AND OR NOT - Logic Gates Explained - Computerphile
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- เผยแพร่เมื่อ 5 ก.พ. 2025
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Basic logic gates explained and all the different ways they can be drawn and represented. Professor Brailsford takes us through the AND, OR & NOT logical operations.
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Hill Climbing Algorithm & Artificial Intelligence: • Hill Climbing Algorith...
Binary Addition & Overflow: • Binary Addition & Over...
How Computer Memory Works: • How Computer Memory Wo...
Easter Egg: • Logic Gates EASTER EGG...
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This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: bit.ly/nottscom...
Computerphile is a sister project to Brady Haran's Numberphile. More at www.bradyharan.com
I already know all this stuff, but I watched the whole video simply because Professor Brailsford is such a wonderful lecturer. This is one of my all-time favorite channels, thanks for keeping with it!
I would love to see a video going further into binary logic, for instance how NAND/NOR are used in flash memory, or how XOR is more generally used.
Christopher Pilcher Same. It’s like getting a masterclass in how to teach this stuff. I’ve been telling my son about propositional logic/Boolean algebra because it seems so useful in so many areas, most obviously computer science
@@SuperBartles what other areas?
ok?
I know that I'm quite late with my comment (3 years it seems), but I really wanted to say how much I like how Professor Brailsford cares about the electronics engineers. Much appreciated!
Computerphile,
you might consider doing an episode on the implementation of logic gates in RTL / CMOS so viewers can learn how all this actually works in silicon.
I think Professor Derek McAuley has some knowledge on this from his discussion on Moore's Law.
Great and interesting topics! Great work.
Probably the only Computerphile video in which I understood everything that was said.
Why does TH-cam offer better lectures than my university?
Great video! :)
This is so clearly explained and so simply put. Honestly, fantastic tutorial
That "easter egg" at 2:00 would've been fun if it lead me somewhere but this was a lot of ones and zeros to begin with. whatever I still had some fun.
You teach this better than my computing teacher 😂💛
2B + ~ 2B
That is the question
You are mixing up the symbols.
2B || ~2B
18vallancel if the 2 is interpreted as a symbol and the ~ applied on (2B) as a whole on the RHS "technically speaking" thats a tautology => true. Did i break Shakespeare yet?
iamterence77 I know :)
True.
Had to learn this if you wanted to use redstone in Minecraft
True
Had to learn this (and beyond) to operate real life.
Similar to real life, only NAND and inverters are efficient in Minecraft, everything else needs extra pieces
But I leaned logic gate through redstone
@@Henrix1998 isn't or the simplest
Omg I knew AND was A multiplied by B but I didn’t know why until just now and it’s so simple and I feel so dumb for not putting that together myself
Professor Brailsford seemed quite happy about explaining this ^^
false.
This channel is a godsend
I like the way this guy explains things..are there more? Can I watch him exclusively?
better than my college teacher
great channel..keep it up
Great video, thank you!
Good video, prof. I am learning logic gates right now. Quite an interesting topic.
I absolutely hated Truth Tables in high school math. I think they got introduced 1st in Like algebra II OR III & got ever more complicated in Geometry & I think also Trig?? I took as many honors classes as I could & I think We even saw them pop up in my Physics class. I wish I hadn’t of hated them so much as this is one of those moments of- ‘If only I knew then what I know now…’ I would’ve appreciated them, tried a bit harder, & understood a helluva lot more about why they exist & their function to everyday life.
Simple but wonderful!
If you want really interesting triggering rhythms in modular synths, you need to learn this.
disappointed that you didn't show the actual mechanics of how these work, personally I think that the logic behind it is pretty simple and intuitive
I am 15 y/o and i learn this in school so this subject is amazing
ok?
Very interesting to a layman like me to see how abstract logic takes on a physical form through electronics! I imagine that's how computer circuits work at a very fundamental level? Computer science must be an interesting subject.
Thanks guys, just doing logic gates with my year 9 class, they'll love this!
Nice thing about treating AND as multiply and OR as addition is that they have nearly identical mathematical properties. So you can write your outputs as a set of math functions. From that point optimizing your logic for least amount of gates becomes the familiar "simplification" stuff we were taught in arithmetic classes.
Nothing's stopping you from writing your outputs using the and-sign, or-sign and not-sign in math language. Just specify the behaviour of the three symbols and your good to go. :D
(max-function for or-gates, min-function for and-gates, "if 1 then 0 else 1"-function for not-gates. Very easy.)
This is helpful it is also better than watching redstone logic gates rather than computer logic gates
The logical addition actually represents the exclusive or and it perfectly makes sense when you realise that the mathematical structure ({0;1};+;⋅) in which you perform your calculations is identical to ℤ/2ℤ, hence 1 + 1 = 0.
+ is merely a symbol and you can define it any way you want really. It's also gotta be said that not only ℤ/2ℤ can form a boolean algebra, any lattice with a couple of additional properties does.
+ for regular old or starts to make a lot more sense when you look at how you'd build it with transistors, which is more or less just "connecting wires" - so HIGH signal + HIGH signal still equals HIGH signal, not LOW.
That "square matrix" is called a Karnaugh map
@KamaCoding Interesting. What culture does not?
@KamaCoding It's simply a way of denoting things more precisely. Heisenberg's uncertainty principle, Euler's Number, Karnaugh Map, Pythagorean Theorem would be Principle, Number, Map and Theorem without the descriptive name of the practitioner who is most closely associated with it. Yes, owing to the time most of these discoveries were made, that being a time in which the preeminent science and math cultures of the world were western ones, many of these concepts have an Anglo name attached. I suspect in the future, we will see many more non-western names associated with discoveries to come.
@KamaCoding No, it's a Karnaugh map. Everyone studying computer architechture/organization knows this.
To bring up culture here is not very elegant or clever.
Thank you for this! Great help in only a few minutes! You guys rock!
For people who are wondering how Not Gates really work. Not Gates technically doesn't turn convert the input into it's inverted state. Your input will just be read not modified. Instead. Gives you an output based on what your input is. Look it up and you'll know what I mean.
Noob question:
At 1:20 when he says 0 and 0 is false, why is that?
Could it be argued that because both are in a "false state" so to speak it is actually true?
True that both are false?
That's because on AND gate, you multiply the two inputs to get the output and 0 in binary is considered false and 1 true, then:
0*0 = 0 > false
I love this. A fantastic free education by true scholars, and the knowledge that any revenue generated will be used to perpetuate education!
NOT is also written a lot of times with a bar over the input designator. For example, if the input is designated as A, NOT A will be written as an A with a line or bar over it.
and still others use a / to denote the negative state, eg "/A", typically when you're using plain text.
You are great sir ❤️
I love your accent, sound, and your flow ❤️
Found the Easter egg. Worth writing it out and adding the slots. Back to the video I go!
2:00 Nice Easter Egg.
What did it mean in text
Akari Insko "easter egg"
As soon as you mentioned multiplication, it hit me that or is just + and xor is -. I’m working on some assembly stuff, so that might come in handy.
Xor is equivalent to minus! I never thought of that
@@tanveerhasan2382 how is it? 0-1 is not 1
@@m_t_t_ it's minus 1
xor is exactly + mod 2, isn't it ?
To our european viewers: The way Professor Brailsford draws his logic gates is not what you'll usually see around here, as he uses a US standard. We simply draw squares with a symbol in it (& for and, ≥1 for or, etc). We also use the little circles denoting not operations for brevity, and all in all I think it's nicer and more intuitive than the random shapes which you have to memorize. Seeing how americans like random standards (three feetsies in a yard!) it doesn't surprise me that they still use it though :P
The US-standard is called US ANSI 91-1984,
the european one IEC 60617-12.
I love how he writes on that old fashioned printer paper. his video might help me pass my Systems Architecture class. Thanks!
In the digram symbol for the NOT-gate (inverter) it's really the little circle that does the inversion; you can also have a non-inverting buffer stage which is just the triangle without the circle.
this just summarize my entire first chapter of my math class
I like a line over the notted symbols, because then you get this little mnemonic:
Break the line, change the sign.
I can't write it with the line over here, but it's a handy shortcut:
!(A + B) = !A . !B
It's also a little easier to read when you've got a complex equation. Fewer parentheses all over the place.
David Attenborough for logic.
Basic gates, good refresher
subscribed
Here in Spain the a.b(Many-times even a dot-less ab) is more commonly used, at least in college, than the a and b. Same thing for the or, but with the NOT we use it like !a, the ¬ is only used in maths.
Also, with CMOS gates, the NOR and NAND are not a gate with a NOT behind, but the other way around, the OR is a NOR with a NOT "glued" behind.
I have also seen set intersection ∩ for and and union∪used for or. This makes sense if you think of a venn diagram. The intersection is where both statements are true and the union is where either one is true.
It was very useful for me. Thank you for the video!
Great explanation, loved it
It's worth noting that you can make an AND gate by inverting the inputs to an OR gate and then inverting the output, which means that AND actually consists of OR and NOT gates, and as such you can make any logic with only those two gates.
It works the other way, too. In fact, when I learned Boolean logic, I was told that NAND is sometimes called the "universal gate" because if you short its inputs together, it becomes an inverter (NOT). Thus, given enough of them, you could theoretically build any given logic circuit. For example, you could use two "NAND inverters" to invert the inputs of another NAND to make your OR gate.
Not is often also represented by the 'bang' symbol "!"
And fun math logic, if you 'not' a logic pair, like a+b, and factorally apply the 'not' to the formula like a multiplier you also flip the operator symbol.
Ex: ! = not
!(a+b) ==> !a.!b
Not(a and b) ==> not a or not b
One way of representing an OR gate mathematically is *a + b - (ab)*
How did you come up with that formula?
You forgot the And + Not for a Nand, as you did the Nor, but yeah I learned 3 notations today, all I knew before was the pictures of them but never the notation so it was neat.
woah great it's so wonderful learning like that
Thank you for this! Now I get logic gates.
Hello,
At the top of the page it is written AND OR NOT XOR
Then in the video we are explained the AND, the OR, the NOT and the NOR
So is an XOR same as a NOR ?
辛格文 XOR is a separate video, sorry for the confusion - XOR coming very soon!
Amelia explained it precisely in truth table form but it's the eXclusive or.
In the exclusive case if A or B are true, then the output is true, BUT if A AND B are both true, then the output is false. To compare it to real life an exclusive or is similar to where you order a meal at a restaurant, and you have a choice between soup OR salad as the side dish. This is an example of an exclusive or as we can have one or the other, but not both.
When dealing with or's we assume them to be inclusive, and because of this fact we have the always funny (but extremely corny) joke:
"A logician goes out to dinner and orders the steak, the server asks if they would like the soup or salad, the logician responds yes."
//_^
Thank you very much!!! Lovely explanation!
This video helped me understand the circuit system in Factorio... :)
This episode was quite interesting but I have two questions about its contents:
- why was the existence of "nor" mentioned, but not the existence of "nand"?
- it is stated that the three basic operators "and", "or" and "not" are sufficient, but why not having a kind of "proof of concept", for instance by creating an "xor"?
I hope there will be a part 2, where these things are clarified, examples are taken, and examples of use are taken (why not talking about the use of "xor" in cryptography, for instance?)
Thanks a lot for the video, sir! The only question I still have - irrelative to the main topic, though - is why you use the music notation sheet (for orchestration, as a matter of fact) for drawing here?))
This is "music lined" computer listing paper - it looks similar to a musical stave but it's numbered for computer code and comes on a continuous feed - aka "fan-fold" paper. Hope that helps -Sean
I want to avoid giving the impression that I have any intelligent understanding of this stuff at all, but it seems to me that that matrix is a really nice way to represent the possible outputs for the inputs.
Do some videos on database and logical modeling, Chen's notation and the such. Im taking it in university so im highly interested in it
I really enjoyed it.
in binary, 1+1=10 and the last digit is 0, so why isn't xor called logical sum instead of or gates?
I can't find any video about 'boolean satisfiability problem' on the computerphile channel :(Are you going to make one?
This helped a lot thanks
Thank you for all this teachers, TH-cam were not wasted by just those garbage video posts.
Thanks to Little Big Planet 2 I already knew that :)
Hello, I'm really interested by computerphile's videos. Are those kinds of lessons covered in computer science or computer engineering?
One of those topics that are actually pretty deep and Scientific yet pretty easy to understand, if only we could formulate all the other difficult Scientific topics like we have the logic gates and boolean algebra in general :D
Nice video on basic truth tables. It would be interesting to see this channel do a video on the NAND gate, which is the truly universal logic gate. Any logic, from the simplest to the most complex, can be constructed using combinations of NAND and only NAND.
NAND and NOR are both universal. And so are four other (uncommonly-used) gates.
Would XOR emulate addition with AND representing the carry bit?
Very useful, thanks.
Thanks! This helped a lot!
Speaking of logic gates, I found out that three-way light switches (where two switches control one light fixture) operate like XNOR gates: both inputs have to be in the same state to produce an "on" or 1 state.
Did you know there are three-way dimmer switches? I really want to try one of those.
The ones in my house don't discern which state the switches are in. The light changes state when one of the switches changes state. Despite pondering over this since age 5 I still have no idea how it works.
Is it not a XOR rather than a XNOR? Better to think "When they are both off, it's off" I know technically they are the same thing, but Adding the extra inversion for no reason to the outcome.
PhazonSouffle
OR is
a0 b0 = 0
a1 b0 = 1
a1 b1 = 1
a0 b1 = 1
XOR (eXclusive OR) is
a0 b0 = 0
a1 b0 = 1
a1 b1 = 0
a0 b1 = 1
You'll see that every switch flip with XOR flips the state, similar your 3-ways, BUT they're (probably) the other way around, so that the light is on only when both switches are in the same position (both up or both down), which is the NOT version of that, the OP's XNOR.
PhazonSouffle
It works the way that Desmaad described, using an XNOR or XOR gate.
In an XOR gate the gate is exclusive, which means that the output only works when only one of the other inputs are on. If they are in the same state it is off.
Now imagine that your lights are on and they are controlled by two switches. The first switch is on, and the second switch is off. If you were to turn the first switch off, the switches would be in the same state and the lights would be off. If you were to turn the second switch on, the switches would be in the same state and the lights would be off. So with this logic it doesn't matter which switch you press, the outcome will be that the output switches states as the switches move in and out of synchronicity.
Nicely explained. Still, I have a query, what is the need of NOT gate, why was it introduced? I want to explain same to a non-IT professional, can you give me a real world example where such implementation exists?
I imagine it is used when flipping bits, before using the Adders to add one, in calculating two's complement, which allows you to sign numbers, therefore representing the negative ones. That's a guess.
Also, to do this would require combining a couple of Nots into a device called a 'Noter', which would be able to invert several bits. This would all be present in the arithmetic and logic unit of the CPU.
This is so nice.
Got here a bit late. But now I have to go see if Karnaugh (sp?) map is covered as the natural extension of this series.
The text from 2:00 to 2:05 is "easter egg" in binary (the annotation said that though).
This helps me remember that AND starts before OR. multiplication before division. Could be a bad way to think about it.
I always wondered how a "not" gate could generate a signal if no signal is applied, where does it take it from if nothing goes in (signal is "off", and is reversed to "on") but it makes sense if the voltage is not "off" but "low" and gets amplified to "high" when it's low, and lowered to "low" when it comes in "high".
Note, that logic gates in electronics are all powered, besides accepting signal inputs. We just don't draw power connections in logic diagrams :)
NOT-gates actually have another input where it takes the power from. You can't see this power-input in logic-diagrams because the power input is not part of the logical implementation, only part of the physical implementation.
Gates need to be plugged in to a power source, you just dont see it
ha! thanks guys :)
The way a not gate is physically realized is actually quite weird imo... (Well it differs, depending). The physical implementation I know uses a transistor that, when voltage is applied, grounds the circuit... It makes total sense, I just found it to be a strange looking circuit :D
I like how his "truth table" is a K-Map. That might be a little ambiguous to the uninitiated down the line if they don't know the difference between a proper truth table and a K-map
Next should be one on how you can build an XOR (exclusive OR gate) out of these components.
Is XOR similar to OR except there can only be one 1 (one true and one false)?
3:15 That really confused me when doing mechatronics, I wasn't sure if it meant and or multiplication but both made sense anyway haha.
For the and gate, output is false if the result shares a row with a false input. Same for any column that contains a false.
Very cool video
Time for logic!
There are three AND gates, one OR gate, and one NOR gate.
One signal is connected to the A on the first AND gate, and one signal is connected to the B on the first AND gate. Signal A is off. This AND gate is also connected to the OR gate. A signal is connected to the A signal on the second AND gate. There is another signal on the second AND gate. Signal A and Signal B are on. The NOR gate has a signal that is on. The NOR and OR gate are connected to the A and B signals of the last AND gate. Is the last AND gate on or off?
It almost feels criminal to not talk about NAND gates. There should be a following video about it. You also need a video about how once you have established a NAND gate your binary logic is completed.
Cool how this transfers to math with like Venn diagrams with the intersect and union stuff
Best concept
I prefer to think that NOT symbol is just that little circle. That way we already know that the triangle is just a simple buffer, so the circle with a triangle is actually a negating buffer.
You Sir>= genius
i've never seen the ~ notation for not. the other one we used in Discrete was to put a bar over the item.
Ain't no problem. Someday I'll understand this.
Nice easter egg. The %20 gave it away.
Can you use group theory notation like Union or Intersect? Seems very similar.
They are similar, but definitely not the same. You don't really use union or intersection to display logic, though you could argue that if you take a set containing something to mean true and the empty set to mean false, then you could perform and and or with them. I can't think of a reason why you would want to, though.
That’s much simpler than the traditional way it is taught.
Why don’t we come up with world standards for electronic symbols? Would make things much simpler.
Thank you.
In my digital logic courses we denoted "not" as a horizontal line above a term.
When it's in that form it's often called the complement or more explicitly the p-bar (replacing p with said input), they all mean the same thing but that one just carries that name as it's often used in math speak where;
_
p = u - p
where u is defined as the universal set.
Yup. We often called it "bar" or "compliment".
nice easter egg!
did you paint the ¬ instead of typing it in the video?