EEVacademy | Digital Design Series Part 2 - Digital Logic Boolean & Demorgan's Theorems

Part 1 of a digital logic desing tutorial series. Boolean Algebra & Demorgan's Theorems explained and how they are useful for circuit simplification.
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[@theslackerengineer9351]

PLEASE KEEP THIS SERIES GOING DAVE!!!

[@Willster451]

The Slacker Engineer YES PLEASE!!!

[@thomasvnl]

Agreed. Very insightful for anyone who hasn't had these kind of "logic" lessons in university (or forgot about them), or anyone who wants to learn more about optimizing circuits. Thanks Dave!

[@maxheadrom3088]

Yes! Keep this series going, Dave!!!!

[@3rdpartyU5er]

This is the only thing I originally subscribed for!

[@lewischalmers7465]

Agreed! I have an exam next friday and this is vital revision! Need K-maps now please! :)

[@vladomaimun]

Dave, you have a big THANK YOU from everyone who is studying this. Please, keep this series!

[@jcobnl]

Demorgan's theorem: "Break the line, change the sign". That's how i've learnt this.

[@james77011]

Yes very tru and super easy

[@mbaker335]

Not touched this in decades and despite being simple I always have to read/listen to everything six times over. Please keep up this series. As an aside, depending what gates you have left over in a design it may save a chip if you de-simplify a design. Assuming you are using near DC and can have tracks going everywhere of course.

[@Pelnied]

Great video. I'm glad you drew the gates out to show people exactly how these Digital laws will transform and simplify logic circuits.

What a pity I didn't have this videos available when I was studding Boolean Algebra & Demorgan's. Continue with this series, I'm sure that it will be very useful for many students and "aficionados". I'm also waiting for more analogue electronics theory videos.

[@WisdomVendor1]

When I was in electrical engineering in college, I loved Logic Design courses. I graduated about 28 years ago and even to this day, I'll design a sequence detector time to time just for the fun of it and test it on multisim. It's an awesome field.

[@WreckDiver99]

Takes me back 25 years Dave. My first digital logic class. Learned all of this there...of course I'm now looking forward to K-Maps!

[@btouw8558]

yes,do the karnaugh-diagram also please

[@worm6942]

Your lesson on Boolean is GOLD!

[@BarriosGroupie]

*This is great, very educational and useful to noobs!* Perhaps you could do an electronic design monthly where people comment on what they'd like you to do, and people upvote the suggestions. I'd love you to do a series on electronic design concepts that revolutionized electronic engineering such as distributed amplifiers, sum-of-product state design, current mode amplifiers, switched mode power supplies, negative feedback etc.

[@wgm-en2gx]

man this takes me back... did all this stuff in college. Did a 6 variable karnaugh map on a board once, almost lost my mind.

[@Nippius]

Awesome video! Boolean logic (all the way to flip-flops and ALU's) was one of my favorite disciplines in university. It would be really could if someday you could make some videos about building a CPU by using the logic gates, writing your own ISA, etc!

[@roberteliassen5020]

This brings back 30 years old memories. :) Thanks! Moving on to latches, flip-flops and adders perhaps?

[@sparkplug1018]

Really liking this series Dave, please do more of these. Would love to see practical demonstrations down the road as well.

[@liamhood16]

Yes! the Dave cad is back, baby!

[@darthvader8433]

Wow - I did this stuff 37 years ago during my apprenticeship.. Thanks for the recap Dave !

[@james77011]

I love this guy teaching ❣️

[@greatbigphil]

I found the video fun, easy to understand, and compelling.

[@EEVblog]

Thanks.

[@pirateman1966]

Dude, Dave, You are all over the place with your videos! Who uses discrete logic any more? Technology doesn't go backwards.

[@HaloWolf102]

If you don't understand 10:57. There is an amazing video named 'Universal Properties of NOR and NAND Gates' by Jim Pytel. Channel name is Columbia Gorge Community College.

[@manojkumarsubramaniam7122]

Great Video Dave !, honestly this is the fist video on your academy series I understand and like

[@jamesmalvern354]

The best lesson I have found reference Boolean. Thank you.

[@ncrdisabled]

I spent 7 years in the NAVY on submarines SSBN 619 634 both built in the 60 s . It was during the 80 s. I was a IC 2 (SS) and just 1 machine was the MK 19 gyro which had over 100 tubes , In the NAVY school I went to taught us the use the Demorgan's to make some of the circuits easier. TO bad I got hurt after 7 years which left me in a wheelchair and a disabled vet. I loved the NAVY and going on submarines . You would not believe the special pays you get. The cost just for my knowledge they taught me was worth over 1/2 a million bucks /Now both subs are razor blades

[@G6EJD]

My university lecture (Douglas Lewin) told me to use these techniques wisely as the maintainer has to be able to (in the day) debug circuits and if too complex through these methods as good as they are, maintenance would be difficult if not impossible.

[@pjakobs]

Building 74 logic stuff was something I did long before learning the tools back at the university, so without knowing the actual rules, I was rather good at intuitively optimizing this stuff up to maybe 20 gates or so. Bit frustrating to see that now, 30 years later, I had to actually mentally follow the signals to find the optimizations. I guess it's use it or lose it as always. Thanks for the time travel, Dave

[@jero1836]

Big thumbs up! Thanks Dave

[@peterdkay]

Excellent presentation

[@kathyquinlan5922]

@7:52 We were taught a different way to remember it which may make more sense to some people "Split the Bar, Change the Sign"

[@xaytana]

It'd be so amazing if EEVacademy could become a collaboration project with Khan Academy. This would be so helpful for people without access to KZbin, which my old school would block YT but whitelist all the KA videos, and for people that want a solid sorce of information; I've had troubles in the past where there's just so much information through YT videos and different forms of presentation, and some people missing information or not clearly explaining it, that it just became frustrating looking for anything off of Khan Academy.

[@oliverthane2868]

I remember back in school we used to remember the saying "not each term, not the lot, change the sign" which I always liked ... maybe some other people will find that nicer than "drop the bah" etc

[@goyabee3200]

Like the new series. Cheers.

[@JSGregg]

Cool! That's a really interesting and complicated implementation of an XOR gate on the chip. Why didn't they just use an OR gate and NAND gate connected to an AND gate? Or an OR gate and an AND gate with a P-channel FET that turns off the output.

[@PatrickMumo]

This takes me back.. spread the knowledge 👍🏿

[@w8nwo]

Please keep the series going, but can they still follow the usual EEVblog numbering scheme? I find it quite helpful to have all of your videos sequentially numbered.

[@ntesla66]

Thanks for the series, Dave. Another vote for K-maps here.

[@jamesmasonic]

Please keep it up Dave! I hope you also teach electronics step by step with some practical info such as reading data-sheets or demonstrating on breadboard with a scope ect. Something like Horowitz and Hayes's Learning the Art of Electronics A Hands-On Lab Course book. Theory supported by some hands on examples would be really unique and fun! I hope there were more of you in the world! Thanks and good luck!

[@billmoran3812]

Good stuff! You are a good teacher. I can't wait to see where this leads.

[@voltlog]

Nice naming Dave! I like it.

[@mohit3189]

Great Video :) Also make a video on K-maps please :)

[@jimporfit]

I aspire to be as energetic as you. Infinite mental endurance!

[@jeffsweeney312]

Huh? I'm smelling ageism and besides, Dave is a youngster.

[@vx-iidu]

>muh ageism how lol

[@TheWP]

Dave, where were these videos when I was doing my EE Digital Logic courses?!?! Good on ya mate!

[@cursoderobotica]

Good theorical video!

[@jerryhubbard8578]

What is all this school stuff? I had to learn this when repairing 7400 logic at TI in 1970. I had a tube back ground. The book I used had been lost for many years. Found a used one on Amazon a few years back, wish it was PDF. I could find it faster now with a computer search. :)

[@MrOverlader]

Thank you Dave for this.

[@keithmiller4358]

Algorithmic minimisation methods would also be a very interesting walk through. I remember a little about Quine McCluskey from CS classes. Unfortunately that is np-hard, and seems of limited use in a real application where there could be many terms. The nice thing is that it can be demonstrated with pencil and paper, and can easily be implemented by a student. Practical synthesis tools apparently use some kind of heuristic for their minimisation step. This would be rather more interesting to understand, and having a practical & visual demo of this stuff beats grinding through some stale technical paper on the theory, or reading source code of some tool.

[@shitholeftw]

Excellent! Very nice format! Keep it up! The drawings (gates) are a bit how you going... :>

[@EEVblog]

I make no claims for my drawing ability!

[@natedunn51]

EEVblog don't worry it's 10/10

[@Gameboygenius]

8:45 and forward That's not right, is it? By just changing the operators there, you are changing the order of operations. For the resulting expression to be correct, you need parentheses around A+!B. For proof, look at the case of A=1 and C=0.

[@roberteliassen5020]

You're right, Gameboygenius. The answer is (A+!B) !C (where ! is 'not'). You have to do it in two steps. Edit: Nope, I was wrong.

[@channel_B5]

It's (A+!B)*C for me. Who is wrong?

[@roberteliassen5020]

Well, what do you know! You're right, B5. My bad. In general, you would do the operation in two steps, not "straight through" like Dave did. In this case he got away with it, but I believe it's not safe.

[@channel_B5]

No, I think your reasoning is correct, and he did not get away with it. His result is NOT correct. Take A=1, B=1, C=0. Original statement results in 0, his solution gives 1. (Provided we stick to the priority order of operations, that is NOT, AND then OR.)

[@Gameboygenius]

Dropping the bar "straight through" is no problem. The switch of operation and sign happens once per application of de Morgan's, so that works out due to parity. The problem here is, as I pointed out, that you need parentheses to preserve the order of operations. It's really likely just a matter of sloppy notation on Dave's part, the hand not being in sync with the brain as it were, but this is the kind of thing that can get a beginner if you don't point it out.

[@Jedda73]

Really enjoyed this, please do more

[@mUbase]

I love digital Logic. Do Karnaugh maps next Dave! Please?

[@DavidLeeMenefee]

Refreshing one's memory is a good thing. Thumbs up....PEACE from electronicwizard

[@Ybalrid]

Have to say, DaveCad 2.0 has a really cool UI

[@1987wlodii]

very impresive for kids is to bulid logic gates with coils (relays), rope or hydraulic pipes. Bulid the complex modules to show that Boolean is not only in electronic.

[@flatfrog69rr71]

Hi Dave -fantastic, will you please keep the two new channels going,they are very interesting Would it be possable to go over the break down of how the gates are made up of discrete components so they could be build on bread board and tested Thanks once again

[@winghui7620]

I LOVE THIS SERIES!!!

[@sagebrother]

Excellent and thanks!!

[@sean999ification]

Great stuff! More please.

[@wojciechjaworski602]

at 9:50: ~(~a * b + ~c) its not equal to a + (~b*c). It should be (a + ~b)*c ~((~a * b) + (~c)) (~(~a * b)) * ~(~c)

[@toddberg3892]

It's an interesting problem - in Dave's form it appears as a conditional statement instead of a gate-wise equation, so yes, boolean order of operations must be applied. The order of operations of the original equation must be preserved (the implied parentheses are carried to the transformed equation.) If a gate diagram was included then the desired order could be established using parentheses, but alas it wasn't.

[@Pelnied]

If you check the Distributive Law on (a + ~b) * ~c you would get ~c*a + ~c*~b which is definitely not right.

[@wojciechjaworski602]

Thanks, my mistake, lost some tildes characters when copied from my scratch book. To be sure I checked again with truth table: imgur.com/a/E4FGr

[@deanrubine2955]

Wojciech Jaworski Good catch, thanks. He just forgot about the parens.

[@jeffsweeney312]

Simple logic is often implemented directly using MOSFETs where it is easy to create NOT, NOR and NAND gates. Are there strategies for simplifying and transforming logic expressions to the minimum number of these three gates? Are there patterns in logic expressions that I should be looking for to achieve this goal?

[@MajinSYGFromTheBT]

This was very useful thank you

[@qubei]

You should consider releasing educational vids like this to a smaller test audience first (on a second channel or exclusive to Patreon subscribers, etc) so they can catch any minor or major errors before wider release

[@lufu3578]

At 11.44 Doesn't the AND Gate in the top right corner need to be a NAND Gate? I Love this Format!

[@JmanNo42]

Good repetition of Algebra didn't even know i remembered some of it, wasn't it called distributive laws and handled expressions doing mulitplications and division. A way to short out(simplify terms out of the equation, i really do not remember.

[@lmiddleman]

It is quite illustrative to show De Morgan's with a truth table. Becomes obvious.

[@mikedrz]

I have an exam re this on wed. This happens to be what I needed to quickly review. Still got counters, latches, flip flops, vhdl, shift registers, 7 seg display, decoders, encoders, multiplexer, demultiplexers. Will you have those videos out before wed? jk haha

[@dah4x]

Digital Logic Design: The Game. its a text-based version of NAND computing using netlists

[@Conenion]

The proof that any boolean function can be implemented using NANDs, NORs was done by Charles Sanders Peirce. Of whom Karl Popper once said, he is one of the greatest philosophers of all times.

[@pidott]

Loving these. Keep it up

[@crocellian2972]

On a substantive level, data sheets never contain details of wafer masking. Second, the burden voltage of die designs plays a significant role in choice of mask implementation. Third, the basic chemical structure of the process (most notably the adoption of CMOS) is by far the most critical practical issue. How about a real live bit of EE and track power consumption on a variety of logic chip designs (not FPGA hacking). Viewers will be amazed to see the real world uselessness of Demorgan's Theorem when confronted with actual implementation. But that would be work.

[@dan_]

That sounds very interesting, can you link me to your video on the subject?

[@15743_Hertz]

"Even though De Morgan's laws seem useless at the outset, they are really an important part of the logician's toolbox" math.wikia.com/wiki/De_Morgan's_laws

[@spammyjenkins87]

our mnemonic for demorgan's was always "break the line, change the sign"

[@Dr3x0w]

Thank u very much for this great video!!

[@mario6279]

I struggled with boolean algebra in electrical engineering courses..

[@PERILEX]

Do you always use the ANSI-Gate-symbols over the IEC 60617-12:1997-Gate-symbols or are you simply used to them?

[@gprgprgprgpr]

There is an error at 9:20. It will be obvious if you add parentheses according to precedence.

[@firebladecbr1k]

"break the bar, change the sign" is how i prefer to remember demorgans

[@jandobbelsteen8953]

Dave, you've made a mistake when explaining Demorgan's laws on inverting boolean formulas. In the video you mention that you should 'drop' the bar and change the operator and that's completely true. What you forgot to mention however is that the order of operation must remain the same. In your example you've got the formula: [(A'.B+C')'] which you rewrite as [A+B'.C] but you also should have added a few brackets to keep the order of operation the same, which results in [(A+B').C] Just fill in the truth table if you like to check.

[@FLyyyT_]

how'd you know this is what my mechatronics class is covering now? thanks

[@tmdrake]

Geeze...I used to remember this real well....been to drunk to keep up now.

[@kentvandervelden]

They stopped teaching K-maps in EE and CprE at the state University ~1998. I'm not kidding. Said no one needed to know how to do simplifications because software would do it for you.

[@mmelt]

Karnaugh next? Quine-McCluskey too?

[@futaris]

Demorgan's. Haven't really touched this stuff since uni.

[@oppongsamaboagye6188]

thanks bro

[@FurkanBahadr]

Logic Design most boring class to study I'm taking this semester but It's also most fun topic to implement in lab at the same time!

[@yaghiyahbrenner8902]

more analog electronics please.

[@raihanadhipratama5982]

love it!!!!

[@ACombineSoldier]

All of these are covered in college algebra. glad I studied.

[@okoZ9]

Will you make part 3?

[@SeltsamerAttraktor]

@EEVblog 9:50 Dave, you are missing parentheses there.

[@JennyEverywhere]

Is it bad that I first read that as "Demogorgon's Theorems"?

[@dylan1234540]

Haha only if t his video was posted a couple of months ago. Would have really helped on my mid term.

[@TosterCx]

Is that smoothdraw?

[@Charentule]

This is a subset of group theory is it not?

[@basileus9343]

Geee Dave, why didnt you make this video 2 months ago? I already did this topic at the university :/

[@james77011]

do anyone know if he didd a video on K-maps?

[@firedeveloper]

3:32 A plus ple? :D

[@rizwanhameed5791]

please help us to make a Rotary Encoder circuit as simple as possible. with out any software. A circuit wich we use in any project. wich will give us simply 0V-10V at output. please.

[@HaloWolf102]

Break the line, change the sign.

[@lexus4tw]

Plus and multiple for AND and OR, I'm not comfortable with that

[@lexus4tw]

Veinous yeah sure, I know this notations, but its a bit confusing, I normally use v for OR and ^ for AND expression, to separate logical operations form algebraic. Sorry for my English

[@lueefour]

From my understanding it is a distinction that separates EE from CS.

[@lexus4tw]

I studied Technical Informatics, at the university we only used the symbols that can found on wikipedia en.wikipedia.org/wiki/Boolean_algebra

[@seamonkeys12y]

I did discrete mathematics at uni last year and I've already forgotten everything.

[@EEVblog]

You and me both.

[@lesterelectronics223]

Bobbeh Mcstuffinshire if you don't use it you lose it!

[@BMRStudio]

I want to know, what can happen, when we randomly put together around 1 million gates with 32 inputs and 32 outputs on the end :) Total random. Somebody? All from DIP TTL chips!