The easy way to convert decimal numbers to binary (base 2)

This video gives a method to convert decimal numbers to binary numbers quickly. This is a variation of the remainder system that is typically taught in courses. I like this method because it gives the answer in the correct order from left to right.
Proof of why it works: math.stackexchange.com/questio...
I also give a proof in this post on my blog (skip down to the section with the proof and the discussion of dividing by 2 and ignoring the remainder) mindyourdecisions.com/blog/201...
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[@martinfranke9766]

You are not actually ignoring the remainders. The ones and zeroes you write below are, in fact, the remainders.

[@xianartman]

Martin Franke I noticed that, indeed acknowledging that might save a step. 13/2 = 6(r1) 6/2 = 3(r0) and 3/2 = 1(r1) Translating to 1101 For trinary it would be: 13/3 = 4(r1) 4/3 = 1(r1) Translating to 111 in trinary.

[@xianartman]

For fun in trinary: 244/3 = 81(r1) 81/3 = 27(r0) 27/3 = 9(r0) 9/3=3(r0) and 3/3=1(r0) Or 100001 in trinary 2014/3 = 671(r1) 671/3 = 223(r2) 223/3=74(r1) 74/3 = 24(r2) 24/3=8(r0) 8/3=2(r2) Or 2202121 in trinary

[@phatkin]

kek

[@galvanizedcorpse]

shut up

[@martinfranke9766]

Yes, the algorithm works for any base.

[@InputBlackBoxOutput]

I believe this is just the usual way binary number is derived from decimal number. Step 1 - Keep dividing by 2 and note the remainder Step 2 - Reverse the remainders

[@santhoshwagle9857]

exactly... sane thing came to my mind... nothing much new

[@sankarshanmishra6326]

So true

[@brightjovanny]

Ya right

[@_vikramhegde_]

Yup the usual method

[@luis_musik]

yeah, you can think of it as extracting the digits from a binary number: 1101 mod 2 = 1 110 mod 2 = 0 11 mod 2 = 1 1 mod 2 = 1

[@raggebatman]

2014 KZbin: nah 2019 KZbin: Certainly, everybody wants to hear about this

[@splashything3001]

I’m actually doing binary tho wth

[@krzysztofmazurkiewicz5270]

well i did miss tgat one so its nice YT reminded it ;)

[@IStMl]

I need it for uni

[@mohammadsaifh.aal-mutairi2358]

Chief, this is it. As silly as it seems I've always been messing up my denary to binary conversions SOMEHOW, but now I finally know an even easier method thanks to you. Thank you for helping us students out

[@jtc9098]

KZbin is a better teacher than your average college professor. Why can't teachers make it this simple? Quick, straight to the point, and simple.

[@zenzen318]

This is just the same thing as normal conversion....

[@Tim3.14]

zeN zeN Sometimes different bases are taught in a way that doesn't make this so obvious... E.g. If someone writes the binary 110110, having first leaned that the places represent powers of 2, I might have been inclined to count the digits, realize the leading one is 2^5, followed by 2^4, etc., and so do 2^5+2^4+2^2+2^1 = 32+16+4+2 = 54, but it's much quicker to do the reverse of what's demonstrated in this video and just start from 1 and say times 2 plus 1 times 2 times 2 plus 1 times 2 plus 1 times 2, which gives 54. I guess what I'm saying is, sometimes educators emphasize the theory and neglect the practical calculation techniques. Probably depends on where you went to school. I'm glad we have high quality math youtubers (for all different levels of math) helping fill these gaps.

[@sargamsandhya8591]

Right bro

[@mahendersahu794]

He is just taking LCM without drawing rows and columns

[@aylinalakbarli5433]

our teacher explained this to us in a different way but this one is so much easier ... thank you

[@lovemagic3692]

This really really helped me! The remainder part tripped me up, until you came along. Everyone wants to be so deep, but simplicity is key!

[@hollowkos]

Very useful! Faster than the method my teacher taught me. I have an exam on Tuesday and I'll have to use this, wish me luck!

[@anthonycooke1889]

This by far is the best method I have been shown so far. Thank you!!

[@thirtyacres7504]

I have a quiz on Decimal, Binary, and Hexadecimal in two hours. Live saver. Truly. Thank you, sir!

[@julezkelly6593]

Simple and to the point, love that its not complicated :)

[@chirag4467]

Awesome,the method you thought was easier and accurate than my teacher thought me.

[@erijqudus6654]

Thank you much. You made the process unbelievably simple. I wish other videos are clear and concise like this. I have recommended this tutorial to my class fellows as well. Great job.

[@edwinloarca9470]

Thanks for posting this mathematical challenges, they are fantastic!. They really have improved my thinking skills.

[@toniokettner4821]

This is possible in any base. Just write sown the remainder after dividing by the base you want to get.

[@jadosmart1298]

Thank you so much. I just started my first semester and I think I might be at the back at the class in terms of performance. And that's all because I forget the concept of binary over the years now.

[@greatbriton8425]

Love the simplicity and thinking behind this

[@joan8733]

This is awesome, easy to do. Will use this method this coming exams. Thank you very much 😊

[@hidden0ne]

The BEST and fastest way to convert decimals into binary. Do not use any other method and best for DCCL testing. Great job and thanks for the video. Excellent work.

[@TechGameLive2905]

The coolest and simplest method ever thanks buddy ❤ it gonna help.me get good marks now TMRW in my exam

[@SgtSupaman]

This is a great trick, but I have to say you aren't actually "ignoring the remainder". You are just going back and placing the remainder beneath each number after the fact. This exact trick can be used to convert base 10 into any base. For instance, 445 to base 4 goes like this: 445/4=111(remainder 1); 111/4=27(remainder 3); 27/4=6(remainder 3); 6/4=1(remainder 2); 1/4=0(remainder 1) 1

[@fuseteam]

yes i agree tho in base 4 you can't reproduce the remainders after the fact

[@SgtSupaman]

@@fuseteam , right, you would want to keep track of remainders as you go in bases higher than 2 (technically you could do it after the fact, but it basically means doing the division a second time).

[@fuseteam]

@@SgtSupaman yep while in binary you just have to look at the last digit of each result to reproduce the remainders

[@martwest3261]

Thank you for pointing out it works for other bases too, even though it's a bit less efficient, it is still easier than what I have been using for 39 years.

[@sajilkhalid6149]

I haven't understood this the entire semester and I got it in 3 minutes!!

[@TechGameLive2905]

Exactly buddy😂😂😂

[@justinnichols9966]

I just learned more in 2 minutes 50 seconds and the short time I spent reading the comments, than I have in my hour long lecture. Thanks @everyone

[@evananderson8452]

This was very clever. Is there a shortcut for hexadecimal? Thanks

[@clientornaka4690]

Broooo bless you! My computer teacher at VoTech was trying to explain this to me and i had no freking clue what he was talking about. ITS SO SIMPLE xD Thanks brother!

[@AnujKumar-em8lv]

Best method ever. Handy in exams. Thanks a lot

[@user-hl7lr8ld2i]

Anuj Kumar this is the normal methode

[@sangramjitchakraborty7845]

This is the exact same method normally used to calculate this sort of thing

[@BizzUK]

@@sangramjitchakraborty7845 not everywhere, we were never taught this method

[@pivottech8881]

@@sangramjitchakraborty7845 I wasn't taught this method...

[@janna9029]

Completely understood after watching this, a simple and easy way to do it. Thank you

[@abeej6960]

why you never tell me this 😡

[@DMatt1974]

I am taking a networking course for my college degree. We are at the point of converting decimal to binary. The way that the tutorials (and fellow) students explain it have made my head spin. After watching your video, I consider myself an "expert" (LOL). Thank you, very much, for this tutorial.

[@ryanjacob8957]

Its so much easier to understand on video then on paper. Thanks!

[@joelleforget3061]

This was so helpful to a newbie! Thank you!

[@Handl3412]

Studying computer science and was so stuck on this , thank your video helped a lot.

[@shivatejachavali787]

Me tooo , I'm a wannabe tho

[@josemiguelplanton4613]

Never my teachers explain this to me. Because they ignore it!!! 👏🏼👏🏼👏🏼

[@marvinmusambi7952]

Best method av come across .Easiest ever!Thank you

[@prony5145]

Wow! Thanks a lot man. Never knew its even possible to calculate binary digits

[@billgates555]

Great video. IMHO a good way to speed up one of the traditional methods

[@aminblm]

That’s the most clean way to calculate binary number I have ever seen !

[@muralinagarajan8305]

Is this what you call a trick ?? This is the very original procedure to convert a decimal number into its binary equivalent.

[@hugowhitacre3573]

I never learned it today, but some people might have already knew that so...¯\_(ツ)_/¯

[@roygalaasen]

This is the method I used when I was 13. Before that, around 9-10, if you had a 8 bit number, I checked if you could divide by 128, if you could you knew that was a “1”, subtract 128, and try 64 etc. That last method I invented myself for lack of having any books or other sources of information, just the English manual that came with my C64. (I didn’t know any English yet.)

[@spotandjake1008]

I think he meant a trick for beginners rather than going online and finding some sort of converter

[@galvanizedcorpse]

if this is too basic for you you can just leave

[@roygalaasen]

Гальванизированный Труп don’t forget: That this video is several years old, and KZbin dragged this out from the void.

[@Time4House]

best explanation of the decimal to binary conversion. thanks

[@reginamartinez6547]

I’m here in 2018. Why in the hell wasn’t my textbook this easy? I was so lost but found this video and now I get it. Thanks!

[@royhj3119]

Teaching is a skill, he is an excellent skilled teacher.

[@leandrodossantos9160]

Oh my god man I really thought I wasn't cut out for math but you just made this brilliant explanation about binary numbers which just blew my mind of how clear and well-explained that was. Thanks for the great video!!!

[@nknnithinabc]

This video made my day, thanks

[@shwaq8890]

OMG THANK YOU FOR GOD'S SAKE IVE BEEN LOOKING FOR THIRTY MINUTES FOR A FUKIN EASY METHOD AND I FIND IT THANKS UR A LIFE SAVER, sorry had to write in caps lock I was over excited hahahahha

[@jaythedrifter]

Finally someone explains this in a way that a fifth grader can understand, and not just assuming that everybody knows where to start! Thank you?

[@coolduderj2652]

very very helpful thanks a ton this man deserves a gold trophy

[@mikhailsalinas]

This is absolutely mindblowing!!! Good job! 👏

[@kunjalpandya]

this was the best and the easiest method i found on the net thanks a lot sir

[@earljando8649]

No way! Thank you so much sirr this was way more easier than i thought thank you so much. This will save me in our exam later.

[@naitiksingh4730]

You solved my problem Bro...I found this method very easy then traditional one...luv u❤

[@AkhiAkter-ti5wd]

Sir your teaching technique is so helpful.

[@MrSeanPires]

hey man thanks alot this helps alot ... question do you have any video to convert into hex & octal ??

[@TechRobot99]

STOPPING BY TO SAY THANK YOU ♥

[@kirsten9782]

This is SO PERFECT!!! Thank you!!

[@shantaeporter3164]

You sir are a life saver great vid u put it in such away that its simple and takes no time to do tnk you!!!

[@leonorreis749]

OMG!!! Thank you SO much. This is RELLY GENIUS!!!

[@literalcode]

I love watching videos of people teaching my native language

[@MsSiranda]

your method is the easiest that I have ever learned.. thaks a lot

[@catalyst0175]

Not sure why there is so much criticism in the comments, but this is an elegant method to convert to Binary from Decimal. I get it that the remainders do not need to be "ignored", but the method of ignoring the remainders and replacing 1's for odd and 0's for evens also works just fine. Thank you to the OP.

[@lonewolf9455]

holy... this method is amazingly quick! Thanks!

[@lpeoples1868]

thank you so so so much I did not understand decimal into binary till you thank you. you have including details and not just steps. stating the place of Odd and Even had helped so much

[@davidnjuguna5474]

easiest method!!!thanks

[@manmann9862]

Why ignore the remainder when it's what you are going to write down at the end anyway?

[@fuseteam]

because you can reproduce it either way

[@dhwaneelkapadia3265]

@@fuseteam wait repeat But slowly

[@fuseteam]

@@dhwaneelkapadia3265 the remainders are derivable from the oddness of quotients

[@leebougz]

@@dhwaneelkapadia3265 I think he means that you'll always get remainder 0 on even numbers and remainder 1 in odd numbers so you needn't note them

[@calebolsen6175]

great video, teacher explained it a bit weird but it clicked when you explained it, thank you

[@leelinkGOML]

i wasn't well when my teacher thought this but now i know thanks man

[@shehani_fernando.9593]

Woa thanks dude! Helped alot in my exam!

[@TheAngelChristine]

thanks this is way easier than anything i've seen!

[@jamesstevenson842]

GENIUS, my teacher just literally told us to do binary by adding.

[@track-past254]

Thanks sooo much..this is the most explainable video and the others are hard to understand

[@Funnyvideos-zy8vb]

it acts like tutorial during my exams👍👍👍

[@julianh7284]

Any ideas where this would be useful in hardware I'd love to hear them

[@MrShwaggins]

Thank you for your tutorial. Please make sure that you are doing this type of calc in the same direction (Right to left) since it does effect the answer. I was trying to figure out 93 and kept getting 29.

[@viswaguntha820]

A really helpful video on binary numbers. Easy for exams.

[@pradeep422]

why only for exam???

[@mohammadfahrurrozy8082]

@@pradeep422 i think what he really means is that this is good for exams too

[@JahMusicTube]

In alternative, you can just annotate the remainders and then read them backwards to get the same answer :P

[@janna9029]

That is the method my teacher taught us.

[@ryashaum]

both work similarly

[@prasadg7777]

Can i apply this technique for all the numbers?

[@chekitatheanimatedskeptic6314]

Best method ever! Will try to understand the proof bellow in the comments, but will really be useful even without the proof considering fast calculations. Thx very much. Will share to ever1 I can!

[@Frontdesk_tragedy]

ok so i thought binary only went up to 8 spaces per thing, so the last one has 11 space, what do the additional 3 spaces equal to? clarification how i am learning binary in class so far [256][128][64][32][16][8][4][2][1] [ ][ ][ ][ ][ ][ ][ ][ ][ ] and by adding this up above where a I is i can double check my math. BUT for 2014 being 111 11011110 what do the numbers past 128 equal?

[@souinguisal416]

Thank you. That is the best way and the best explanation. Thanks again

[@praiseonionrings182]

does this work for other bases?

[@jkrai9684]

yes, but because its base *2*, that's why you divide in half. for other bases, u probably have to divide by whatever number bases

[@RealLifeInChina]

The binary numbers are just the reminders of each division. It is better to directly write the remainder for each division, so you can keep track of each step.

[@wenkexing6777]

Omg thank u so much ur a life saver!! The way ur explaining it is so understanding and easy to understand, thank u so much u save my life!! BEST method very useful for exams i must say so myself😁✋🏻

[@aparnapriyanka2404]

It is very useful and clear . Thank you. :)

[@burhanchowdhury1544]

Dear...thanks a lot..it helps me most...can you tell me how many technique book you published in math and computer(ict) related? How much does it cost? How can i get in bangladesh..

[@shamekaharris5106]

OMG I finally got it! You’re the best!

[@CLC9209]

Thank you for this video, much appreciated.

[@suashok785]

thank u sir, it is so easy when u explain

[@sriharianne5229]

Very good and easy technique. I like it. Thank you very much.

[@jjelhachmi14]

thank you so much for posting this video its help me understaind and pass the quiz thanks again

[@30IYouTube]

Hey! The last example you showed was the year this video was posted!

[@TOONSSTATION]

Subscribed to your channel because you are best!!♥️♥️

[@tonytiger7896]

this will be my cheat sheet for my test tomorrow thanks!

[@ajinkyabujone3532]

Thank you a lot Sir thanks for the very good method keep making videos like this..

[@melanies3247]

FANTASTIC! Know 4 other ways to do this, but wanted something faster. Thanks!!!

[@i-evi-l]

Nice! Thanks for the simple explanation!

[@AbdiPianoChannel]

Thank you. Great example

[@belikeadbi]

Thank You so much, It was so easy, I din't know! Thankx

[@scienceblossom6197]

Awesome for IP addressing calculations :D Thank you

[@dhairyagandha2937]

what should we do for a point decimal number ??? for ex - (899.65) in decimal then how to convert it into binary ??

[@Kaleabe25]

Do you have for hexadecimal?

[@riadussalehin--]

It's cool to think of it this way!!