Binary Addition and Subtraction With Negative Numbers, 2's Complements & Signed Magnitude

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  • Опубліковано 25 гру 2024

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  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +23

    Binary - Free Reference Sheet: bit.ly/3CkOHhB
    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections

    • @femijames3389
      @femijames3389 10 місяців тому +2

      Please can anyone give the reason why he use 5bit for the -7 in the sign magnitude😢🙏🏼.
      I don't get that aspect.

    • @sylviabryan3164
      @sylviabryan3164 7 місяців тому

      The question may ask for that​@@femijames3389

    • @Imperator_27
      @Imperator_27 5 місяців тому

      ​@@femijames3389 Because he wanted to keep the same number of bits also for -12 and -15 in the demonstration. So he chose 5 bit and not 4 bit

  • @littlebuster07
    @littlebuster07 4 роки тому +1145

    You are God's gift to students with professors who either don't speak good english and/or they don't teach the subject this well. I feel like my time in class is a waste of time and you are my real teacher. Bless you, brother

    • @bobross3880
      @bobross3880 2 роки тому +17

      Unfair comparison. It’s a thought out, planned video. Giving lectures in real time when people have questions and/or don’t get it and can’t pause to think is nothing like a video.

    • @littlebuster07
      @littlebuster07 2 роки тому +47

      @@bobross3880 🧢

    • @gingee_8186
      @gingee_8186 2 роки тому +9

      My college teacher is just an arse (hard r) so I don’t ask him any questions and go online to learn.

    • @masonp1599
      @masonp1599 2 роки тому +1

      Ditto

    • @scared3267
      @scared3267 2 роки тому +2

      @@gingee_8186 same here 🤐🤐

  • @latedeveloper7836
    @latedeveloper7836 3 роки тому +801

    0:30 Worked example 1 - Writing -6 as a number using the signed magnitude method (4 bit binary)
    1:55 Worked example 2 - Writing -7, -12, -15 using the signed magnitude method (5 bit binary)
    2:43 Converting +7 in binary to -7
    6:00 Expressing negative numbers using the 2's complement method
    7:25 How to check your negative binary calculations in 2's complement
    7:48 Worked example 3: -12 as a binary 2's complement number
    9:50 Binary subtraction 2 ways - subtraction and 2's complement
    12:05 2's Complement Subtraction
    12:55 Changing +25 into -25 using the 2's complement method
    15:30 What to do with a carry over / overflow number
    16:34 Worked example 4: Subtracting 2 binary numbers
    18:45 What to do when you can't borrow
    19:52 Subtracting with the 2's Complement Method (by adding!)

  • @keivanipchihagh2115
    @keivanipchihagh2115 4 роки тому +388

    This is the equivalent to the 3-hour lecture my professor gave. Great Job!

    • @foreverseethe
      @foreverseethe 3 роки тому +11

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    • @DarcMagikian
      @DarcMagikian 2 роки тому +28

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    • @egyptianplanner
      @egyptianplanner 2 роки тому

      The same without understanding alas ..untill I find this video

    • @ethanholmes5677
      @ethanholmes5677 2 роки тому +3

      Same for me. 2 hours condensed into a half hour. Watched at 2x speed, it becomes 15 minutes.

    • @kithenry
      @kithenry Рік тому

      Keivan my boy, i taught and you said you understood.

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    @learntoearn6612 5 років тому +118

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  • @user-du9zt5rp5x
    @user-du9zt5rp5x 3 роки тому +35

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    @GamerTheTurtle 5 років тому +1513

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      @flimflam6652 4 роки тому +92

      Doing the pre-research before making a video and an inherently good memory would likely do it

    • @DearHRS
      @DearHRS 4 роки тому +26

      there you go now you have (1000000)2 numbers of likes :(11)2

    • @brandonhughes645
      @brandonhughes645 4 роки тому +20

      Years of intense study after high school does the job. And revision before the video.

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      @jean-marcndongekouaga5267 4 роки тому +23

      interest is probably the answer

    • @MDMD007
      @MDMD007 4 роки тому +9

      tutor for a reason

  • @mariaanica8412
    @mariaanica8412 4 роки тому +32

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  • @Nic-of1sr
    @Nic-of1sr 4 роки тому +61

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    • @femijames3389
      @femijames3389 10 місяців тому

      Please can anyone give the reason why he use 5bit for the -7 in the sign magnitude😢🙏🏼.
      I don't get that aspect.

  • @belalkasem4140
    @belalkasem4140 3 роки тому +6

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  • @imahopeime509
    @imahopeime509 4 роки тому +8

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  • @TSanya98
    @TSanya98 2 роки тому +3

    I solved a past paper question using your method of calculation it’s 3:46 am and I do pray I ace my exams thank you so so much

  • @zibusisondlovu5577
    @zibusisondlovu5577 3 роки тому

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  • @mikatch8067
    @mikatch8067 3 роки тому +11

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  • @brendanbuckley13
    @brendanbuckley13 4 роки тому +175

    This was explained wayyyy better than how my professor did. Thank you so much lol

    • @AMF884
      @AMF884 4 роки тому +2

      i was thinking the same thing , those so called Pro.Dr. they tryna make my Life harder than what it already is !!!

    • @User-ow7rn
      @User-ow7rn 3 роки тому

      really? if you understand very well then help me with this.
      ////
      i did not understand what you wanna prove. at 3:26 you said -ve of +ve number can be done just by replacing leftmost 0 as 1 but at 13:35,you are saying that leftmost value of 1 as -64 and calculating other 1s as resmebling bits in positive, but if we apply that rule at 3:26 for -7 (1 0 1 1 1) then we will be -16+4+2+1=-9 instead of -7

    • @huzibutt4410
      @huzibutt4410 2 роки тому

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    • @eccrowy
      @eccrowy 2 роки тому +3

      @@User-ow7rn its been 11month but im still going to reply it anyway. These two that you stated are different thing. Binary at 3:26 is signed magnitude whereas binary at 13:35 is 2's complement.

    • @adithyadavidm
      @adithyadavidm Рік тому

      ​@@eccrowyglad you responded...that's right both are different representation

  • @yogitanaulakha4603
    @yogitanaulakha4603 3 роки тому +1

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  • @learntoearn6612
    @learntoearn6612 5 років тому +58

    Please sir make for us a Fourier series video
    You're our teacher

    • @MTMT_HITHESHNAIK
      @MTMT_HITHESHNAIK 4 роки тому

      and also laplace transform and its inverse. please

  • @ninminion
    @ninminion 4 роки тому +18

    As always, you have a great way of breaking the concept down and explaining it so that it just seems like common sense. I recommend you to everyone I meet. You are my go-to guy for everything math, science, or logic related. Great job... again!!!

  • @ianobi2842
    @ianobi2842 5 років тому +14

    thanks to u, i did great improve at the night right before the final exam. love u so much.

  • @aribakhalil3195
    @aribakhalil3195 3 місяці тому +1

    this dude explained in 20 mins what my prof couldn't in 2 hours

  • @sukesukieatmyheart
    @sukesukieatmyheart 4 роки тому +12

    I really appreciate your teaching, cause it helps me go through every subject that I don't understand. And thank you very much for teach me.

  • @hamzahhamdoon5453
    @hamzahhamdoon5453 Рік тому

    i missed my 2's compliment and sign nd magnitude lesson and i was strugglin so much. this guy saved my life

  • @charpad6690
    @charpad6690 3 роки тому +2

    Thank you for the info at 9:38; I could not understand how to do -7 +(-5) in 2s compliment until you showed that you just do the sign bit (-16) + all the ones.

  • @grawlix4419
    @grawlix4419 3 роки тому +1

    I cannot even express how much this channel has helped me...

  • @Chainless_Slave7
    @Chainless_Slave7 2 роки тому +49

    If you need to convert a binary number to its two’s complement form, you can use the
    method indicated by the video but there is a quicker method. For this you start at the
    least significant bit and move left ignoring any zeros up to the first 1, which you also ignore.
    Change any remaining bits from 0 to 1 or from 1 to 0.
    For example, expressing the number 10100100 in two’s complement form leaves the right-hand 100 unchanged, then the remaining 10100 changes to 01011, so the result is 01011100.
    ------------------------------
    Edit:
    For negative numbers,
    Convert the positive version of the number to 2's complement and then, just add a "1" to the right of the most significant bit.
    Just adding 1 converts a two's complement to negative. DONE!
    Example:
    2's complement of 12 ----> 0100
    2"s complement of -12 -----> 10100
    See there is an extra 1 at the right end.
    -------------------------------------------
    Extra note:
    While 2's complement of 12 is 0100, it can be written as 0000000000100, u can have many 0s at the right end
    But for 2's complement of -12 is 10100, you cannot write it as 0010100, u gotta write it like 1111110100.
    See what I did there?
    1 is the default right end of negative binary numbers,
    0 is the default right end of positive binary numbers
    ( talking in terms of two's complement)

    • @andreamazzai1969
      @andreamazzai1969 2 роки тому +5

      Thank you, great trick

    • @aadityapradhan5694
      @aadityapradhan5694 Рік тому +1

      I might me wrong but this trick may not always work, like for example -12
      12 in binary 1100
      using the trick it would be 0100 but the actual 2's complement would be 10100 which would be the result using this trick if you write 12 as 01100.

    • @Chainless_Slave7
      @Chainless_Slave7 Рік тому +1

      @@aadityapradhan5694 Well, same process for negative numbers but you add a 1 to the right end of two's complement of 12. Thanks, I have now added this step for negative numbers to my original comment

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    @arnavajitbordavekar5071 2 роки тому +1

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  • @AmahGivenz
    @AmahGivenz 7 місяців тому +2

    This video has transformed my understanding in just 25 minutes. Thanks alot😊

  • @lyons2547
    @lyons2547 2 роки тому +1

    BEST UA-cam TEACHER EVER...God bless you. Wherever you are.... you’re really making computer science easier for me 💕💯🔥🔥🔥

  • @teatea_.3801
    @teatea_.3801 Місяць тому

    Your videos helped me understand all of number system in a day , absolutely amazing work man.Couldn't thank you enough.

  • @smoshfann24
    @smoshfann24 3 роки тому +10

    A helpful tip for finding the 2's compliment: flipping all of the bits and then adding 1 is the same as starting from the rightmost 1 and flipping all the bits higher than that.

  • @Dukebozo
    @Dukebozo 3 роки тому +1

    You’re gonna be a legend we will speak about you how you got us through school forever

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    @hreigi14 2 роки тому +5

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  • @kevinochola3984
    @kevinochola3984 6 місяців тому

    You are a gem ,God sent ,my professor could not explain for me this to understand thank you so much

  • @samanthapennington4232
    @samanthapennington4232 8 місяців тому

    This is brilliant. I was teaching this and then watched your video and when we got to the -8 + 1 = -7 and -16 + 4 = -12 I was OMG this much easier than the way I was trying to teach it.

  • @arahani2409
    @arahani2409 4 роки тому

    you help me a lot right now, my lecture just teach me using slide and the other day the lecturer give me exercise, its my first time learn sign magnitud,two's complement, i dont understand because the lecturer dont do some handwrite on how to do this, just show the slide make me dont know how to do it, and cant imagine how to calculate it and make me really stress......thank you so much for helping me alot!!!!!!!!

  • @drunkboi5887
    @drunkboi5887 4 роки тому +2

    dude u r a god sent, thanks to you i can pass my infrastructure classes in uni

  • @tinashelionelchenyika5612
    @tinashelionelchenyika5612 2 роки тому +1

    Thank you so much kind sir l have never got a chance to understand this concept until today. May God bless you with more knowledge

  • @mohammadahnafhuq9364
    @mohammadahnafhuq9364 2 роки тому +5

    Nice Job! You made two's complement way easier than the way my teacher taught me :)

  • @jasmencolinares8071
    @jasmencolinares8071 3 роки тому

    Just want to say thank you very much for your videos. I learned a lot. Our instructor didn't bother to discuss this topic to us. You're an angel sent from heaven 😊

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    @kev.j.goodwin8612 Рік тому

    I wish I'd had you as a maths teacher at school in the early 1970s. Your explanations are great for those of us who are not natural mathematicians - wasted so much time with 'teachers' who really couldn't put the subject across.

  • @LeiaKitsune
    @LeiaKitsune 3 роки тому +2

    Thank you so much. My teacher didn't explain everything clearly like you did and I was so confused but you saved me 😪

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    @kaberaclapton783 3 роки тому

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    @johndent8653 Рік тому

    I have taken multiple classes dealing with binary arithmetic and this provided me with a better understanding about it thank you so much

  • @TheseOfWe0112
    @TheseOfWe0112 11 місяців тому

    No matter what math I look up, you have a great video for it! Thank you!

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    @realknight9562 3 роки тому +6

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    @haddachannel6228 2 роки тому

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  • @oceanmoyo3966
    @oceanmoyo3966 4 роки тому +1

    chaaai you are heavenly sent what my college lecturers couldn't explain in two weeks ,you finish in less than 30 mins ,thank you so much,i have an exam tomorrow and i know i have passed...please make tutorials on mechanics as well especially circular motion

  • @rimjhimsingh703
    @rimjhimsingh703 4 роки тому +22

    How do you know 6 is 4 bit and 7 is 5 bit ? Like how do you decide which number to replace in signed magnitude method?

  • @paul8920
    @paul8920 2 роки тому

    Wow!!! You are the Bomb!! You taught me what I could not learn in my four years in the university in just few hours. Thank you

  • @jackwho6085
    @jackwho6085 4 роки тому +1

    This guy is a legend! Way better than my teacher at teaching. Love your videos dude

  • @thepixelgamer3d913
    @thepixelgamer3d913 Рік тому +1

    9:11 video, Theres a shorter way we can do it, like consider the last digit of the 5th bit as "-16" and then just do regular algerba, i.e -16+4= -12 , SO set "16"and "4" as "1" and the rest "0" since we didnt use others. IN BINARY it will be 10100 . TRY THIS!

  • @iambored.k.
    @iambored.k. 5 років тому +28

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    @mahmoudwahman8110 4 роки тому

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    @devrajparida828 4 роки тому +1

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  • @aries3690
    @aries3690 3 роки тому +1

    Thank you so much! Your examples finally helped me understand how the first bit form the right is the least significant bit! It's the carry!!!

  • @nathanreed2087
    @nathanreed2087 Рік тому

    7:18 I was so confused as to why me negative results were so huge. But now that you mention the most significant bit being negative and all the rest positive, they add up to the correct decimal result, so I haven’t been doing it wrong

  • @cordelldev
    @cordelldev 4 роки тому +5

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    @ricardobarnes9232 Рік тому

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    Thank You! Keep Going, learnt a lot ....................studying at Computer science faculty.

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    @ArshdeepSingh42108 Рік тому +1

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    @rajveerslife1923 Рік тому

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  • @anastasiamartinez9526
    @anastasiamartinez9526 4 роки тому +1

    Dude thank you!! You are the first person who explained why the twos complement makes it a negative number!!!! Very happy girl thanks!!!!!!!!

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    @khonzaizzati4836 4 роки тому +2

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    @theburntwaffle7390 3 роки тому +1

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    @davidnguyen7785 2 роки тому

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    @abhivaryakumar3107 2 роки тому

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    @asherb5134 3 роки тому +1

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    @triplet8248 10 місяців тому

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    @ramanrazdan5894 5 років тому +3

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    @landonscott4347 5 років тому +7

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    @AbhishekModak-zw7fh 3 роки тому +1

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    @yawcoder 4 місяці тому

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  • @quosswimblik4489
    @quosswimblik4489 4 роки тому +1

    you can also flip in parallel bitwise to it's bijective form and you can deduce certain things in parallel and make many more deductions about numbers.

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    @kekoHere0610 3 роки тому +1

    Thanks a lot. why can't our professors teach us this well. Thank you .

  • @SakatzuCat
    @SakatzuCat 2 роки тому +1

    Oh my god when I understood the 2's complement.. You seriously are a lifesaver, thank you so much!

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    @shishirthapa4167 3 роки тому +1

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    @amardeepvishu7523 Рік тому

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    @Benbeckmann3739 Рік тому

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    @goldenffshorts 2 роки тому +1

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    @Vladimir_Nzeke Рік тому

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    @ajiboladamilola4311 Рік тому

    I had been looking for the Mr chemistry video on the 2's complement. I'm so happy I know it so well now.

  • @VishnuprabhuR
    @VishnuprabhuR Рік тому

    This was the best video for bitwise operation. Thanks Bro.

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    @revanthjayakumarkannan137 Рік тому

    i spent 6 god damn hours listening to my teacher rant on and on about 2's compliment for 2 hours and 40 minutes and this guy though me this stuff in like less that half hour.

  • @znoran
    @znoran 2 роки тому +1

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  • @TechLord79
    @TechLord79 2 роки тому

    Great video! Now it clicked why they say in floating-point that for negative numbers, leading 1s are like leading 0s for positive numbers - they're superfluous! As a 6-bit number 10 0100 is also -28!!!

  • @mirzapurrailways007
    @mirzapurrailways007 3 роки тому

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    @CarlC9898 5 років тому +12

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    @NicoDeInfluencer Рік тому

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  • @bhavana1186
    @bhavana1186 10 місяців тому

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  • @Muhammad_Waleed
    @Muhammad_Waleed 2 роки тому

    7:15 Can't explain how awesome this technique feels🔥
    Maybe because it's 5:21 in the Morning

  • @503Squash
    @503Squash 2 роки тому

    you are the best in this youtube
    i really benefited from you

  • @mustafare9729
    @mustafare9729 5 років тому +13

    There is a very easy way of taking 2's complement.Start searching for the first 1 from right side of the binary number.As soon as you found that 1, change(the opposite) the numbers left on it's left side.
    example:
    0011001100
    2's complement version is: 1100110100

    • @user-hq4zk6eg5n
      @user-hq4zk6eg5n 4 роки тому +1

      Thats the 1's complement in
      2's complement you need to add a 1 to last digit

    • @gouthamtadali5072
      @gouthamtadali5072 4 роки тому +1

      is there another easy way of taking 1's complement...funny
      simply take 0 as 1 and 1 as 0....as simple as that...
      by the way, you are talking about 1's complement.
      in 2's complement, add 1 to LSB of 1's complement.

  • @patmula9504
    @patmula9504 4 роки тому

    You are a living savior

  • @nordinzaidi2286
    @nordinzaidi2286 2 роки тому +1

    Lifesaver man! Greatly explained.