Logic 1: Binary Propositions, De Morgan’s Law, What is an Implication - Tutorial 1/4

[@alfaalfa99]

I took Digital Logic as a class more than 10 years ago. A teacher over there made us build the basic ALU using shift registers and gates in several boards. It was nice to notice how everything builds up from a simple transistor to the emulation of logic.

[@georgeallen7487]

My teacher was not explicit about what we were building and the reveal near the end was very satisfying. He basically tricked me into doing something I had always dreamed of doing as a very young kid.

[@kirillholt2329]

@@georgeallen7487 relatable…doing it right now

[@xravenx24fe]

Glad to see more videos coming up! As a visual learner, you do a great job of making technical material really easy to digest for me with all the nice graphics to compliment your explanations.

[@muzzletov]

there is no such thing as a visual learner. moron.

[@Bisqwit]

@@muzzletov I will never understand people who feel compelled to suffix their statements with an insult. Like, what value does that add? What is the outcome you are trying to achieve? Does it bring you some satisfaction? Do you derive satisfaction in your life from denigrating others? What a sad, sad miserable life, and what an awful world you are trying to build around yourself.

[@muzzletov]

​@@Bisqwit do you really want an answer as you're superficially trying to derive scenarios where my actions would fit the narrative. i also dont owe you any explanation. and also a. i cant speak for anyone else as far as motivation goes and b. you will resort to cliche anyways, as you already did. but then, i am in believe that this is all to comfort your viewership, rather than understanding. also, what kind of romantic/prose bs is that phrase "... what an awful world you are trying to build around yourself"? nvm. im out.

[@bkz6133]

I'm currently taking a similer course in my university. And you just covered a few lectures worth of content in 16 minutes. And the weird thing is I got a good understanding of logic from your video alone than I did from the lectures I took at my university. Thanks :)

[@muzzletov]

this is such a stupid comment and i see it all the time "woah, man, i just learned everything, even though i didnt and my brain needs time to manifest process what i got taught at uni and i dont have a fucken clue of how my brain works and i am just here to show how clueless i am of the fact that this is how matters are"

[@figboot]

Wow, I'm taking a university course that covers exactly what you're going over in this series. Excited to see more episodes!

[@AT-zr9tv]

You are the perfect teacher for me on this topic. Just as your tutorials about many computer science topics and video games are fun, clear and very well explained. When, some day,you have the time and will, I think you'd write a terrific book of computer science curiosities.

[@totalledzebra483]

I can imagine watching this during a lesson. Very easy to understand with the examples.

[@katsumikougen8351]

This is a very good presentation here, Bisqwit. Nicely done, not too mind-boggling, and fairly understandable. That's what all your videos are about: tutorials with a soothing Finnish accent narration, amazing examples and lightning speed code-input in real time (no sped up footages). You could theoretically give Engineer Man and One Lone Coder a run for their money. If only KZbin's unholy algorithm did not suck balls...

[@1st_ProCactus]

The world needs more logic

[@Filaxsan]

If Bisqwit share a video, then we will watch it. Very simple Implication. Amazing job, keep it up brother! 💪

[@treyquattro]

yay, a new Bisqwit video! I learned De Morgan's theorem and Boolean algebra decades ago and they're still top of mind any time I'm doing complicated conditionals!

[@Bisqwit]

Thank you for sharing! Say, would you happen to have a good example at hand, either a real one or a plausible made-up one, that has four different conditions (inputs), say, A B C D, and which has the same truth table as D || (B && C)? The more complicated, the better, but it has to look at least plausible. You correctly notice that A cancelled itself out. The conditions can any expressions that return a boolean value, but preferably the expressions themselves should be simple, for example (x >= 5) and that sort. If you could come up with one, I would like to use it as an example in the next video, to provide the rationale for the Karnaugh map optimization I am going to introduce.

[@treyquattro]

@@Bisqwit Hi Bisqwit, I searched through source on my machine but of course don't have anything that meets the criteria of "complicated conditionals". The ones I was thinking of were in production code that is no longer accessible to me! The leap year calculation does fall into the pattern you wanted (except for the self-canceling A term), although I'm not certain it was what you were really after: bool leapYear = (year % 400 == 0) || ((year % 4 == 0) && (year % 100 != 0)); I was thinking more about the readability (and correctness) of e.g. (!A && !B) vs !(A || B) which de Morgan tells us are identical. I find this sort of thing useful especially when dealing with compound negations in conditionals. Alas it's more of a nicety to other human readers, I think, because modern compilers are so smart that they can correctly deduce what the programmer actually wrote, and very likely in a more efficient manner. This wasn't always the case, but here I'm I'm considering the state of the art from several decades ago!

[@Bisqwit]

@@treyquattro Thank you for your effort. Yes, that leap year formula is exactly the optimized form. What I was looking for was a _non-optimized_ form that is logically equivalent with the former, but which looks plausible.

[@eleganteatinginjapan659]

What a great timing for this series! I've just started my Computer Science Degree and I'm also taking a Logic Course. Looking forward to the next parts. Thanks

[@Acceptable76]

Great to see you back Bisqwit! Good stuff!

[@crashniels]

I currently have logic in university so this seems like the perfect video to watch

[@mattepcro3188]

OMG this is wonderfull, I'm taking a course on this right now !! Studying formalization problems, definitely need more videos on this topic

[@The242511]

This is a great tutorial, would made my life much easier if it had been released when I took this course.

[@muzzletov]

nope. it wouldnt have.

[@Saturos02]

Making such a video must be great for consolidating knowledge, as well as useful for viewers!

[@neon-rust]

Nice! This was a blast from the past. I studied electronics and computer science at university, but was during the previous millennium... 😲

[@Joshk326]

I wish you would’ve posted this video years ago when I took my logic design class. Good work you explained it so well!!

[@xtdycxtfuv9353]

I learned some of the American/millitary logic symbols and their apparent meanings from a video game called "Little Big Planet 2". That game, now that I think about it, did a very good job at teaching logic.

[@kryptoid2568]

0:43 yooo stanley parable? this man is cultured. BASED even

[@sorescythe3960]

It kind of shocked me how this topic just recently came up in my class and now you have a video about it...

[@harshgandhi100]

Boolean Algebra was one of the easiest but it was quite foundational in nature. It has been always fun to learn. I never learnt about IEC symbols or notation in my courses, I did know about them. Thanks for the informative video, Bisqwit.

[@crankyfox]

Excellent video. I really enjoy your tutorials!

[@imlxh7126]

Wasn't expecting a Stanley Parable joke, but I'm here for it. :D

[@tonym5857]

Hi B. We know how busy you are, it s always nice to see your videos, hope you are doin great with your studies and life 💪

[@55sombreroman]

The king has returned.

[@li82576]

great! it's very easy to understand with the examples. thank you

[@MarcelMaatkamp]

thank you for making these and I look forward for the next one!

[@SimGunther]

NAND: the most beautiful logic gate that fundamentally creates all other logic gates

[@Bisqwit]

As does the NOR, as shown in the video at 5:29. The implication is universal too (provided you sometimes give 1 or 0 as a constant input): ¬a = a→0 a∨b = (a→0)→b a↑b = ¬a∨¬b = a→(b→0) a↓b = ¬(a∨b) = ((a→0)→b)→0 a∧b = ¬(a↑b) = (a→(b→0))→0 a↔b = (a∧b)∨(a↑b) = (a→(b→0))→(a→(b→0)) a⊻b = (¬a∧b)∨(a∧¬b) = ((a→0)→(b→0))→((a→b)→0) And, if you allow wired AND, which requires open drain design, even even XOR and XNOR can be used to create all other logic gates. For example with XOR, ¬a = a⊻1 a∧b = simply two inputs tied together and connected to output. a∨b = (a⊻(a⊻b)) ∧ (b⊻(a⊻b)) where ∧ is as above. 0 = a⊻a

[@starc0w]

Awesome! Thank you Bisqwit! Excellently explained - very clear and original! (I think you forgot to replace the AND ^ symbol with a OR v in the truth table in the second slide 3:56 ?

[@Bisqwit]

Good catch! I also had forgotten to replace them in the bottom part at 3:51 (as people who have seen my five preview videos for this episode have maybe noticed, though failed to tell me), but I noticed it before publication and fixed it. But I missed the same in the truth table. Oh well…

[@starc0w]

@@Bisqwit Annoying - but never mind Bisqwit. The video is excellent. The best books have an erratum.

[@ricardo.mazeto]

The antecedent is sometimes called precedent. Logic really becomes fun when you get into fuzzy logic.

[@briankimathi5033]

He is back.

[@prog4925]

Wonderfully explained, Thank you.😊

[@viliamjr]

Great video! Very good analogies.

[@aaaaaaaaaaaa4788]

it's all fun and games until your professor says "enough about propositional logic, time for predicate logic"

[@not-on-pizza]

Good introduction! About the only thing that I'd add is that I've seen EOR instead of XOR in a few places.

[@Bisqwit]

Good point, I have seen EOR as well. I will add it to the sidebar for next episodes if I have time to regenerate them.

[@valizeth4073]

Kinda fun you going through this considering we talked about de morgans law on my previous lecture ;)

[@childfs6865]

Man, material implication bugs my brain to no end... Thanks for the vid anyways

[@RETROMachines]

My life is complete. I can die happy now.

[@tdelfino2509]

3:29 Took me a few tries to figure out if that was a video error or not 😁 Also MHRD is rad, I'm fighting the urge to write a program to find the best solutions automatically (at least until I've figured them out on my own). Can't wait for Part 5 of this series where we make a hardware 3D renderer using only NAND gates

[@Bisqwit]

Not a video error. Game developers did not anticipate that a gamer could create a situation with small Mario having fire power, so when Mario shoots fire, a big sprite appears temporarily because there was no small sprite for that purpose.

[@DjVortex-w]

When it comes to logic circuit optimization, the next video will be interesting.

[@Bisqwit]

@@DjVortex-w Not only logic circuits, but also boolean expressions in programming languages.

[@voxbine4005]

My brain is in pain, but pain makes you more stronger

[@eroc1944]

Love your content.

[@CurrentlyObsessively]

This reminds me of a book I think you would enjoy very much! The Elements of Computing Systems by Nisan and Schocken.

[@tiagosilva5476]

Nice video!

[@MrDroenix]

I'm starting to question the Disjunction truth table presented at 4:13. There's two types of ORs, inclusive and exclusive. Inclusive being either statements can be true, and exclusive where only one of the statements can be true. The truth table seems weird to me-- wait a second... I had written more, but now I realize the truth table is just presented differently. Usually, I see A and B side by side with the output in the 3rd column. B is in the 3rd column, and the output is in the middle or 2nd column.

[@Bisqwit]

Yes, like I said in the video, there are multiple styles of writing truth tables. In digital electronics, usually the output is put in the rightmost column, but the advantage of putting it in the middle is that you can create a truth table of a complicated expression at once without repetition.

[@shadowrealm8937]

4:40 how can power goes out if no power goes in? From some battery?

[@Bisqwit]

In digital electronics, each logic gate also has separate inputs for +VDC and GND. That is, they are always powered on regardless of their inputs. Without this arrangement, inverting gates like NOT would not be possible, and due to losses, long chains of gates would be impossible as well.

[@ricklorion]

Great stuff

[@NullPointer]

I wish i had this video when I was baack in university 4 years ago

[@paco3447]

Did you know that Exclusive disjunction OR was a royalty based patent from 1976 to 2007 (now expired) held by a not allowed to mention here corp? Though in its cookie cut method for dynamically displaying images stored in RAM. In fact Commodore's CD32 system was sued and banned to commercialize in the US due to such infringement.

[@Bisqwit]

I did not know that!

[@paco3447]

@@Bisqwit It's real. As long as yt's algorithm deletes every comment with either the patent number, corp's name or logic acronym for the exclusive OR, you can find such patent via Amiga CD32 Wikipedia entry (Eng) and read the Release title second paragraph.

[@paco3447]

@@Bisqwit Not only that, but every single terminal in the late 70's early 80's (cursor blinking), computer, mini-micro computer, game consoles (cookie cuts, blitting ops) etc. of that era had to pay fees up to 2007.

[@Bisqwit]

Quote: “pay 10 million USD[6] in patent royalty to Cad Track (U.S. Patent 4,197,590)[7] for their use of their XOR patent” That is horrible. Although now that I read the patent application, it seems to be about a method of computer graphics generation. There seems to be a lengthy bit about XOR… But reading that excessively obfuscated application, I have no wonder a poor patent clerk approved it.

[@paco3447]

@@Bisqwit Yep, it's about graphics memory copy operations. But it happened to be in mostly every single one used back then. Just think of blitting operations, cookie cuts, cursor blinking and so on. So basically a patent abuse.

[@HugRunner]

Awesome as always! :) This logic doesn´t account for "bit-flipping" caused by e.g. high energy particles, so perhaps there could be a scenario where the thief is barking at the dog ;)

[@raghul1208]

thanks for this

[@tis-go0n]

quality content

[@discontinuity7526]

Ahh this takes me back to university days

[@discontinuity7526]

So nostalgic

[@efa666]

I always loved Binary logic, I studied in the place where the great George Boole taught.

[@joelyole3431]

God bless you Bisqwit! You're really smart.

[@liryan]

"logic is logic is logic, right?" Proceeds to Stanley Parable as an example. Picked a game famous for its illogical design, well played there

[@Bisqwit]

But 2+⃗2⁴⁄₇₈ = Fish! kzbin.info/www/bejne/g5aQpKtjhraLqNU Anyone who disagrees is probably not a person.

[@nero008]

you should try S. Epp

[@m4rt_]

There was a book published where they used he entirety or the book to use logic to prove that 2+2 is 4 I think it might have been Principia Mathematica, but I'm not shure. I watched a video on it a long time ago

[@alessiocaffi5992]

nice vid and review for new tech. student. Bisqwit I wanted to ask you this Q. in last vid when you said you were attending university it strikes me and just wondering why? A) you choose to get a degree because perhaps you want to work for a company and they're demanding someone with a degree or B) you felt could gain extra knowledge. or furthermore for... C) the fun and for the title (the paper) . Yes because for me a guy with a MS degree in CS from MIT knows less that you and if I was that company I would definitely give a person with your expertise the job in CS. My reasoning comes from the fact that many people over internet are saying that one don't need to attend university to land a job ,especially in CS/programming /developer, if you are good at it that is. Be a good self made man , learn the stuff from the many free resource (yt etc) . After seeing your incredible videos and many other good tech youtubers I kind of believed that . Now your choice of getting a degree contradicts this myth . Otherwise if true no one would attend ivy league universities because certainly to the eyes of most people a paper from these top uni. even if one sucks is worth much more vs less famous/known university e.g like mine (degree in EE)! and even more so to self made man. I don't think so. Bisqwit I would appreciate your sincere point of view on this matter. Thanks. Cheers.

[@Bisqwit]

Thank you for your thoughts. There are several reasons that I can think of. - I am once again approaching the point in my work where I feel like I am going to need a break. - Like I told earlier in my FAQ series, working as a teacher in Finland requires a masters degree (barring temporary substitutes), and it has been an ambition of mine. - I believe that getting a degree will improve my feeling of self-worth. Who knows, if this goes well, I might try and aim for a doctorate. But it is way too early to make plans for that. It would be a way for me to redeem my past of dropping out from the path of education soon after vocational school (which by itself is also looked at as inferior to high school/gymnasium). - I may like the challenge. So from your list, all of A, B, and C are correct. There are also reasons why I didn’t do it earlier. - Starving student is a thing. I am now financially in a situation where I can afford a prolonged absence of work. Luckily, enrollment costs in Finland are negligible for Finnish citizens. - It has literally taken me this long to be _receptive_ to the idea of focusing on other studies than computer science, even though I regularly read Wikipedia and watch KZbin on a vast number of subjects other than computer science. - Until recently, I had absolutely no idea how universities work. How enrolling works, and so on. This is reflected in my FAQ video part 2/4, published just 1½ years ago, where my chart got more hazy and inaccurate the further down education path it went. - I have a friend who has undergone similar studies, and is now working as a teacher. Their life story may have influenced my decision, and having someone that can relate to my experiences is always comforting.

[@alessiocaffi5992]

@@Bisqwit thanks for your reply. Good luck on your studies. I did get my EE degree in a costly US Uni. but somehow now wanted to believe in the "open source" of learning experience/tuition and self made. Guess as long as there will be Universities, bureaucracy and companies demanding that paper this openness will remain just a myth even if you were self thought and much better than someone with "THAT" degree.

[@appdata8476]

I failed logic 1 and 2 last year, in my University (in Spain) we do both the same semester. I must say I understanded the think, but failed because of time. There is no second chance exams there :( I will try again with logic next year.

[@Bisqwit]

Sorry to hear that, and surprising that there aren’t retake exams. Best of luck to you the next time, and I hope this video series will help. The hardest part to me was natural deduction, and this will be covered in part 4.

[@Morphinof]

I'm sad because i really like your content and youtube does not alert me when a new video comes out, click the bell they said but bell does not work 😔

[@aleksandr2245]

I apologize for asking such a question, but how old are you?) I'm 35 and I hesitate to go study to university, I think I'm too old for that :( Thank you for interesting video as always!

[@Bisqwit]

43, began my studies 4½ months ago.

[@teachies902]

anotherbisqwitvid:)

[@suncrafterspielt9479]

Did you study at Aalto?

[@Bisqwit]

No.

[@suncrafterspielt9479]

Is SISU used at other universities too?

[@Bisqwit]

@@suncrafterspielt9479 I was under the impression that it is specific to University of Helsinki. Looks like it is also used in Aalto, TUNI, LUT, and JYU.

[@suncrafterspielt9479]

ok cool thanks :D and where did you study?

[@Bisqwit]

I _began_ studies in the University of Helsinki 4½ months ago. Before that, I graduated 25 years ago from a vocational school.

[@Asdayasman]

Leave it to a university to take simple, easy to understand concepts, and wrap them up in impenetrable language.

[@liondukan7667]

the mathematical logic of numbers is direct, assuming it is universal, because there are universes with different concepts and different mathematical logic. Have you heard of a curved right angle?

[@Bisqwit]

”there are universes with different concepts and different mathematical logic” [citation needed]

[@victorfds]

Why did you stop to saying "Shalom" at beginning while a Hebrew versicle was shown on the screen?

[@Bisqwit]

I have done greetings in various languages in my videos. As for the logo, I vary, but the one in this video is one that I had designed for me.

[@dodzhtv]

btw Minecraft Redstone is basically logic gates in a nutshell

[@DarklinkXXXX]

No one gonna talk about how he was tiny fire Mario though?

[@yourfutureself4327]

💙

[@MzHSky]

trying to understand

[@alegz]

Mario? Who's Mario? That looks like PERSON to me 🤔

[@thepianoaddict]

I saw the burglar in the thumbnail and thought this was a denome video

[@gledianlalushllari9577]

logic is logic is logic is false because logic is logic is true and true is not equal to logic.

[@Bisqwit]

In mathematics, expressions like a ≤ b ≤ c are not evaluated like (a ≤ b) ≤ c, or a ≤ (b ≤ c). It does not become a comparison against a truth value.

[@docwhogr]

25 years programmer, never used implication..

[@tbird-z1r]

This stuff always seemed like common sense. Never studied it in university though. Surely anyone with an IQ over 115 understand what "and" and "or" mean.

[@Bisqwit]

Much of mathematics appears self-explanatory and obvious once you know it, but it still takes _someone_ to formalize it. And until something is proven, there always is a doubt whether some alternative would be better. If you want to feel an intuitive example of this phenomenon, start playing Go and try solving tesuji problems. These are small puzzles where you simply have to figure out the best move. Until you gain enough intuition and calculation skills to do it yourself, it appears very difficult and there always remains some uncertainty, but once someone points it out to you and explains it, it seems very obvious.