Twos complement: Negative numbers in binary

How can we represent negative numbers in binary? There are several ways. This video compares using a sign bit, ones complement, and twos complement. Twos complement is the most commonly technique because it's relatively easy to implement in hardware and it makes addition and subtraction with negative numbers easy.
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[@DUANEYAISER]

Please tell me you're a paid instructor, and that you're paid well. You deserve it! This isn't just a KZbin series, this is a full fledged course Thank you!!

[@IvanEedle]

He used to be employed by Khan Academy. I'm not sure, maybe still is.

[@dendritedigital2430]

@@IvanEedle monetized youtube? He has 400K subscribers.

[@anandrajofficial1]

kzbin.info/www/bejne/pnuQq61-etiLkKc 2's complement shortcut

[@ReasonMakes]

@@dendritedigital2430 KZbin's monetization is a joke; they don't pay creators anywhere near industry standard. Half a *million* views is about $1,000 based on my experience making videos (and according to Social Blade he got $246 at worst, $2,000 at best). To get the avg salary of a Computer Science Professor he would need to do that 114 times a year (10 videos like this every month, excluding how many videos might be flops, excluding weekends, etc.) But that's an impossible expectation. This is his 9th most viewed video of all time. Social Blade estimates his revenue at $296 - $4.7k monthly (probably $2,500). That's minimum wage. I hope I'm wrong and he's getting more than that. I wonder if he has a Patreon?

[@dendritedigital2430]

@@ReasonMakes Patreon, Development Kits, etc...

[@SJohnTrombley]

I probably had two's compliment taught to me half a dozen times in college. I get how it works. The properties are nice. Not once has anyone ever told me "treat the sign bit as a -(2^n) bit." This is a borderline life-changing revelation.

[@jetison333]

@美遊エーデルフェルト why?

[@crs-t]

Some people need to visualize things, which in turn gives deeper understanding of subjects. I found this video while i was searching for a better understanding of 2s compiment and 1000 == -8 was the piece i needed to feel i understand it, because it helped visualize the whole thing. And in turn visualize very basic ALU operations better.

[@mayukhbera]

SAME HERE

[@alonebuthappy33]

@@crs-t how do we write positive 8 then 😅😅😅

[@salesv]

@@alonebuthappy33 You use more bits :) If you have 4 bits and 1 is for sign, you actually have only 3 bits for numbers, so you can represent at most 0b111 = 7.

[@livium9184]

By far the best explanation of two's complement.

[@oussamaelhriki8160]

especially the -8 part

[@NoOne-oz7lc]

@@oussamaelhriki8160 true

[@focus-freaks]

true

[@srivatsarupadhya6116]

For sure!!

[@Shredcheddar]

It really is. I'm reading Harris' "Digital Design and Computer Architecture" which covers binary numbers in chapter 1 and although it's a fantastic book, its explanation still falls short of Ben's. Ben really shows the logic behind the pattern for those of us who need it spelled out. Mr. Eater you the man.

[@hasnaa7316]

the way you first worked with flawed methods and then built your way to show us why adding 1 to the one's complement works better was really amazing . thank you so much

[@mariobrito427]

Been fiddling with bits for 20 years and I don't think i've ever seen this explained as clearly as this. The video is a joy to watch, great work!

[@razsamy4274]

A great way to explain not just the process of negative binary numbers but actually why two's complement is used.

[@Kokurorokuko]

Exactly!

[@zakariatalukdar2552]

My random opinion as a random person would be that: considering the fact that 1 is being subtracted from each bits. We end up getting it's negative version. But... Since the représentation is basically 1 less so after everything we have to add back this 1 that we have taken from. But that is not full fledged and doesn't explain the fact that we have taken 1 from each bit. But collectively add 1 and we get to the original result. It's odd fr. 🤷‍♂️

[@CastorTroy212]

This is far better explanation than the paid course at my university. Thank you so much.

[@TF2Gaming101]

Oh my gosh the two's compliment is beautiful and I realized this at 12:18 that -8 makes so much sense

[@Fera-gr5mm]

Especially because you have 4 bits so you can have 16 numbers. Given that 0 has no sign, you have to assign 1 more number to either positive or negative side.

[@swarnavasamanta2628]

It's not only -8 ;) when you have more bits the most significant bit is always treated as a negative value of the highest bit order. If you really compare the signed representation to 2s complement you'll find that the series just goes in reverse ;). And the extra negative number is there only because there is 1 zero

[@curie5312]

i didnt understand it until this timestamp thanks lol

[@adrianolariu3767]

A couple of years ago I had to learn those things for university, and I did, and got a good score, but due to the fact that I'm going to be a SW Developer that programs microcontrollers, I had to re-learn these things and watching this I've realised that I didn't understand the complement method the way I was supposed to. My teacher just told us to add 1 and that's it and now, after 4 years, I have finally understood why. You are awesome. I really hope a lot more students watch your videos.

[@tomc642]

Wow, best explanation ever. You explained it! In school they just say, here is the Two's complement, take it and don't ask why it works.

[@indjev99]

That moment when you find a great channel, but the last upload is 2 months ago. And then the next day 3 videos go up.

[@SpaceJesus25]

wat

[@akshanshkmr]

I never understood the need for 2's compliment before this video Thank you so much

[@gorillaau]

I have sat through a few bad explanations of what's going on here... probably due to the tutor/lecturer not understanding it themselves.

[@thepvporg]

Nice, you just said something that made sense. When I was in computer class in school, we were presented with a lesson on binary and it wasn't explained why these are one's or two's complement, just that is what they were called.

[@RetroHoo]

You are a hero in my book. Amazing how you present these video's, you keep it interesting and the build-up is just right. Keeping it interesting while teaching is important but I always think that making people feel smart while teaching is equally important. In my opinion you nail both.

[@user-kh8ez5si8p]

Thomas Cremers couldn’t have put it better

[@TechnoSan09]

most just teach that 2 step process for getting negetive numbers but u explained how that 2s complement steps works thats really genius you are amazing brother

[@nicholasantonini6730]

THANK YOU. I have been taught this by 2 instructors at a college. NONE of them simplified this like you did. IT FINALLY CLICKED!!!

[@YaroKasear]

Another neat property of two's complement is sign extension. In some architectures you'll often find yourself converting a number between sizes. So for example, we have a 4-bit number we want to resize to an 8-bit number. 1010 = -6 When we extend the sign, what this means is when we convert to a larger number, every added bit copies the value of the most significant bit from the smaller number. 11111010 = -6 This also works on positive numbers: 0100 = 4 00000100 = 4 The only drawback is ou have to make sure your hardware does not keep trying to sign-extend on an unsigned number. 1000 = 8 (Unsigned) 11111000 = 248 (Unsigned) Fortunately, the same hardware used to drive signed number behavior in twos-complement should be able to also ensure sign extension only kicks in when it's in use.

[@bluesillybeard]

O: my mind has been blown for the second time today

[@PhoenixClank]

I see a lot of people with blown minds in the comments, at the fact that the "sign bit" is actually just a negative-valued bit. I'm *so glad* I was taught it like this in university. It just fit right into my head. It made sense from day one.

[@hypergiray2225]

the realisation that 8's coulumn is actually -8's coulumn has saved me here. Thanks so much.

[@l6e6i6n]

i love how you explain everything bit by bit

[@Shockload]

I see what you did there

[@chrishadjipetris6059]

I remember at the digital logic lab when we had to design a 4-bit ALU that included logic AND, OR, XOR and add and sub, and with a 2-bit select signal we had to choose any one of the operations. As bonus, we had to build any other adder, except from ripple carry, display the result on a seven segment display in two digits and find a way to display the minus sign for negative numbers by using the third seven segment display and the negative numbers as positive ones next to the minus sign. I was the one who managed to do all these three, and I chose to implement a carry look ahead adder

[@willsi]

Wish I had found your videos earlier in the semester. You've been better in a few minutes than my professor all semester. Click comment, but very true.

[@darshanbilana5338]

Been searching articles for more than 30 mins and didn't find any good ones and later found this . Easy and clear explaination . Thanks a lot

[@szyszkienty]

You are definitely one of the best teachers I've ever seen. Your ability to give concise and interesting explanations that are in-depth, yet devoid of jargon and any unnecessary minutiae is truly marvellous! Thanks a lot for your amazing work!

[@alejskates2287]

I feel really smart now considering how my own professor refered our class to this video and in this video, you came to the same conclusion as I did when I realized that the negative numbers are just -8 + whichever positive number the remaining 3 bits represent.

[@DavidCourtney]

Glad to see this series continuing

[@samuelstermer6437]

I've watched several videos about twos complement and am in a CSCI 101 class where our professor explained it several times. This is the explanation that really landed for me. 10/10 would learn again

[@hanzofactory]

Was watching this to prepare for an interview, and it completely blew my mind, thanks!

[@vivekvijaykumar43]

I wanted to teach students how to solve pseudo-code and got stuck in bitwise operators. By far the clearest explanation of two's complement. Thank you, sir. I'll be teaching it exactly as you have done here.

[@RishabhKumar-bn4qj]

THIS IS THE BEST EXPLANATION EVER ! I LITERALLY LOGGED ON TO COMMENT ON THIS VIDEO. KEEP UP THE MIND BLOWING WORK

[@ayasswain]

The best explanation i have ever seen so far on 2's complement.

[@dnjj1845]

This is by far the clearest explanation on the topic I've ever come across, every digital design book needs to footnote you.

[@Longuncattr]

I'd never thought of the high bit in two's complement as meaning -(2^(n-1)) before. That's incredibly useful. Thank you so much!

[@randybobandy9208]

13:06 My professor always had us yell, "Flip those bits!" when talking about twos complement. :D Great video!

[@jmckinney0040]

You are the best! I needed to learn exactly this!! I searched found some other video didn't like. When I saw a video recommended in the sidebar from you I didn't even finish the other video. And you did not disappoint! You started exactly with what I understand and then proceeded to show the different ways to encode a negative number! Man soooo good. Thank you so much Ben!

[@linusporter1091]

Thank youuuuuu, this has been confusing me about *why* we do it like this, and your -8 (or negative MSB) trick really makes it go from "a nuisance but necessary" to "check out this cool trick".

[@Luiza-fy2og]

I've been desperately watching videos on yt trying to understand this but none of them could help me understand it at all. thank you very much for helping me w this.

[@Akahatoo]

I have to say, even if it's an older video, the way you teach stuff is a real eye catcher, simple to get and understand.

[@Wanttoknowabout]

Great to see that you are uploading videos again! I had been waiting for this. Your videos have been really educational. Keep it up!

[@bpccmath251calculusiihitch4]

First video of yours that I've seen. It was so great that I subbed immediately. GREAT explanation: short, simple, to the point, and, above all, it connects all the dots!

[@lefauteuilparesseux7328]

Thanks for the very clear explanation! I randomly looked for this information while having no background knowledge and you made it understandable to me.

[@shrinathbhoslay3014]

My university teacher never explained me like this. Thank you very much sir. This is the best explanation on 2's compliment.

[@gaiusjuliuscaesar9296]

This is probably the best explanation of twos complement I've heard. My professor completely glossed over the meaning behind adding 1 and it never made sense to me. Thank you.

[@ServitorSkull]

We went over ones and twos complement in my assembly class and had no idea why. Thanks!

[@julinization]

Where were you when I was in college? Awesome explanation

[@BloodAsp]

My class didn't explain this, so I jumped right to youtube, and knew your words would be the winner, wonderful explination, and many thanks!

[@osscar29]

Thank you so much for this explanation, I've been struggling with this on the coursera "nand to tetris" course, this is by far the best explanation I can find. cheers.

[@reblackened]

Just adding my voice to the choir Ben. I'm trying to learn assembly programming for the 6502, and yet again you've done a great job in teaching the fundamentals. Outstanding! Not just this video, but so many of them have been so helpful to me. I'm not as sharp as I used to be in my teens and I'm grateful for the pen and paper approach. I mean, if you can distil this sort of knowledge down to something that can be conveyed on pen and paper, it makes is so much more accessible to so many people. Just look at your video on the stack and stack pointer. Pen and paper! Thankyou for sharing your expertise with us all.

[@lazarus6983]

This video and the assembly to c code video might take the crown for most saved computer architecture exams😊

[@AlexBlack-xz8hp]

You’re literally my favorite teacher!!! Learned more about computer fundamentals from this series than years of searching around the internet

[@alexanderelea8032]

Your explanation is getting me through my circuits class, well done sir!

[@thecurious6721]

Thank you very much Ben. I read about twos complement several times and didnt understand the logic behind it. You explained it in 10 minutes. I cant explain how much I appreciate your work. Thank you! 🙏

[@lemtzas]

This is the first time this has ever made sense to me. Thank you.

[@tonyashworth1500]

I've been struggling with this concept for a long time, but your explanation has now made it very clear to me. Thank you.

[@dilby3246]

Incredibly helpful, thank you. We are learning this in my electrical engineering class, and you explain it so well.

[@bemep0k]

I kid you not, I think it's the best explanation on the internet. Thanks!

[@stephenesebre7908]

I don't know how to say thank you. You made this really simple. Some books and videos were driving me nuts ! God bless you man !

[@CrispyCircuits]

I was 12 years old with a Timex-Sinclair 1000 which did BASIC and assembly. I had problems understanding the binary math, but assembly was fun. I dabbled with assembly again a few years ago, which really clears up some subtle things about C programming. I still found the complements thing confusing. This video put things together in just the right way, explaining the three ways. It all makes sense now. You make very good videos. Thank you.

[@greatoutdoors6318]

I've tried to understand two's compliment before with no luck. This is the first time its made sense. Thanks!

[@almasabdrazak5089]

did university teachers leave so many dislikes because they are jealous how this guy easily explains hard concepts for free ?

[@majeebsharif6191]

You are a really good teacher, I studied electronics at college and this was apart of the course and the lecturer was no where near this level of explaining

[@user-gf2vz7tu1d]

Best video so far about the 1s and 2s compliment .I hope my tomorrows exam goes well thanks bud !!

[@passionableaira3]

Thank you so much for this video, I can see how much care you took to make sure the steps and explanations flow well and all the questions I've had were answered. I didn't understand this at all when I was in class! Thank you so so much!

[@leander11]

Thank you for these videos. I just started electronical engineering school and don´t always get everything right away, your channel really helps.

[@AAAAAA-es1rm]

This is the best explanation ever for 2s complement. It made me understand 2s complement and the other ways of representing negative numbers for my university course. The same goes for all your other videos which I use to revise for Electronics. I hope you upload more videos in the future with new content for Electronics Engineering and, if possible, in Maths and other Engineering areas. Thank you for this video.

[@ling6701]

best explanations on two complements I've ever seen so far, now I've got it. Thanks.

[@eternalblithe]

WOW. Thank you. This is the most helpful two's complement lesson I've ever seen. I finally understand.

[@arielkruger9547]

Absolutely FANTASTIC video. I finally am able to understand this concept that seemed so foreign to me just minutes ago. Thank you!

[@montexto69]

Unbelievable how good your explanation is. It makes it look so easy.

[@-303-]

This is a fantastic explanation. So clear. This is the best explanation I have seen yet on KZbin.

[@girlmath-abolisher]

Thank you so much for the video and your beautiful explanation. I have always 'understood' complements but never really been able to grasp the fundamental significance. This video changed that. Again, thank you!

[@expansivegymnast1020]

This is by far the best explanation of this concept on the internet. Thank you so much!

[@eldarmusayev7653]

I love that you started with a simple but incorrect version to show the progression of the idea

[@BK-tv4mw]

My electronics engineering/ logic and digital systems design teacher took 2 hours and still couldn't explain what this man explained in 13 minutes in clear details.

[@hakarali6289]

Yesterday night I was suffering so much because of this binary calculation,but thanks to you everything is going so well now. Hope to see more.

[@whenthethebeansstrikeback6728]

I've been having trouble and this cleared a lot of stuff up! And that -8 placement blew my mind!!

[@Mekinhumbel]

How lucky am I that I landed here on a cursory search of how negative binary numbers work? Liked and subscribed!!

[@stevenshumadine1887]

Very well done. You explain the concept so that it may be easily understood. Thank you for this video.

[@rothenbergt]

You are an amazing teacher. Thank you for these high-quality videos.

[@aldrineusebio192]

from this day onward, i will never tell myself im stupid, it's just a matter of what type of teaching and learning apply to me, YOUVE ANSWERED ALL THE QUESTIONS I HAVE IN MIND, THANK U SIIIIIRRRRRRRRRRRRRRRRRRRRR

[@nytr]

Thank you so much, you've made it very clear and explained why it works and showed us from what was it derived. It helped me understand this much better than other YT videos! Thank you again!

[@bonbonpony]

12:06 Wow! This is the first time I'm seeing someone assigning a (negative) place value to the sign bit, and it makes sense indeed! :o :D And I thought that I won't learn anything new from a two's complement arithmetics video. Silly me... :D

[@MozartJunior22]

This blew my mind. I wish I was taught this earlier

[@oussamaelhriki8160]

very wonderful

[@dragospahontu]

@@MozartJunior22 for real

[@ayushjindal4981]

Very nice...generally people explain how to take 1s and 2s complement, but dont explain the science or the logic behind it. Great Work!!

[@Kokurorokuko]

I finally understood why ones complement wasn't good enough and why twos complement was needed. Thank you!!

[@rangita2]

This is the best video on this topic that I found on KZbin. Going to send to my students -- thanks!

[@Handleme23]

Wow you made it seem so easy. Thank you for uploading and taking your time to do this!! You are awesome

[@juanmanuelllaury4912]

The best practical explanation I've seen on the subject. Thank you.

[@laureng312]

I love this video! Thank you so much for such a comprehensive step-by-step breakdown.

[@raminmdn]

Best explanation of two's complements so far. Really recommended for starters :) .

[@kentrothermel5242]

Thanks Ben, Great explanation of 2's Complement. This is a required session for anyone interested in IT, Automation, H/W, S/W, Data of any kind, etc!

[@kingshukcs]

My God...This video is revolutionary. Where did u learn all of this😮😮😮. This is just fascinating!!!

[@warecamel]

You did a better job at explaining this than the lecturer at my university, thank you.

[@nitishkushwaha3821]

So nicely explained, now I understand the whole story behind two's complement.. this video made my day. thanks a lot !!

[@grandhigayatri5501]

I have never seen such an amazing explanation sir!! Thank you

[@vicr123]

No one ever told me about the place value trick. Completely blew me away when you pointed that out 👀

[@kumarAjitesh]

Really this is the best video in youtube for understanding 1's and 2's complement. Love from India.

[@deqnski890able]

Thank you so, so much... I was reading my lecture and it was so confusing... Less than 14min later, your video makes everything so much clearer. Thank you

[@codewaz]

Video time: 12:15 To get the value (decimal numeral) of "looks like a sign bit" immediately, do this calculation: -(2^(n-1)) Where n is the number of bits you have. For example: If you have 16 bits, the calculation is: -(2^(16-1)) = -32768 Video time: 12:48 An easier way to get a negative value from a positive one, is to flip all the numbers starting from "looks like a sign bit" until you get to the last 1, leave it as a 1 (don't flip). The rest of the 0's after the last 1, leave it as a 0 (don't flip). 3 examples all in eight bits: A) 10 is 00001010 , so to get -10 in eight bits is 11110110 B) 20 is 00010100 , so to get -20 in eight bits is 11101100 C) 56 is 00111000 , so to get -56 in eight bits is 11001000

[@abdulazizmohammed7715]

This has helped me to implement a binary indexed tree efficiently. Thanks!

[@saykharng]

Thank you! Ben, your explanations are beyond awesome.

[@rsalehin]

Very well organized and well-thought presentation. Thank you very much!