Binary 2 - Two's Complement Representation of Negative Numbers

This is the second in a series of computer science videos about the binary number system which is fundamental to the operation of a digital electronic computer. It covers the two's complement system of representing positive and negative integers in binary. It demonstrates how two's complement allows computers to perform subtraction operations, and explains with examples three different methods that can be used to convert negative denary numbers into binary.

[@swedishguyonyoutube4684]

I am humbled by how pedagogical, clear and efficient you are in teaching this material. I'm a former teacher switching careers to work in IT, and your videos have been incredibly helpful and instructive. Thank you very, very, much!

[@ComputerScienceLessons]

You're very welcome and thank you so much. I too switched from teaching to IT, but I came back to teaching again. :)KD

[@talharashidi366]

this is easily the best video on youtube for learning 2's complement.

[@ComputerScienceLessons]

You are very kind. Tnx :)

[@ApteraEV2024]

I❤u 2's!!❤🎉

[@oliver4003]

so I spent hours reading this section in my textbook trying to understand it with no luck. So i decided to watch this video, and 12 minutes later I fully understand the concept. Thank you so much!

[@ComputerScienceLessons]

You are very welcome - glad to help :)KD

[@T3chBeatz]

Kevin's delivery of these tutorials is just brilliant - Thank you!

[@Jayson223ad]

I have exam in Discrete mathematics in a few days and this is one of many topics. I knew how but not why. Thank you so much for making this so so clear. My teacher never explained the first 1 stands for -128! nor the book or notes . If all the teachers were like you the civilization would be much more advanced.

[@ComputerScienceLessons]

You are most welcome :)KD

[@rancorjoy5412]

I do not think the first number stands for -128! ~ -3.856205e+215

[@cesarvides9729]

Just when I thought I had learned an easy method, you pull out another one. This video had me on an emotional rollercoaster.

[@ComputerScienceLessons]

I hope it was the exciting part of the ride. :)KD

[@TheLonelyLPer]

This is hands down the best explanation I've had for 2's complement! Thank you!

[@ComputerScienceLessons]

You are very welcome :)KD

[@adamyagaur9638]

This is learners gold. Short , crisp & clear . Thanks a lot!.

[@ComputerScienceLessons]

Thank you :)KD

[@veryangerymanminecraftisco9048]

Thank you so much dude, I never mange to find people who speak English on youtube that teach these sort of thing.

[@potatochannel1948]

-Sir, you are a saver, my prof at the university only gave us the two's complement method without explaining where the hell that came from . I very thankful for you sir!

[@exactzero]

Awesome explanation. You didn't just teach the how but also the why which is the most important of all. That last technique was mind-blowing!

[@ComputerScienceLessons]

Thanks for the comment. Delighted to help. :)KD

[@xr.melissa]

Excellent video! My coworker was trying to teach this to me but it's hard to follow without strict examples, so thanks for this!

[@ComputerScienceLessons]

You are most welcome :)KD

[@boudieraurelien8531]

To be honnest, if you were in front of me, i'd have hug you ! You just made me so happy, i finally understood why i can use the 2's complement. I didnt understand why i had to use it. Thank you soooo much!

[@ComputerScienceLessons]

You are welcome. Things are much easier to understand when you know why! :) KD

[@rationalsage1084]

This is an incredible insight, I've never understood this, my teacher only taught me the shortcut to the conversion.

[@ComputerScienceLessons]

Underlying concepts are important if you want knowledge that you can build upon. Thanks for the comment :)KD.

[@nicestcatoutthere3221]

This was truly the best video on complements.

[@ComputerScienceLessons]

Thanks for the lovely comment :) KD

[@amanrubey]

your videos are simply superb. it's the same as watching some interesting documentary. I'm loving it. True Gem on the internet

[@guzman-do]

What a great teacher you are, Sir!

[@ComputerScienceLessons]

You are too kind.

[@cheapwisdom918]

Thank you so much. Why the universities cannot make their material as easy as this? Thank you millions!

[@ComputerScienceLessons]

You are very welcome. Thanks for the comment. :)KD

[@blank-vw2sb]

AWESOME, i don't find this depth in two's complement. Really Nice

[@soz824]

Great voice, super well made video and excellent explanation!

[@sandipghoshal2122]

This so far the best video on two's compliment

[@ComputerScienceLessons]

Thanks for saying so. :)KD

[@SuperSayiyajin]

Thanks for your playlist.

[@mariiasafonova5510]

Oh my Godness. It's so great explained. I find it just wondersfull so you can pause the video or watch this one more time till you get the idea...not like at the uni.

[@ComputerScienceLessons]

I very am glad to hear this is useful. There is a lot to be learned at university too. :)KD

[@hammam92]

The best video on KZbin, Thanks so much

[@ComputerScienceLessons]

Thank YOU

[@ehsanmavaei5380]

Awesome people like you who help people understand better are loveable and admirable

[@LindaLawton]

You might want to add a link to the first series in the description. Make it easier for me to go check that one out :)

[@abhishekdutta8089]

Thank you sir for this wonderful lecture on representation of binary numbers.

[@ComputerScienceLessons]

You are very welcome. Thanks for commenting :)KD

[@user-dv7kw8ew2q]

Thank you for simplifying this

[@user-fg6ng7ej6w]

very clear explanation. cool that you presented 2 ways of dealing with it

[@ComputerScienceLessons]

Thank you :)KD

[@thimalifernando7164]

Awesome explanation. Thank you!

[@ComputerScienceLessons]

You are very welcome. :)KD

[@SusmitMohan]

Really very impressive work. Thanks a lot.

[@ComputerScienceLessons]

Tnx :)

[@deedewald1707]

You are confident and capable to teach complex concepts !

[@ComputerScienceLessons]

Thank you. I've been doing it for nearly 40 years :)KD

[@deedewald1707]

@@ComputerScienceLessons I put this method into Excel such as your teacher skills are excellent !

[@Technogrammer]

Excellent Work Done!

[@ComputerScienceLessons]

:) Tnx

[@LimeriuxasLT]

Awesome video!!! Thank you so much!

[@ComputerScienceLessons]

You're welcome, and thanks :)KD

[@yangliyeh5510]

Thanks a lot! Very clear!

[@TheAltKryptonite]

This video is awesome, thank you!

[@ComputerScienceLessons]

Thank you for the awesome comment. :)KD

[@tavongampofu9561]

wow really helpful i was struggling with this for a while thank you

[@ComputerScienceLessons]

You're welcome :)KD

[@fatimakhan3084]

Best teacher ever!!!

[@ComputerScienceLessons]

Wow - thanks :)KD

[@monjasonsteng7861]

Thank you. This was great!

[@ComputerScienceLessons]

You're most welcome :)KD

[@ThePandaGuitar]

Fascinating!

[@mmmpz2298]

You safe me from failed the test😭 thank you so much😭

[@theonesongchannel9513]

Just Beautiful!

[@ComputerScienceLessons]

Thank you :)KD

[@user-gd6il5zb8l]

Very good video, sir.

[@ComputerScienceLessons]

Thank you kindly :)KD

[@lumennganje2721]

wonderful. thanks so much. God bless you

[@ComputerScienceLessons]

You are very welcome :)KD

[@astheffander_alexander]

Got stuck because of the "online class" didn't help me.... But this video help sooooooo muchhh... Thanks!!! 😭

[@HealthConsciousUpdates]

Thanks sir It's too much useful video👍👌 Love this video from Pakistan

[@ComputerScienceLessons]

Thank you :) KD

[@williamtylerwillis6417]

Thank you!

[@ComputerScienceLessons]

You're welcome :)KD

[@abdullateefjabasa1656]

How amazing you are!

[@mahmoudbasha4838]

sir great work i spent a week to try to understand this topic but thanak to u it's done.. i wanna know sir what is the program u using to make these effects in the videos

[@NoName-tj8dm]

Thanks for the great video. I am confused how system will be able to identify that left most bit is -128 of the bit is 1

[@idensoneltume627]

I was mind blown 🤯

[@DigitalGuruLK]

what is the maximum negative number in two's complement... how it represent large negative numbers....?

[@ComputerScienceLessons]

That's where floating point binary comes to the rescue

[@fadhlyrafi]

3:09 how about 2s complement table for 16 bit binary?

[@MusaYmc]

you are a saint

[@indikajayasinghe9579]

best of best

[@ComputerScienceLessons]

Thank you :)KD

[@Kenzo-0-]

Ty a lot

[@ComputerScienceLessons]

You're welcome

[@akshaybodla163]

Im really confused about binary addition. I have a few questions that i hope you can answer, thanks! 1) At 10:03 why is there a subscript of 1 at the last zero? 2) And for -122 in binary why does the addition of 0 and 0 in the two's place create a 1? 3) When is the result a 0 or 1 when adding bits

[@ComputerScienceLessons]

When we perform a similar calculation in base ten, we add pairs of digits and, if necessary, we carry a digit. In the example below, 6 + 9 is 15 so we write down 5 and carry 1. The 1 is then added to 5 + 8. 4 5 6 +7 8 9 ___1___ 5 _______ In base ten, 1+1 = 2. We represent 2 in binary as 10, so 1+1 = 10. In my video, I write down the 0 and carry the 1. The green bits are the bits that are carried. In my example for -122, the the 1 that was carried from the previous operation is added to 0+0. I just haven't shown the carry bits this time. I hope this helps. will will make a quick video on how to add binary numbers together soon. KD

[@v380riMz]

Bruh this becomes so easy when you know that MSB should be -128 for negative binary numbers

[@ComputerScienceLessons]

That's the trick 💡:)KD

[@voiceoverworld4036]

Where does the green 1's come from?

[@ComputerScienceLessons]

They are the carry bits. 1 + 1 = 10, so write down the 0 and carry the 1.

[@kenshinhimura8708]

Thank you so much! Why can’t textbooks explain it the way you did from 0:00-7:00?

[@ComputerScienceLessons]

I'm happy to help. Thanks for the comment. :)KD

[@MrMeeseeksPiano]

You say that I can represent up to 256 positive numbers with 8 bits but then doesn't specify wether the MSB is -128 or 128 for the exercise at 8:03? Was I supposed to guess it?

[@ComputerScienceLessons]

The left most bit is -128 as described earlier in the video. The left most bit is always a negative value with two's complement.

[@kavereon]

holy...moly. I understand!

[@ComputerScienceLessons]

That's music to my ears. :)KD

[@rx25251]

Can you please explain how the computer identifies a number as a negative number before storing it in registers in its 2s complement form ? How does the computer know the result of arithmetic operation is negative so that it can be stored in its 2s complement form.

[@ComputerScienceLessons]

Hi Ravi, a computer system stores POSITIVE numbers in two's complement as well. So that fact that it is negative, or positive, is part of the encoding. Ultimately, negative numbers come from outside the computer. When you input a negative number, you probably type a minus sign in front of it, the value you have input is then processed and stored accordingly. When it comes to arithmetic operations such as addition and subtraction, negative results take care of themselves (that's the beauty of two's complement) as you will see if you study floating point addition and subtraction later in this series. By the way, in this series, I am talking about general principles used by a range of different types of computer system. Modern PCs encode floating point numbers using the IEEE 754 standard, but the same arguments apply. :)KD

[@rx25251]

Thanks for the explanation! One follow-up question however - How do you represent a positive number in its two's complement form ? For example +57 in binary is 00111001 and two's complement of 00111001 is 11000111 So will the two's complement of +57 i.e., 11000111 be stored in the registers ? But the first bit is 1 which denotes a negative number. 11000111 from above is in fact binary representation of -57 and its 2's complement is 00111001 . what will be stored in the registers to represent -57 ?

[@CraigEaton]

This has confused me for YEARS and I have to teach this soon. This video just makes it so easy. I do have one question tho 1011 1011 How would one know which number is representing the negative?

[@ComputerScienceLessons]

By convention, the sign bit is the left most bit. Inside a processor register, one of the bits will be allocated as the sign bit, usually on the left, but it might vary from processor to processor. This is decided by the designers of the processor.

[@user-gd6il5zb8l]

You just have to agree with whomever you talking to that you both use the same system. It's just like with character sets - it only works for you and your friends because you've agreed to use the same method of representation (encoding). If all of you will use different encodings (for example, like the ones before Unicode came along), you'll end up with the same binary numbers, but different interpretations of those (thus different characters).

[@alexmartini8087]

At 11:35 for the example -44: how does the 3rd bit go from 0 + 0 = 1, but the 4th bit goes from 0 + 0 = 0?

[@ComputerScienceLessons]

With the third pair of bits there is a 1 carried from the previous pair. With the 4th pair of bits, there is no carry. Take at look at this: kzbin.info/www/bejne/iom9c6Sqm6aCprs :)KD

[@phy_dude]

❤️

[@barrydevine]

Does the system whereby the MSB becomes a negative (ie -128) have a name?

[@ComputerScienceLessons]

It's called 'two's complement' :)KD

[@barrydevine]

@@ComputerScienceLessons In this video you seem to have 2 methods of making negative numbers: 1 - changing the MSB to -128 2 - 2's complement. Am i mistaken?

[@oneminutedaily6394]

Which method is the best?

[@ComputerScienceLessons]

Two's complement lets you subtract a number by simply using addition. Sign and magnitude makes subtraction more difficult but is good for fast conversion.

[@oneminutedaily6394]

@@ComputerScienceLessons thank you so much sir 👍🏼 keep it up with the good content provided. No doubt u're a hidden gem in youtube 😄

[@shah144]

How would u do -7.5?

[@ComputerScienceLessons]

Good question. You would need to use floating point binary. :)KD

[@AviPars]

what about positive binary to 2s complemenmt

[@ComputerScienceLessons]

Same method - just put a 0 in the left-most place value. In two's complement, positive numbers always start with 0 and negative numbers always start with 1. :)KD

[@Mike-vj8do]

hey man, what if we are asked to do it in 6 bits

[@Mike-vj8do]

instead of 8 bits

[@ComputerScienceLessons]

You might. The biggest number you could encode however would be 63 (64 possible values including 0). Perhaps there is an embedded system out there that only needs to work with integers up to 63. Some types of processor might allocate 6 bits of the current instruction register to the operation code, which means a maximum of 64 commands in the instruction set (as you'll see if you start looking into hardware architecture and low level code). :)KD

[@ComputerScienceLessons]

see below

[@user-fi4zx3eb4k]

im from chile, if is -32'768 for 16-bit binary numbers, i would stay it as -32'768 since doing two's complement of -32'768 does nothing.

[@Redheadredification]

I love you

[@ComputerScienceLessons]

Love U 2 KD

[@ghalibazad5961]

How did you subtract 38 from 90...can you explain? At 2:09 .....

[@ComputerScienceLessons]

Column subtraction in base 10 is explained here www.bbc.co.uk/bitesize/topics/zy2mn39/articles/zc78srd :)KD

[@ghalibazad5961]

@@ComputerScienceLessons thanks

[@osianpetts556]

11:59, is what you're looking for Osh

[@milestailsprower4555]

127 is possible in 8 bit twos complement.

[@ComputerScienceLessons]

Indeed it is. The range is from -128 to 127 :)KD

[@Democracy_Manifest]

Why this was published on April Fool's day I'll never know. Great video tho

[@ComputerScienceLessons]

It's hard to believe it was nearly 4 years ago. What a fool I was then! Thanks BTW. :)KD

[@ryanalnaser914]

thanks for anything or where I stop

[@ToanPham-wr7xe]

😮

[@Gravityys]

Denary = Decimal for those who don't know

[@Gravityys]

Great video btw,really helping me grasp the basics of cs and understand them.

[@ComputerScienceLessons]

Glad to be help :) KD