Boolean Algebra & Redstone Logic Gates - LRR #3
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- Опубліковано 4 тра 2024
- In today's episode, I go over the basics of boolean algebra and their corresponding redstone logic gate implementations.
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Boolean Algebra Wikipedia Page en.wikipedia.org/wiki/Boolean...
More on Logic Gates • Understanding Logic Gates
Crash Course video on these topics • Boolean Logic & Logic ...
Solutions to the Expressions:
A | B | A v !B
0 | 0 | 1
0 | 1 | 0
1 | 0 | 1
1 | 1 | 1
A | B | !A ^ !B
0 | 0 | 1
0 | 1 | 0
1 | 0 | 0
1 | 1 | 0
A | B | C | !(A v (B v C))
0 | 0 | 0 | 1
0 | 0 | 1 | 0
0 | 1 | 0 | 0
0 | 1 | 1 | 0
1 | 0 | 0 | 0
1 | 0 | 1 | 0
1 | 1 | 0 | 0
1 | 1 | 1 | 0
-------------------------
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Open Redstone Engineers (ORE): openredstone.org/
0:00 Introduction
0:40 Boolean Algebra Overview
1:17 NOT
2:17 OR
3:05 AND
3:36 Connection to English
4:09 Laws
5:22 Analyzing an Expression
7:20 XOR
8:20 NOT Gate
9:00 OR Gate
9:31 AND Gate
11:14 XOR Gate
12:46 Sentiment
13:43 NOR, NAND, XNOR
15:08 Subscribe!
Music (in order):
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Mokka - Spicy Cream • (No Copyright Music) F...
Harris Heller - Golden Age • Golden Age
Harris Heller - Streamline • Streamline
LuKremBo - Biscuit • (no copyright music) l...
Infraction - Photograph • Vlog lo-fi Anime Fashi...
LAKEY INSPIRED - Chill Day • LAKEY INSPIRED - Chill...
Harris Heller - Guilty Spark • Guilty Spark
Harris Heller - In My Shadow • In My Shadow
PRNV - Happy High • Happy High || happy lo...
Creo - Place On Fire • Creo - Place On Fire - Ігри
Now i Love mathematics And Redstone Study :'1
what about the buffer tho?
*the buffer gate
@@underdeveloped_loser no im not ready for that :
No
Just wanted to redstone, learned computer science.
This guy and Sebastian Lague have beautifully explained Boolean algebra and logic gates. Wonderfully done!!
Sebastian is a legend. His Digital Logic Sim is amazing for playing with Redstone circuits (or even IRL on breadboards)
Are you planning on participating in SoME 3? I really think you'd do great. Otherwise, I appreciate the quality of the content you do make! I already understand most of the concepts you've already taught, but I have learned new insights and am still captivated.
some 3 will be a thing?
@@azteriaaa it has already been announced
That would be genuinely really cool, and he could probably score quite highly despite it being minecraft lmfao
nice it happened
@@epixiel9993 what i was thinking
Love your videos! A small tip: when you are showing things (like the truth table for A NOT A), use f3+c to copy your location and angle to your clipboard so that you can teleport back to the exact same spot which I think will result in smoother cuts
🤣
That's some advance level stuff lol
Oh, that's useful, thank you
Scaaaaaaaaaaaammmm
I might be remembering this wrong, but doesn’t that keybind just crash your game?
This is the first time I've heard about boolean algebra! Definitely saves a lot of headaches trying to understand schematics. And the fact that there are online simplifiers is just amazing!
Ill be studying electrical engineering next year so this will come in very handy 🙂
I just graduated in electrical engineering less than a month ago. You'll definitely experience logic gates, as well as circuits, amplifiers, EM waves, signals, all sorts of fun stuff! The major is conceptually and math heavy, but a blast. Hope you enjoy it!
Good luck!
@@samuelowens000hi, I’m interested in EE but I’m not experienced with coding or programming. Is it a big part of the course? Otherwise I’ll do ChemE.
@@a.b3203 There's a little bit of programming in EE, but depending when you chose to specialize in, you may need very little programming. If you're like me and choose to go into computer engineering, you will need a lot of programming classes.
@@a.b3203there’s def some, but it’s packed into your course-load. You don’t need any prior programming knowledge to get through it. You will learn to code and in my opinion it’s an absolute blast. I prefer it over a lot of my other classes. I’m not EE but a computer engineer. Very similar track tho.
This is literally a great way to learn real life computer science. Taking an AP course at school took so long, but it was worth it to understand the deep down way that computers work. I already knew programming and higher level things. But I learned so much about how computers work at the lowest level possible :3 ty for this amazing series which is actually teaching people real life things in the fun world of minecraft
Your lessons should be shown in schools!
man, here in Brazil ive learned it in my school
@@arturmg2068 that's AWESOME!!!
I know my old computer science teacher would use this person's videos if she knew about them.
Someone who has struggled with math his entire life just understood this entire video Matt I hope you know that
9:10 Yes, this is true with real wires too, but it's not really used because you can have signals going backwards and breaking things. This is true in redstone as well, I just haven't seen it mentioned as much.
Yup, wired OR gate. If you need to avoid that in redstone, you can abuse the fact that signals cannot travel downwards on glass, but can go up. No need to introduce delays with repeaters.
Can't you use diodes IRL?
@@theseangle yeah, but I don't think that's normally how it's done(possibly because of the voltage drop across a diode)
Isn't it used in AC?
@@matthias916 could you elaborate?
400 views in 8 minutes??? Man, your community sure loves you
Dude very cool series. I found your channel a while ago and every video is so exiting!. Sadly i dont have that much time to see this whole video now but i will be coming back to it, although i know this stuff, it is still good to go back to the basics and see how people explain them and you did a very good job!. See you around.
I think a good sign that you're doing a good job is that before I watched any of these videos, I had no idea what I was doing with redstone or circuitry in general. Managed to figure out the AND gate just by what you explained.
Keep up the good work, man
So far I'm really loving this is series, it's much easier to follow along with than the original
Fun fact! For DeMorgan’s Law, a common mnemonic is “Break the line, change the sign.” This is used because an overline is another symbol for NOT, so !(A & B) = !A v !B.
I can see this video being used in university for programming. It's extremely well explained!
Not really necessary, we covered algebraic logic in the computer hardware module. It covered almost everything in this video and was probably the easiest module overall.
Such an amazing video, absolutely clear and precise. It was easy for me to understand even though I am not that good at figuring things out!
No joke, I literally realized de Morgan's law (not knowing that's what it was) when you showed the truth tables, wrote some simple code to test it, realized it was correct, and unpaused your video to you telling me what I just did has a name
One thing I learned in school where talking about Bool algebra is that the AND is a multiplication (and that make sense since multiplying by 0 the output is 0), the OR being + and that also make sense if we say that 1+1=1… else that was a great video !!
You can also think of OR as MAX and AND as MIN ^^
@@echoes6092 I tried doing this with 0-9
and - MIN(x, y)
or - MAX(x, y)
not - 9-x
The symbols in the video are rooted deeper in mathematics and logic, the common symbols in computer boolean algebra application would be + and * for OR and AND while NOT commonly is denoted by apostrophe. A + B'C , A OR B NOT AND C
@@user-fp7jz4ot6f so what does xor gate do in decimal system?
for the xor gate with comparators, if you just get rid of the block and have to redstone out the back it gives a much longer signal strength, love this series learned a lot!
I love your style of writing out info and math in blocks~
Amazing explanations again, I would have loved it if a video like this existed when I learnt boolean algebra at Uni
THANK YOU SO MUCH BRO not only you helped me understand redstone better u also made computer science at school make way more sense!
even with only the first three episodes I feel like im getting better at Redstone so far this series has been so helpful tysm
This is useful for even just electronics and computer science. I think the Redstone laid out next to the Truth Tables really helps visualize how it works
I used to do alot of piston related mechanisms and now as I'm watching ur vids I can see how compact I can make things!
You explained it so good!
я люблю смотреть твои видео! Благодаря тебе, впервые узнал о двоичном сумматоре)
Can't wait for the next episode!
XOR Gate instructions unclear, accidentally gave birth to an unexpected NAND Gate
Incredibly well-explained 🏆
Thank you Good Sir 🎩
This is one of the most clear explanations of logic gates I've ever seen, well done!
Side note: I respect you so much more now... you used an awesome Creo song for your outro XD
LOVE this series Matt
If I was a maths teacher I would just watch your videos in class (or watch them in preparation). I have experienced so many teachers and even profs making a complicated mess out of these topics giving me a rough time wrapping my head around, though it's really not that difficult. Your explanations are brilliant.
Great video! If you ever dare to make a video teaching the logic on how to convert a real code into logic gates like that, I'd be astonished!
i figured out the and gate using the demorgan's law you taught us! it made me feel so smart.
I understand redstone pretty well but I have a very basic understanding in computers. Great videos and i can't wait to watch them all!
This is absolutely fascinating to me. I’m a philosophy major and intro to Logic was a mandatory class. The fact the the logic system Aristotle used in Ancient Greece is now used in programming is amazing. It’s also nice that this video was more of a refresher course for me.
This video is so helpful. I think it might've been easier to use X', XY, X+Y, etc, so it's easier to understand especially for people unfamiliar with boolean algebra.
you are a incredible teacher
In every single one of our computing classes we use A̅ for "not A", + sign for "or" and mutiplication for "and", that way you can stitch them together as A̅B̅C̅DE for "not ABC and DE".
An XOR gate for example; A⊕B = AB̅ + A̅B meaning "A XOR B = A and not B or not A and B"
This was amazing, its so funnn
There is also another cool way of looking at Boolean algebra! We can also approach it from set theory and probability, where we would represent the "and" operator as a intersection of two sets, and the "or" operator as the union of two sets, with each set representing a bit. Which would mean that the probability of finding a value in the union or intersection will be the and or or operator of the two variables in the sets!
Quick note : the symbol for union and intersection very closely resemble that of the and and or operators.
I tried Boolean algebra with a few really simple circuits and it made them complicated but when I tried it with complicated ones it made it simpler.weird how that works. W vid.
I already love math, thx for making me love it even more
I LOVE THIS
ITS SO FUN
Such a great video
Wow, cannot believe it, i saw the video within 21 minutes, good thing subscribed xD.
As a learning programmer, you explained this with ez!!!
Amazing "tutorial"/explanation
I love this series
Awesome stuff
This was a super cool lesson!
amazing video, thanks!
Literley just learning this stuff in my engeneering class the other day and thought about how it could help in redstone.
I love this channel.
Nice video, keep them up!
I wish you would have taught us my favourite tidbit of information regarding nand gate: every other gates can be made solely with nand gates. It can be a fun redstone challenge.
fantastic!
THANK YOU VERY MUCH
This is literaly just computer sience and I love it.
WE SKIPPING SCHOOL WITH THIS ONE 🗣️🗣️🔥🔥🗣️🗣️🔥🔥🗣️🗣️🔥🔥
For those who are really interested in simplifying boolean circuits/equations/truth tables, I recomend looking for karnaugh maps.
The red stone torch on the side is actually a NOR gate with 3 inputs which are the 3 other sides of the block. NOR gates output true if none of the inputs are true.
Note that the NOR and NAND gates by themselves constitute a "logical formal system", which means you can use NOR to express any truth table out there, same with NAND. You need NOT, AND, and OR together to accomplish the same thing, this means any circuits you build with those 3 gates can be built with just NOR gates, and your single torch is on the side of a block is a NOR gate.
I have a suggestion for your next video: Could you explore some creative applications of logic gates in non-computational redstone projects? Such as two levers controlling an iron door through an xor gate
I really wanted to get into this things but ı font have much time for this in these days because ı am preparing for the exam to graduate high school but in The summer ı am gonna get into redstone computering. You are encouraging me this video is awesome
i didnt understand my systems class lecture in college so here I am learning the redstone equivelant
How I'm thinking about the XOR and XNOR gates: they work based on symmetry, like you said. The XOR gates return TRUE for asymmetrical inputs and FALSE for symmetrical inputs. Flipping one of the inputs beforehand also flips the symmetry, and so the XOR gate can now work as an XNOR gate.
Appena iniziata la prima superiore informatica e mi stai aiutando molto
Cool tthing about NAND (also NOR) is that you can build any other logic gate using only NANDs. :)
I have a maths exam for comp sci on Monday so this is basically my revision
So happy i tried to make the AND gate and got it right! altho my redstone wasn't as compact as the answer he showed us haha
Thank you, now I got maths^redstone knowledge in my brain(really I appreciate it thank you)
This is the first thing I learned with logic.
WOW! Minecraft redstone logic. PSYCH! EAT THIS AMAZING CLASS ABOUT BOOLEAN ALGEBRA!! Amazing explanation, class grade worthy Matt. You're a genius!!!
There is a good book about not only boolean algebra, but more algebra as well, called "How To Prove It". I dont remember who made it, but its pretty easy to find.
Thanks!
Ahhh, that Bob statement brought me back to good ole geometry class when talking about deductive and inductive reasoning.
"Pigs fly when it rains."
If raining and do not see pigs flying = false
If not raining and don't see pigs flying = true
So far some good stuff!
it's funny i'm just revieuwing my math class and you explain it better thx
FYI you can make transistors by putting a comparater in subtract mode and putting a lever on the side.
Excelente video!
I believe the compact XOR logic gates uses the reduced expression of it:
A XOR B = [A AND NOT(B)] OR [NOT(A) AND B]
Because the comparator allows that one lever sets A AND NOT(B) mode or the opposite.
Also, the reason of the negation of the XOR gate just need to have one input negated is because of this:
If I negate the A, the expression above becomes on that:
[NOT(A) AND NOT(B)] OR [A AND B]
That is the negation of the XOR, that I call "coincidence AND" that is true only when both inputs are true or false at the same time.
logic topic in high school math made me understand this video to the end
thanks math
This would've been very useful for my computer science exam yesterday T~T
There's a bunch of minecraft mods that expand or improve on redstone logic gates, but what I'd really love is a configurable "Truth Table" mod. Essentially opening a GUI of a truth table and selecting what input conditions should trigger an output
De Morgan's is such a life saver for simplifying circuits
You summed up an entire second year university course in a minecraft video. Well done
You were the 256th comment
If you've seen episode 2 of this series you know the significance
Fun fact : In pure logic (so, not talking about redstone or circuits), all operations can be expressed using just NOR (which can be written ↓) or just NAND (which can be written ↑ or |). This is mainly because ¬P is equivalent to both P ↓ P and P | P.
Here's how you do some common operations using just NOR and just NAND :
A & B :
(A ↓ A) ↓ (B ↓ B)
(A | B) | (A | B)
A v B :
(A ↓ B) ↓ (A ↓ B)
(A | A) | (B | B)
A ⊕ B :
((A ↓ A) ↓ (B ↓ B)) ↓ (A ↓ B)
(A | (B | B)) | ((A | A) | B)
A ⊙ B (XNOR) :
(A ↓ (B ↓ B)) ↓ ((A ↓ A) ↓ B)
((A | A) | (B | B)) | (A | B)
A ↓ B with NAND :
((A | A) | (B | B)) | ((A | A) | (B | B))
A | B with NOR :
((A ↓ A) ↓ (B ↓ B)) ↓ ((A ↓ A) ↓ (B ↓ B))
Is it completely unwieldy, ridiculous and insane? Yes. But I think it's funny how it's actually possible to do everything in logic with just one operator. I also think it's interesting that the operations for AND and OR are swapped in their structure when you switch from the NOR system to the NAND system and vice versa. Same with XOR and XNOR. And how the NOR formula in NAND, and the NAND formula in NOR have the exact same structure. I think it's cool.
You are the best! Thank you for the simple explanation! But I want to see the advanced world of comparators... can you please make!?...
In 1.20...
yay new vid
I feel so jealous of those simple xor gates. Years ago I built a basic redstone calculator (I believe I started before comparators were in the game) and my gates were slow, bulky, unintuitive messes. Redstone has come such a long way since then.
I'm over here learning algebra for minecraft, instead of preparing for my tomorrow's exam
as a student who has computer science major this feel nostalgias
as someone who's gonna enter university soon, this feels fun.
Very good Matt next episode 4 Matt 😅
Before watching this video, I knew of De Morgan's law, not what it did. The book on boolean algebra I had talked about it, but I didn't know it.
Building that and gate actually made me feel super accomplished lmao
Yay I made an AND gate myself :D
1:10 To make an or gate, combine AND with NOT to make NAND, then use NOT in both inputs of a NAND gate to make an OR gate.
7:18 I almost thought you are gonna say "I want to thank to our sponsor..." :D
im happy i was able to do the and gate without the tutorial
I am studying my logic circuits course at uni with these videos lol
Thanks for the new vid, matt! Happy to follow your videos and learn more about computational redstone! You have been a big part of my journey.