Combinational Logic - Adders and Subtractors

A description on how to design a half adder, a full adder and a multi-bit ripple carry adder. This video also describes how to create a subtractor circuit using the fact that A-B = A+(-B)...so a subtractor can be made from an adder if one of the inputs is negated.

[@unknownsoul7043]

legend has it he became a ULTIMATE level engineer teacher, and is sitting back watching us toddlers figuring things out and smiling saying hunny look at this.

[@m.naveenvamshi1154]

This is the best video because all the lectures i had seen till no are very long & boring to hear it is simple way he explained & short also.......

[@ElectronXLab]

What you need to keep in mind is that when you are doing arithmetic with these digital circuits, you must define the type of number system that you are using. So with your example of '1011', if you define your number system as unsigned, then the value is 11 but if you define your number system as 4 bit two's complement, then the value is 5. The result of the operation in the adder/subtractor circuit will be the same, the difference is how that result is interpreted. e.g 0011 + 1011 = 1110

[@lj54]

This is one of the best explanations on KZbin with regards to adders. Your hard work in making this video is much appreciated. Thank You!

[@frettbuzz13]

I missed my lecture on adders and subtractors and this helped. Thanks for the great video!

[@shanenolan8765]

Great tutorial you explain it far better & easier than my lecturer. Cheers

[@TheMightyMedia]

i'm from Singapore and i think u explain better than my asian lecturer =)

[@ryanforeally]

amazing lesson dude you really broke it down as simple as can be, thanks! gonna ace my midterm next week!

[@akkig1759]

Much appreciated these great lectures.You made things easy...thanks a million for all of these videos and god bless you...

[@arslanyaqoob3697]

Awesome...hats off to you for making me understand which i couldn't from my teachers : )

[@ElectronXLab]

Thanks for the comments! Currently, no plans for VHDL tutorials, the course I am teaching now doesn't cover it, maybe in the future...

[@fayemccabe7183]

This was so well explained. Thank you very much, you have helped clear up much of my confusion!

[@NickTheHunter]

I should transfer my tuition for my course to you O_o ahahaha

[@Michael-gn7te]

Thanks man. This video helped a lot! Just to clarify: one of those full-adder blocks is a 1-bit adder?

[@gaget3hsage]

Great video, though you should turn up the audio in subsequent releases!

[@jmd2479]

Awesome video! You've explained this so well.

[@nailuj100]

I thought of a better example to show the way I think about this. Let's say I wanted to subtract 1 from 1 and put light bulbs at the end of the subtractor to represent the answer. Of course, if it subtracts, neither bulb would be on. A subtractor takes the two's complement of a number. 1 negated is 0 plus 1 is still 1. Since the circuitry is the same circuitry of an adder and the number is still the same, why wouldn't the subtractor just add 1+1 instead of subtract? What makes the subtractor

[@Krutchtacular]

Thank you so much. Very clear and extremely helpful.

[@tenzinchoetso3836]

great video! very useful

[@tareqmohammed24]

THANKS A LOT !!!!!! Your videos help A LOT !!!!!!!!!!!!!!

[@benlandry5]

Thank you! Makes much more sense now!

[@ElectronXLab]

0011 + 1011 = 1110 can be interpreted as 3 + 11 = 14 if the bits represent a 4 bit unsigned number or as 3 + (-5) = -2 if the bits represent a 4 bit 2's complement number.

[@MrSubha010]

I really like it..Thank you so much..It is so helpful for me even in my examination :)

[@trojsi]

thanks, found it very helpful.

[@ranakrakacan1881]

such a great video.thanks its reallly helpful

[@lifutao3446]

you really the man, I appreciate you

[@laurendreams962]

Thank you so so so much

[@itpugil]

thank you so much man!now the fog is cleared :) this helped a lot,i hope you'd consider doing some VHDL tutorials :D

[@sweetsazd11]

Yes, it makes sense and it's very very helpful, thanks a lot sir :D

[@harneetsingh07]

you rock bro! best tutorials!

[@masooma1188]

you saved mee thank you sooooo much 😢👍

[@nailuj100]

I understand how an adder works. But, I don't really understand the subtractor. I don't understand how the subtractor knows how to subtract instead of add, when it cant tell the difference between positive and negative. Also, what stops the subtractor from using the two's compliment number as just a different positive number and adding? For example, the two's compliment of 5 (0101) is 1011. But, that could also be a positive 11. So, what makes the subtractor take that number as a negative....

[@shayanarman1914]

Thanks so much! This really helped.

[@nailuj100]

how would it know to tell the difference between an unsigned number and a two's complement number?

[@gadamson12]

I skipped a few videos so now mind = blown

[@nailuj100]

Thank you for answering, though I'm still confused... But, what makes the subtractor use the number that certain way? Why would it subtract 5, instead of adding 11?

[@ElectronXLab]

Yes these logic circuits are implemented in hardware. You probably know that computers are made up of transistors which are basic semiconductor devices. Those transistors are put together to create logic gates (AND, OR etc.), those logic gates are put together to make things like adders, multiplexers, flip flops etc. Then those more complex circuits are put together to make your computer.

[@smtkl]

he is using quartus software from altera, hope it helps

[@prithivipandey1814]

B'C'+BC gives ( B XOR C)' , U can try doing it in truth table. Then its A'(B XOR C)+( B XOR C)'A which is A XOR B XOR C

[@nailuj100]

have an output of 00 (no light on) instead of an addition output 10(1 light bulb on)?

[@SahilChaturvedi]

Hey I have a question.. It's probably really stupid.. But are these adders, and logic gates implemented as hardware somehow? Or is just a symbol for some software?

[@gilakot]

nice, you did in 22min what the professor does in 2hrs.

[@ApEaZed]

You didn't explain in your video's how to do that algebra with the xor or did I miss something ?

[@ElectronXLab]

No, I didn't explain the algebra for using an XOR instead of an OR. Either one will work though. To convince yourself, create the truth-table for the following two expressions...you should find that they are the same. Cout = XY + Cin(X+Y) Cout = XY + Cin(X XOR Y) Basically what happens is the XY term covers the case of both X and Y being one, so XOR can be used instead of OR

[@keenkennyny]

Can anyone help me with the sum equation for the full adder? It starts with Q = A'B'C + A'BC' + AB'C' + ABC Using distributive, Q = A'(B'C + BC') + A(B'C' + BC) Q = A'(B XOR C) A(B'C'+ BC) and I'm stuck there, how does he get A XOR B XOR C? I feel like B'C' + BC should be equal to something. Their 1 only if both are 00 or 11. I don't know of any logic that does that except for conditional statements...

[@puvan5555]

hi there sir , i have a question. How to find the test bench and coding for "Ripple-carry adder and 4-bit block carry skip adder" in modelsim. Can you help me on this

[@HenryTechBoy]

Thank you so much!

[@venom21wow]

Is there any videos that you have that explain how to do boolean algebra with the XOR?

[@Mgapcdev]

How do you get it to subtract below 0... like 2 - 3 = -1 ?

[@kaifpatel7833]

thanks....dude. helped a lot.

[@stevie_efbabyy]

would the carry out be considered the strobe pin on a 4 bit input mux?

[@Jaliyagodage]

Thanks

[@mayaz.t9359]

thanx ..

[@Gotallofthem1]

That's exactly what I get also a normal OR; not sure whey he has it as XOR

[@marcusshep]

So, where is the info on subtractors

[@ALLDay550]

just use a full adder with a 2's complement of the number you wish to subtract. Example 1100 - 1101 = 1100 + (-1101) = 1100+0011 because 0011 is the 2's complement of 1101

[@nonkurdish2680]

i still don't understand why do we use them :(

[@juryben]

Thank you!!!!

[@2454014]

What software do you use?

[@ApEaZed]

it would be nice if someone could explain me the first expression in the adders concerning the Carry out. A'BC + AB'C + ABC'+ ABC = C(A'B + AB' +AB) + ABC' = C(A+B) + ABC'. Then I'm stuck.

[@ElectronXLab]

+ApEaZed and +jake Lary ...Start off with a different factoring term (i.e., factor out AB where you can and C where you can):: A'BC + AB'C + ABC'+ ABC = AB(C' + C) + C(A'B + AB') = AB + C(A xor B)

[@hadasg11]

Cout in full adder (around 10:30) actually should be : "Cout = XY + Cin (X+Y)" and not "Cout = XY + Cin (XxorY)"

[@ElectronXLab]

Either one will work. The XY term takes care of the case of X and Y both being one, so XOR can be used instead of OR. To convince yourself, create the truth-table for the following two expressions...you should find that they are the same. Cout = XY + Cin(X+Y) Cout = XY + Cin(X XOR Y)

[@alyabayani871]

how to design 8 bits adder and sub tractors generated over flow

[@montyasesto4909]

You talked about faster adders...are they combinational circuits too or wut?

[@ElectronXLab]

Yes, fast adders are combinational circuits too. They calculate the all the carry bits in parallel, so that you don't have to wait for the carry bits to propagate from bits of lower significance to bits of higher significance.

[@ohyesthelion]

Hi! What's the name of the simulator? Thanks

[@antonynepgen2045]

Its name is Steven. Its a pleasure. (its Quartus II)

[@ilovenutella08]

thank you :D

[@MirzaHaseeb1]

isnt that cout should AB+BC+CA

[@venom21wow]

Also, you should of showed us how to solve cout=..

[@Mgapcdev]

Thanks now my minecraft calculator can subtract :D

[@moodzlists]

in 20:05 le last carry 1 of the addition is the sign of the sum ..

[@thengpanhavuth7402]

this example is for adder ??? how is example of Subtractors ??

[@ALLDay550]

just use a full adder with a 2's complement of the number you wish to subtract. Example 1100 - 1101 = 1100 + (-1101) = 1100+0011 because 0011 is the 2's complement of 1101

[@keenkennyny]

Forget the + ... Q = A'(B XOR C) + A(B'C'+ BC)

[@restore006]

Note: B'C'+BC=(B'C+BC')'

[@Pages_Perfected]

Interesting

[@Maha-dn6eh]

I wish that you write with many colors :(

[@nailuj100]

.... 5 instead of a positive 11? Could someone please explain? Please be detailed, but don't use too much technological terms... Thank you.

[@minhtri941]

9:00 why Cin = 01010101

[@andresession2235]

+Minh Tri He's just doing all combinations possible with 3 input bits, so in this case, it's from 0-7.

[@tometori]

C'mon you could have used a Karnaugh map at around min 10:00

[@ElectronXLab]

tometori True, but K-maps give you an expression in a minimal SOP or POS form. For the adder, I need to have XOR expressions.

[@lcddglcddg3447]

David Williams Cin is equal to A X B X C..... right? 1 X 0 X 1=1 how come? 1x 0 =0 ....then multiply the 0 to 1 it will be 0

[@Prakashkumar-qd6ip]

hi

[@killZtheterrannoob]

I should transfer my tuition for my course to you O_o ahahaha