

Teu ngarti aing bngst:(

[@ashishdaniel169]

@@giorgibujiashvili3942 still waiting for that report

[@andrewthompson5755]

dawg this was the best explanation I've ever heard

[@Yunho_Park]

woah woah I didn't ask to be personally attacked watching a youtube tutorial video lmao

[@EMMIR_KC]

The best video i've seen discussing this topic so far!

[@gloriaxiaoluzhang4430]

agree!

[@danteeep]

I'm subscribing cause he nailed it

[@DragonDePlatino]

Thank you so much! This was an immense help and I wasn't able to find such a straightforward explanation anywhere else.

[@JayoomJay]

In case someone is wondering why there is a need to use bias. It is to make fast magnitude comparison of floating point numbers possible in hardware. By using a bias we are effectively avoiding the need to store the exponent as negative numbers. If we had allowed the exponent to be stored as negative number (probably as a 2's complement), then during the occasion when there is a need to compare two exponents of two FP numbers, we need to obtain the magnitude of the 2's complement representation of the exponent by performing the 2's complement (need CPU cycles) operation (this is how you obtain the magnitude of a negative number represented in 2's complement form. If the number was represented in sign magnitude form, bits other than the sign bit would have directly given the magnitude) So if there is a bias, we can just forget about the negatives and just compare the bits of two exponents and say which one is larger.

[@stevenpetryk6869]

Good to know! Thank you for sharing this.

[@alexbourlis]

love your way of explaning mate, i think you meant the only way to score 100 is to watch your video ;)

[@madhurjyadeka5569]

Yeah who does that lol😂😂😂

[@edwinsanchez4973]

"If you were going to get 100 on this exam, you wouldn't have to watch this video. Anyway-" 1:23. Did not need to do us like that my man

[@mrarcticaaa1101]

Thank you so much. I definitely wouldn't be able to graduate without youtube. I'm glad I'm studying university at this decade :D

[@johnrex9612]

That video will help me to get 100/100 on exam. Thanks from Poland

[@heron_]

This was the best explanation ever. Why couldn't my professor break it down this simply. Thanks for this video.

[@saturdaysportscentral6129]

Watched this for my exam today, no way you had the right to drag me like that😭 1:17

[@standinonstilts]

Ma boi steven roasting these kids expecting him to be perfect, love it

[@vinayak8100]

Watching this from India- there's like hundreds of tutorial vids on this topic from Indian channels and none is half as good as this one. Thanks a lot sir :D

[@LaplacianFourier]

WHOA... when some guy out of a billion in the internet you've searched is using the same pencil as you.... pffssshhh MIND BLOWN!

[@g0ballistic]

You're a legend. Best video about IEEE-754 on youtube.

[@TheFlyguy31]

Definitely the best 'pencil-pen' i've seen.

[@mitchallcowell5166]

this saved my ass before an exam, great video

[@volodymyrzmazhenko4060]

Thank you, Steven, it help me to understand IEEE 754 much more better than others!

[@ns_down]

Saving me for my final exams mate, thank you.

[@deshanesims2196]

this is the BEST explanation of floating point!!! thank you Steven!

[@krullebolalex]

Thanks a bunch! Very helpful, straight forward and clear. Other videos try to explain the concepts behind them too but that just confuses people.

[@katrinagonzales1575]

How did you get the binary of 132? I don't get it:((( help

[@samannoysingha5259]

Just like how he gets the binary value of 45 😊

[@foobar_eve8813]

I wish you were my Comp Org TA! :-D You're delightful, and your videos are outstanding.

[@tomislavvinkovic6652]

How is 5 equal to 132?

[@0fficialRatedR]

he added to 127

[@opatechnus]

what he converted to binary and how

[@puskalpulami8246]

at first, he just added exponent(i.e, 5) with 127. And their sum is 132. Then he converted 132 (132 is decimal numbers) to binary numbers.

[@klauspeter2199]

9:58 that arrow is sooooo smooth!

[@danielmapiti6891]

Steven, when recording the results at the end, on the mantissa, why didn't you consider the fact that 1100 is repeating?

[@rosiebahrani9895]

Good for you! What university do you TA for? I wish our TAs did that for us too. :)

[@maxgobel]

Are you the voice behind Casually Explained?

[@ProductionsOfPauls]

I was thinking the same thing haha

[@halio8012]

He even makes the same jokes... How many channels does this guy have???

[@JoseFloresEC]

woah, very helpful, thank you so much :) literally couldn't find anything else anywhere else online

[@brianvandenberg4467]

5:45 - 5:51 #BRAINinitiative Move from #Wired to Wireless IEEE’s MultiDisciplinary approach could do it...Wonder, what is their Motivation? @Outcomes_Matter

[@asakhhh]

actually the last bit of the mantissa will be one due to the rounding (check on hardware)

[@calvinlan6568]

ditching my professor's video in favor of some random guy on youtube -seriously though, thank you for making this easier to understand

[@badong4878]

you might have just saved my finals thanks

[@PerpetuallyTiredMillennial]

"If you were going to be getting 100% on the exam, you wouldn't be watching this video." Out here sayin what every TA wants to say, hope you're doin well.

[@mustafaahmadov3896]

hello , i dont get last three 1100,why you add?okay you want to get 23 bit ,but why 1100?

[@joaquincandalaft2124]

awesome explanation, quite short and totally clear

[@aditopguy9785]

Which textbook do you recommend?

[@kucuksamuray]

Thanks for your video Man, very helpfull really. Im watching you from France, keep going

[@ItsMeSphax]

Im pretty sure thats not how to write 255 8:09

[@stevenpetryk6869]

Thank you for your feedback on my handwriting from 6 years ago

[@ItsMeSphax]

@@stevenpetryk6869 Its just a joke cause it looks like "ASS"

[@stevenpetryk6869]

@@ItsMeSphax it was a self portrait.

[@minsookim13]

Heyy Steven, what if it is a negative decimal

[@korneliuspasztor7465]

I know this video has been some years ago, but do u have a video with fractions? :O

[@azizko2046]

Is this CasuallyExplained?!

[@joecomplexgeometricshapesr3348]

Hey Steven great video, but does the exponent always equal 132? What is the significance of the 5 and the 132 , thanks EDIT Nevermind just got it lol

[@exoxDiD]

wait I still don't ;;

[@sorrefly]

The exponent is coded in excess 127, so you just add 127 to the value of the actual exponent 5 + 127 = 132 keep in mind while converting back from iee754

[@exoxDiD]

thanks a lot! I get it now

[@sorrefly]

jongup__ no problem :)

[@sorrefly]

Why does the IEE754 converter here puts a 1 at the end? because of rounding? www.h-schmidt.net/FloatConverter/IEEE754.html thanks for the video by the way :)

[@rickthebrick12]

What is going on with the exponent ^5? How did you convert it to 132 (1000 0100)?

[@stevenpetryk6869]

I added 127. The physical register represents numbers as 127 higher than the actual exponent value. So if the flip-flops in the computer show 1000 0100, the actual mathematical exponent it’s representing is 132-127 = 5

[@rickthebrick12]

@@stevenpetryk6869 if my exponent comes out to be 3, I would add 3 + 127 = 130?

[@stevenpetryk6869]

@@rickthebrick12 If you're going from paper -> electricity, you add 127. If you're going from electricity -> paper, you subtract. For a mathematical exponent of 3, the bits in the register would be 3 + 127 = 10000010₂.

[@anilkadiyala]

If Paper (decimal) to Ieee , then map ur math into this 1.M * 2^(E-127). Evaluate M and E , later arrange them as S E M. That’s it

[@RTimo]

Can you make a video for a negative decimal? Like (-4.75)???

[@S3iF3]

What if the mantissa wouldnt be repetetive. Would you just fill the last bits with 0's?

[@Preposter]

Yes

[@vladGabriel2107]

So, what if the fractionary part process ends up without a repeating cycle? How many digits should i take as a result? Example: for 0.01

[@Oreoezi]

Usually the question will specify, most professors would be ok with doing it 6-7 times. Theoretically you'd have to do it until all 52 bits are filled.

[@KansasFashion]

The best Video I've ever seen about that

[@kareemashouri1429]

my number is 454.125 and when i started converting the second part (0.125) it stopped at a whole 1 so it went like this: 0.125 * 2= 0.25 0.25 * 2=0.50 0.50 * 2=1 did I do it wrong?

[@stevenpetryk6869]

No, you’re right. 0.125 is represented as 0.001 in binary (2^-3 = 1/8). You’ll notice that if you continued you’d just get more and more zeroes: 0.50 * 2 = 1 0 * 2 = 0 0 * 2 = 0 Which is the same as just adding more zeroes to any decimal number’s decimal side: like how 10 = 10.0000 (ignoring precision, which computers don’t usually encode ). So your number in binary is (I think-doing the math on my phone right now): 1 1100 0110.001

[@kareemashouri1429]

@@stevenpetryk6869 I actually did not get the same answer my binary number came out too: 011000111.001

[@stevenpetryk6869]

@@kareemashouri1429 if you Google “454 in binary” you’ll see that something went wrong with your conversion. I’d recommend trying again.

[@stephennnamani8647]

My teacher always want us to normalize the mantissa... why?

[@hixamjocular6591]

why you repeated that loop of binary fraction representation at the matisse case , normally you should complete the mantisse result by zeros !!

[@fruitlover7073]

finally someone who speaks english

[@SuperCracker123456]

I'm really confused. So they decided to bias an exponent. Why didn't they just used 8-bit signed number for it?

[@Matthew.Sweeney]

Partly, I think because it is less efficient. For example, you would wind up wasting multiple values to represent zero (positive zero = 00000000 and negative zero = 10000000). The reason it is not 2's complement is because the circuitry would be more complicated than just having an extra step of subtracting 127.

[@patelav21]

Hello, Can you help me on this one -0.045625(ten) to binary? I tried doing it your way. But I'm trying to do it without calculator since our professor don't allow it. Can you show me?

[@TheStrelok7]

ok how to convert 0.0059 any help

[@aldrinaldrinald]

Best video bro.. Thank you so much 🙂🙂👍👍👍

[@moralniprocvat2205]

what if 'E' negative?

[@ayurmahajan1650]

Actually U @Steven Petryk missed a rule.....Coz in mantissa we need 23 bits..We write 23 bits as u said, but the rule u missed is that If 24th bit is 1 then 23rd should be 1 Else 0......

[@thomaswolf1143]

45 is a palindrome number in binary. So reading in opposite order isn't really explained.

[@hekk_tech5975]

my professor makes a test with more exercises (110%) than usual but in the same amount of time with the amount of exercises for 100% so that more students can hit 100% :)

[@ochuodhoisaya9017]

why have you not 127 for mantisa

[@nicoli108]

Thank you so much! I'm struggling a lot to understand this but you definitely made it easier. I was trying to convert -0,75 to binary and I did this: 0,75 * 2 = 1,50 0,5 * 2 = 1,00 When I get only 1.0 I need to stop. So my number would be 0.11 so 1.1 * 2 ^ -1 1.1 * 2 ^126 0 | 01111110 | 100000000000000 Is this logic correct?

[@ddn65]

Yh, but your original number was negative so your sign bit would be 1 instead of 0

[@nicoli108]

@@ddn65 thank you!

[@Tibia390]

Thanks Bro!!!! You helped myself. I'm Brazilian spectator.

[@Preposter]

8:58 It's 127, not 128. 127 = 1111111 128 = 10000000

[@alta-sh]

Ok but that's a 7bit exponent. He used an 8bit exponent. So, the largest number you can represent is 11111111 or 255, which when subtracting the bias of 127 from gives you 128. That is how he's got the max value to be 128. The minimum is -127, you can represent this by just having the exponent register as all zeros: 00000000. This when subtracting the bias from would give you -127.

[@Preposter]

Oh dang, thanks for the info.

[@chrystheo808]

1:28 ummmm what if I'm watching it a month before the exam bc it's a little thing I don't have in my notes? Good video but sorry to break it to you, many people who have watched this had a 100%. And that's the goal with HOW TO's, you know, to help people do sth better.

[@stevenpetryk6869]

Thanks for explaining! I wasn’t sure what the purpose of this video was but now I know.

[@chrystheo808]

@@stevenpetryk6869 dude you said anyone watching is probably not going to get 100%, don't insult your viewers.

[@adamroach43]

Very helpful and well explained. Thanks!

[@Xudas]

Pov: You came from tintok

[@gabethedogmeme3651]

Yes

[@stevenpetryk6869]

The fuck is a tintok Xudas

[@lanamusleh4246]

Yes

[@monkey8600]

@@stevenpetryk6869 tik tok

[@stevenpetryk6869]

@@maneverman nope! I’m also not You Suck at Cooking. I wish I was though.

[@tr_998]

Shouldn't the exponent have the value 6

[@etien613]

what if the we have something like -0,123

[@darksynthesis1273]

The bias is 127 not 255

[@darksynthesis1273]

Yep! 7:44

[@danteeep]

2^8 -1 = 127 For the listeners(like me) that got confused or dont know what is going on. we use (2^8)-1 cause its 32 bit so (S^k) - 1 becomes 2^8 -1 . if it was 8 bit then k=3. so the exponent part is whatever you got on top of 2^this. and the (2^8) -1 . so its 5 + 127 = 132 . transform that into binary and voila you got your exponential. so sign + exponential + mantisa and you re good to go

[@brianvandenberg4467]

Whoa this 127 reminds me of loopback....255 reminds me of multicast “Broadcasting” Or portion of Network....Or...SubNet.... Don’t get me started on those “Admin” or “Research” Numbers that always return inAdd-ARPA..”Advanced Research Projects Agency...Or DARPA “Defense” Advanced Research Projects Agency....We gonna use this “New” Nanotechnology to cure CANCER & provide safe FOOD & WATER.... Or you “Defense” & “Research” Folks on the Take....North & South America going to get FOOD dropped in by air.... Like Africa et al “Hellenism” for profit....

[@brianvandenberg4467]

Why has Law Enforcement Not stepped in....?

[@Rayyankhantheboss]

Guys just to clarify the bias = 2^(8-1) - 1 = 127

[@justdledfruitloops]

Very clear explanation! Thanks alot!

[@nafisah9499]

"If you were going to get 100 on this exam, you wouldn't be watching this video" way to be discouraging lol

[@stevenpetryk6869]

Don’t take it too seriously! I made this video to help my students get 100’s :)

[@JonathanCollett-g7m]

Great Video and explanation

[@Akatsuu]

THANK YOU MY PROFESSOR COULDN'T EXPLAIN THIS FOR SHIT

[@jahedulislam3438]

Man you saved my ass. Can you make a video for double precision?

[@fayeezullah9628]

why is sign bit 0?

[@vejaleier]

sign bit zero means the number is positve. sign bit one means its negative

[@DrNinjaPhDofPAIN]

Outstanding, thank you for this

[@AC-fi8ge]

You are AWESOOOOOME ! 10/10

[@leogourbin9752]

You saved my life dude !

[@jennyggf3556]

Excellent explanation

[@JasonJason210]

Brilliant thanks. How would you convert a number like 0.0000000025 to IEEE 754?

[@paulolopes5939]

one question if i have a negetive number like for example -18,125 should it be represented in complement 2??

[@thekyreefuller]

I do not understand why 5 maps to 132

[@stevenpetryk6869]

That is how the exponent register is defined. The number in the register is offset from the actual mathematical number. I don't quite know why. You just have to accept as truth that in the "exponent alternate reality", 0000 0000 = -128, and 1111 1111 = 127.

[@ezzermaya4082]

thanks! my exam is tomorrow :~)

[@johnybonny8262]

Buddy u should convert binary by using 1,2,4,8 pattern it is easy

[@andrewbrenner9375]

Wonderfully explained 😅

[@ExecutechTutorials]

how do i convert 23.1675, im racking my brain out

[@tooru]

got 100% thanks to this video

[@asmcriminaL]

I found this video in my old "watch later" category... I watched it many years ago. All I have to say is the crap they taught is in school is mostly worthless.

[@stevenpetryk6869]

You’re right! I barely remember this stuff. I did find it cool to learn, though.

[@serkan3743]

Karrrrdeşimmm biliyorsun bu hayatı

[@rishiupadhyay3956]

Pencils are important. Indeed!😊😊

[@michaeladekola7307]

Hi Steve, how do you convert 75.03223 to single precision floating number. I’m stuck in converting .03223 to binary

[@megaquickunboxhope6268]

Check solution is 0 10000100 01101011100.... Check bec video is blur not able to see ans.

[@mehdibadaoui1658]

really appreciate the video

[@BsharatAhmed]

thank you man your the best !!!

[@lemonbirdo1353]

Why does OP sound like Josh Dun?

[@BrunoPorro1618]

I was given 3.248x10^4 no explanation on this subject, they ask me to convert this number to IEEE but for what understand, this is for floating point numbers, the number given is technically 32480 so what can i do with it?

[@XxXDerCheckerXxX]

127 not 128!