Binary Subtraction using 2's Complement

[@kelseywhite1333]

You explain things so clearly that my professor can't even make clear in a 3 hour lecture. I was so confused about aspects of digital logic but now I understand after watching some of your videos, thank you so much.

[@asishcodes]

Fr he does

[@aakashnailwal2249]

@kelseywhite1333 holy shit ! sweety where you from ?

[@amjad6361]

as always Saved my time after hours of researching

[@tarqabdullah1954]

اهلييين سعوديين في كل مكان ماشاءالله

[@FatimaMohammadAbid]

i was so confused about the subtraction using 2s complement but your video was so excellent that now i able to solve properly.You explain much better than my teacher,Thank You:)

[@arp1001]

thanks a lot for this ... everyone had complicated this so much... but u really helped me to clear my concepts.... it helped a lot for my exam...

[@RahulMadhavan]

To clarify bit further on what sir mentioned at 05.30, the addition becomes simplified when we assume 5 bit number system (as representing 9 in 2 complement notation needs 5 bits - the 4 bit range is from [-8, +7]) A = 01001 = 9;B = 00100 = 4; Y = A - B = A + (-B) = 01001 + (-00100) = = 01001 + (11100) = [1]00101. In this notation, the overflow bit (in the square bracket) can always be discarded and the sign of the most significant bit shows the sign of the number. 0 means positive and 1 means negative ---- Just as a check, B-A = 00100 - 01001 = 00100 + (-01001) = 00100 + (10111) = 11011 = -(00101) = -5 ---- (i) Check minimum number of bits required (ii) Convert everything into 2s complement notation in those number of bits (iii) Add -------- In this way, overflow only happens when MSB of the two numbers added is the same, and they are of opposite sign to the MSB of the result obtained.

[@alinasrollahzadeh7610]

OH MY GOD, ARE YOU PROFESSOR YOU? YOU EXPLAINED THIS THING IN 30 SECONDS WHILE I CAN'T EVEN LEARN IN 3 MONTHS IN LECTURE CLASS I THOUGHT I'M STUPID

[@animesan3687]

Me too😌

[@yama_tv_69]

My book has given the link of this video

[@animesan3687]

@@yama_tv_69 wch book?

[@yama_tv_69]

Computer for you with AI

[@lokenath3810]

ye sab asan hai but bohot practice ki jarorat hai nahi to bhul jata hu

[@Amisha-nt4vu]

Thank you Neso Academy 🌟 Your presentation was amazing! Take a bow!

[@amirghorban2044]

for 3rd problem i think --> (+15) in 5-bit = 01111 so now (10110) -(01111) = 00111 in simple binary substraction means(A-(+B)) and with methoad two means (A+(-B)) you should sum 10110 with (-15) so (10110)+(10001) = 00111 so with two methoad +7 in 5-bit is 00111

[@ONLY_GAMER2.0]

Yes 👍🏻 right same ans

[@sayandip2]

Really amazing u r sir I nearly completed everything for my digital electronics from your lectures sir Thank u sir

[@diyadey1654]

Can you say the answer of the question given below? -8-4=-12. I cannot perform this substraction by using binary 2's compliment Using the method which sir told.... Kindly if you can pls solve it

[@thomasw.eggers4303]

The video is very good. I thought I could add some details for the truly nerdy, and for those who have an interest in how computer hardware does binary arithmetic, particularly subtraction. If you are new to binary, I suggest you skip this posting. There needs to be a way to represent negative numbers. There are three common ways: (1) Sign magnitude (2) One's complement (3) Two's complement; this is by far the most common, and the description follows: All of the explanation will be given assuming 4-bit words. Extending the description to 32 bits (or n bits) is left as an exercise for the reader. (LOL, don't you just hate it when instructors say that?) The 4 bits have the weights: -8, +4, +2, and +1. Note: --- Only the left most bit (the sign bit, the most-significant-bit MSB) has a negative weight; All the other bits have positive weights. --- If you set any bit to a 1 (except for the sign bit), the number becomes more positive (or less negative). --- The zero value is represented by 0000 --- All ones, 1111, has the value -1. (Since -8+4+2+1 = -1). To get the negative of a number (that is, to get -N given N), the rule is "complement all the bits and add 0001". First, define the bit-complement operator ~ to be: "Change each 1 to a 0 and each 0 to a 1". Examples: ~0000 = 1111, and ~1111 = 0000 ~0001 = 1110 ~1010 = 0101 Proof: note that N + ~N = 1111 = -1 Example: 0101 + ~0101 = 0101 + 1010 = 1111 = -1 Rearrange: ~N = -1 - N Rearrange: ~N + 1 = -N Finally: -N = ~N + 1 (QED) Examples using the complement+1 negation rule: +1 = 0001; -1 = ~0001 + 1 = 1110 + 1 = 1111 -1 = 1111; +1 = ~1111 + 1 = 0000 + 1 = 0001 +5 = 0101; -5 = ~0101 + 1 = 1010 + 1 = 1011 -5 = 1011; +5 = ~1011 + 1 = 0100 + 1 = 0101 0 = 0000; -0 = ~0000 + 1 = 1111 + 1 = 0000 (Notice: negating 0000 results in 0000.) And finally, negating twice returns the original number, a requirement. Now any two numbers, positive or negative, can be added or subtracted. To subtract a number, first take its negative (using the complement+1 rule given above) and then add. NO "BORROWING" IS EVER NECESSARY. The subtraction method used by hardware inside a computer CPU is: Change the subtraction problem to an addition problem (by negating the subtrahend using the complement+1 rule), then add, propagating the carries right to left. Note that the longer a computer word is, the more carries need to be propagated. The time to propagate the carries is proportional to the length of the word, O(length), which is slow for long words. There are "carry skipping" methods which reduce the carry time to O(log(length)), but these methods are another topic. Addition and subtraction can cause the integer overflow exception: -- If two positive numbers added result in a negative (MSB=1) sum, overflow has occurred. -- If two negative numbers added result in a positive (MSB=0) sum, overflow has occurred. Adding a positive number to a negative number never results in overflow. The negative of 1000 (= -8) results in 1000 and overflow, since the largest positive number is 0111 = +7. In hardware, it is easy to calculate overflow by looking at the carries into and out of the MSB: Overflow = ExclusiveOR(CarryIntoMSB, CarryOutOfMSB). Note that there is always a "strange" number for any of the three number systems: --- Sign magnitude has the number 1000 = 0000 (-0 = +0) since the MSB is the sign and has no value; there is no +8 or -8. --- One's complement has the number 1111 = 0000. Again, -0 = +0, and there is no +8 or -8. --- Two's complement has the number 1000 = -8, but there is no +8; the largest positive number is 0111 = +7. Two's complement has the "strange" number in the most out-of-the-way place, so it rarely causes a problem. The other two systems have the "strange" number at zero, which causes all-to-frequent, and unexpected, computational difficulties.

[@charangowda4586]

thank you, very concise and to the point.

[@aakankshanidhi4989]

1) 0010 +ve in true form 2)1001 -ve in 2's complement form 3)00111 +ve in true form

[@nishantpandey5435]

In 2nd question the final ans is 0111 right?

[@snehilgupta6201]

@@nishantpandey5435 no it's 1001 only!

[@nishantpandey5435]

@@snehilgupta6201 ok i got it....brother...🤟🤟🤟

[@anushamm7403]

@@snehilgupta6201 How? I got 0111

[@anushamm7403]

@@snehilgupta6201 How? I got 0111

[@tawseeftaher9109]

summary of process is: 1) do 2's complement on the 2nd number. 2) then add 1st number and 2's complement of 2nd number 3) if the result's sign bit is 1, then the result is positive. Ignore the sign bit, we get our answer If the result's sign bit is 0, then the result is negative. Ignore the sign bit, do 2's complement on remaining part. then, we get our answer

[@trishaseal7782]

thanks!

[@ArnavVerma-oy4dc]

no we don't do 2's complement in second case, thats just to check our answer

[@anushapoojary4709]

Tq sir for this video I understood clearly your explanation is very good tq so much👍

[@Alexander-zc2ju]

Thanks for the great videos. Very informative.

[@divyaanshuagrawal3383]

Thank you so much! Amazing lecture!

[@JenilSoni-qj7yx]

thanks for providing knowledge to teachers

[@MK2EA]

Saved my ass for the exam thanks! You may have an accent but you explain very well with good a good structure!

[@anonymous-404]

MK2EA if you're really concerned with his accent, I believe you have seen a strong accent. His speech is very clear for a non native speaker

[@amnaiqbal8016]

Really an amazing way of explanation

[@amitanand0310]

3rd problem You can't represent 1111 (15) in 2's complement just by 4 bits. So, make it 01111 --> 1's complement --> 10000 --> 2's complement --> 10001 Now, A + (-B) = 10110(22) + 10001(-15) = 100111 --> MSB discarded for the same logic --> 00111 (7)

[@anshuldhok3407]

Thanks bro

[@theb4stguy332]

Why do we convert 1111 to 01111 at start?

[@fatimatuzahra8945]

@@theb4stguy332 because A is a 5 bit number and B is a 4 bit number, therefore to convert B into a 5 bit number, we add up the zero to the extreme left

[@theb4stguy332]

@@fatimatuzahra8945 👍

[@LakshyaGaming_mcoc]

No this method is wrong you have to take direct 2's compliment or else you would get stuck in 2nd problem where also (1110) is 14 so according to your approach (0111) -(1110) taking 2's of 14 will be 10001 Then adding you will get 11001 which is +ve 9 which is wrong ❌ As 0111(7) -1110(14) = -7 not +9

[@rikhilkulal122]

I had a doubt with another channel video but u cleared it thank you kal Mera exam hai🙃

[@myonlynick]

9:30, a practical example? x'y'z + xyz'

[@amayraarya]

You are amazing........ ❤

[@ARMWRESTLIN273]

Fillnaly ❤❤❤❤ thanks sir I searched whole day

[@soumo3464]

Always the one stop solution 👍

[@UECAshutoshKumar]

Thank you sir

[@toptech6913]

neso academy is the best

[@harshitha6160]

1) 0010 2) 1001(2's complement of 7) 3) 00111

[@gauravkumar-ff8gu]

2nd answer in incorrect take 2's complement of 1001 because the sign bit is 0(5th bit)

[@achchhelalgupta3176]

0111 + 0010 (2's complement of 1110) --------------------- 1001 ( now as there is no carry the result have to be converted in 2's complement form) ---------------------- hence the 2's complement of 1001 will be +7 i.e 0111. for 3rd question could you explain me ...

[@sandeepkumar7357]

@@achchhelalgupta3176 for 3rd ques answer is 00111 B is 01111 2's of B will be 10001 10110 +10001 ------------ 100111(final carry is one ) so neglect 1 answer will 00111

[@amankarn3025]

Its only 1001 or 10010

[@shikharashish7616]

@@sandeepkumar7357 thank you , i was confused in 3rd question as i didn't add extra 0 for B at the MSB

[@adamamaral5949]

1) 0010 (utilizes overflow discard) 2) 1001 (-7 because 2s comp = 0111 +7) 3) 0111 (utilizes overflow discard)

[@adamamaral5949]

S M yeah I was always confused with questions like this one. if u left it as -7 or put it back to +7?? I just looked at the original question. 7 - 14 = -7, hence why I left it in its 2s complement form (1001)

[@utkarshshukla231]

Are you sure for 3) ?? 😬

[@NicolastheThird-h6m]

3) and 2) is switched

[@gojosatoru2005]

​@Anirudh I don't think so I have the same answer too

[@akimchili7103]

i) 0010 ii) 1001 and (1001)2= -7 iii) 0111

[@ayushpattnaik3977]

Last one should be in 5bit

[@AmanGupta-fe8jk]

3.10111

[@komalkumari-mu2qu]

3) 00111

[@bubunmazumder]

1.0010 2.0111 3.01001

[@snehashishbanerjee2575]

My last ans is coming out to be (00111)₂

[@cyberdyers]

when you use 2's comp. Expect an overflow.

[@MrAlbashiri]

thank you very much for the amazing video. you are the best

[@VictoryVidya]

Thank you sir helping me this subject

[@laundrybasketmemes]

nice video it really helped me out

[@sanjeevanibhandari5652]

1. 0010 2. -0111 3. 0111

[@spmsheikh8192]

mrs 3rd one is wrong

[@JakVah]

Im pretty sure Ex2 is wrong. Using the 2's complement representation, 0110 in binary is equivalent to +6 in decimal, while 1011 in binary is equivalent to -5. So in deicmal number system, the task is to perform the following subtraction: +6 -(-5) = 11.

[@serendipitous5497]

Task is performed as6+(2's comp(5))=-11

[@aadhiyanth5969]

thank you neso

[@Quenchedfooty]

You are a savior

[@suheladesilva2933]

Thank you so much.

[@siddharthashome3890]

When we get -5(right) in last qs. Then why are we doing 2s' complement again to get +5(that is wrong)?

[@neeharbindu6564]

Ans:- (1) 0010 or 2 in decimal (2) 0111 or (-7 ) in decimal (3) 111 or 7 in decimal

[@sahilprasantachoudhury911]

2nd ans wld be 1001

[@ZOZO-px9qh]

​@@sahilprasantachoudhury911 exactly how do these wrong answers get all these likes XD

[@LakshyaGaming_mcoc]

@@sahilprasantachoudhury911 no it's should be 0111 only and here it represents -7

[@dharmikmistry8781]

Thank you 😊 sir

[@uniqueversalunicorn2412]

Thank you dude

[@hemasaini3380]

I'm starting ❤️ with you now 😁

[@HelloWorld40408]

Thank You SIr

[@voice6905]

1. ans = 0010 2. ans = 2's complement of 1001 is 0111 3.ans 00111

[@8bviews91]

3 rd is wrong

[@8bviews91]

and 2nd also

[@guliyevshahriyar]

thank you very much

[@tahmeenafirdous5626]

@3:00 sir how come is the result positive if the carry is 1? .. That has to be negative then no? Please explain

[@vedasiva695]

this is exclusive for two's compliment method. Not taken in general .

[@BenardOnchieku-ny5qc]

Using 2's complement (0110)2 -(0100)2 =0010 and (0111)2 -(1110) =1001

[@wubethiopia982]

0 sign bit indicates a positive number and 1 indicates negative

[@aqilahfedurailahi9496]

Sir I have a question, if A - B = A + (-B). Then what about A + B ? is it the same like the A -B formula ?

[@SrcasmMy2ndLang-IsMyXid]

A - (-B)=A + B

[@mdnawabali8992]

Subtrsction (5 and 5) by 2's compelement.

[@Subhasish3030]

12:12 the answers are ----------------------- 1) 0010 2) 0110 (-ve) 3) 00111

[@mohamadm7648]

Let me make your lives' easier: Subtraction with Complements The direct method of subtraction taught in elementary schools uses the borrow concept. In this method, we borrow a 1 from a higher significant position when the minuend digit is smaller than the subtrahend digit. The method works well when people perform sub- traction with paper and pencil. However, when subtraction is implemented with digital hardware, the method is less efficient than the method that uses complements. The subtraction of two n‐digit unsigned numbers M - N in base r can be done as follows: 1. Add the minuend M to the r’s complement of the subtrahend N. Mathematically, M+(r^n -N)=M-N+r^n. If M > or = N, the sum will produce an end carry r^n, which can be discarded; what is left is the result M - N. If M

[@santhipriyapriya9828]

Thank you...

[@nour_780]

Thank youu so much

[@charchechiragke]

Hw: 1) 2 2) -7 3) 7

[@oviya.n1317]

U said the carry leads to overflow but u add a 4 bit number which doest fall into that range. Sir actually we are dealing with signed numbers so 1001 is a negtive number so we should not guess the number directly and take 2's complement . So 1001 is -7 and 1100 is -4 and subtrating them we will get -3 101 or 1101 right?

[@snehashishbanerjee2575]

🔴 H/W Problem 1: ✔️ ans: (0110)₂ - (0100)₂ = (0010)₂ ............................................................... 🔴 H/W Problem 2: ✔️ ans: (0111)₂ - (1110)₂ = (-0111)₂ ............................................................... 🔴 H/W Problem 3: ✔️ ans: (10110)₂ - (1111)₂ = (00111)₂ ...............................................................

[@olaayman1900]

thank you

[@chandanaapriya]

If carry is 1 out put should be negative right

[@Statusking-vp6xw]

1. 1 0010(+2) 2. 0 0111(-7) 3. 1 00111(+7)

[@Yavi609]

Same

[@muzammalhussain4887]

1-0010 +ve 2-1001 -ve 3-00111 +ve

[@oggy107]

your last one is not correct it's 10111

[@muzammalhussain4887]

@@oggy107 thanks i will see this

[@alfredhercules]

1. 1110 2. 0111 3. 01001

[@kumar.n3380]

1:0010 2:0111 3:01001

[@intothefilms]

At 5:42 you are mistaken, If the sign bit is “0”, this means the number is positive in value. If the sign bit is “1”, then the number is negative in value.

[@MATHSBYSURENDRATHAKAN]

yes correct man.

[@mihirvaghela2185]

No that is the rule of 2s complement addition.. they're correct

[@aadityavijay3837]

yeh example 2 mai 1011 final answer hai ya 0101

[@Yourdelusionalgirl]

so in the second example do i express my answer in 2's complement form or live it as it is??

[@vikasprajapati6582]

how we can solve 3rd question sir, result will come 5 bit or in 4bit

[@akarshsaxena7810]

sir aapne last video m kha tha 1's comp. of A is -A and now in this video 2's comp. of A is -A......but 1's and 2's comp. of 6 is not equal explain......

[@vikashchandra6262]

Same doubt... How is it possible?

[@barsilgen120]

thanks

[@mukulmalviya1605]

sir you can use shortcut method for finding 2s complement

[@Honeyypaaji]

if 1's compliment means negative of a number then how can 2's compliment also be negative of the number ?? please explain.

[@ganeshmula4508]

H. W problems answers 1)0010 2)0111 3)00111

[@WiseTells]

If we have 5 and 4 bit no. How we know carry is generated or not.

[@Eng-Ara_2023]

is the final answer when there is no overflow after taking 2's comp or withtout taking 2's comp ?

[@khayalipulao6588]

1.) 0010 2.)0111 3.)0111

[@anuragbhadauriya4027]

bhai last ka solution kese kiya 5 bit main se 4 bit kese

[@fragranceofphysics]

Ans are 2, -7,7

[@atanunayak6637]

**(Copied Comment for self)** summary of process is: 1) do 2's complement on the 2nd number. 2) then add 1st number and 2's complement of 2nd number 3) if the result's sign bit is 1, then the result is positive. Ignore the sign bit, we get our answer If the result's sign bit is 0, then the result is negative. Ignore the sign bit, and do 2's complement on the remaining part. then, we get our answer

[@gaganrajchandrakar]

ans are 0010, 1001 and 0111

[@aanchalvyas3480]

1. 0010 2. 1001=-7 .. to Check find it's 2's =0111=7

[@gamar1226]

1) 0010 = +2 2) 1001 = -7 3) 10111 = -9

[@_Ramyavardhini_Basani]

I guess answer for 3 is +7

[@rippen526]

@@_Ramyavardhini_Basani yes thanks

[@ajaykumar-17p8g41]

Sir, in previous (last) video you have said that 1's complement was negative form of number but in this you were saying that 2's complement was negative form of a number.... So which one is correct....

[@AnasKhan-pj5pk]

Hello Sir! i have a doubt in example no. 2 where you got the answer without a carry and again you are performing 2's complement. why is that?

[@akashchakrabarti9639]

Anas Khan The result which was obtained was negative and in its 2's complement form. So, to know the magnitude of the result (in this case +5), you have to perform the 2's complement of it(here -5).

[@afjalmd5164]

1-0010 2-1001. -7 3-0111

[@Cybernetic1]

Sir when I substracted -48-23 (-48)+(-23)=-71 11010000 is 2's com.. of 48 11101001 is 2's complement of 23 Adding both we get 1 10111001 so we got carry 1 and is case of overflow and I neglected 1 the answer should be 10111001 which is not equivalent to -71 You said we need to take 2's complement of result when we don't get carry. If we get carry we simply ignore it and that is the answer but here even after neglecting Carry we don't get the answer please help sir I request you

[@preranadash9640]

Did you get the answer from any other source plz reply

[@diyadey1654]

I am having same type of doubt ... Like -8-4 =-12. On performing 2's complement I am getting a carry and if I ignore the carry the ans which I am getting is not the correct ans... So pls if you both get the solution of this problem then pls give a reply

[@Facts_4_you_12]

From which which countries the commenters are ?????? I m from India 🇮🇳 ♥

[@childgagana4537]

1) 0010 (+ve true form ) 2) 1001( -ve 2's comp form ) 3) 10111( +ve true form)

[@bakeronews1]

I don’t understand that for the sign bit of 1 is positive and 0 is negative. To my mind, it’s should be the opposite. Would anyone help clarify this situation please???

[@amrmohamed6207]

so if i want to get the negative of a number should i only do the 1's comp and thats it or add 1 :3 im a little bit confusesd

[@thomasw.eggers4303]

My suggestion is to forget about one's complement arithmetic. Yes, it is sometimes used, but two's complement is FAR more common. To get the two's complement of a number, change all the 1's to 0's, change all the 0's to 1's, and then add 1. You must always add the 1. This works for both positive and negative integers.

[@jjww2788]

Sir, I am still confused with overflow. Based on your condition for overflow, the example 1 will be indicated no overflow, since x'y'z+xyz'=1'0'0+100'=010+101=0 no overflow, but in your first example, you said it was overflow. Are we supposed to consider the discarded "1" as the sign of result? even though, the discarded "1" is considered as the sign bit of result, it will be like this: 1'0'1+101'=011+100=0+0=0. it is still 0, which is no overflow in terms of your condition for overflow.

[@gauravav1635]

It's actually, x-sign bit of A y- sign bit of (-B)

[@kalef1234]

so for example 2, I got the same answer when I subtracted 1 and THEN took the 1's compliment of the result. Is this okay to do or did it just work out in this example? Thanks

[@rohitnade5097]

how the second answer is solved plz explain in detail sir

[@JustA-Smile]

Is there anyone who can make mr understand the condition for overflow with a example i can't understand the thing...🙂🙃 9:17 9:17

[@lounes9777]

6:40 nah that's definitely not the reason

[@AnonymousUser17059]

what's about (-42) - (-13) ??

[@KvrKarthik6433]

sir you said with binary number like 1011, etc. But how to do with numbers like (1011.10)2 - (110.10)2 ??

[@clemaloy6269]

How to subtract larger number from Smaller number

[@BridgeNotWalls]

A=0010 B=0111 C=1001