EEVacademy | Digital Design Series Part 3 - Designing Combinatorial Digital Logic Circuits
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- เผยแพร่เมื่อ 9 มิ.ย. 2024
- How do you convert a logic truth table into a digital logic circuit?
Dave shows you how with the Sum Of Products method.
Part 3 of the digtial logic desing tutorial series.
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i love K-Maps, it's like you play a little game and a side effect is some Boolean algebra getting done. heh
😹😹 yes, most definitely
Keep it coming. I do enjoy watching your videos.
Cool, I have an exam on this next week, this is great repetition.
It's been 15 years ago, but i still remember this stuff. Very useful, and whoever said it has no use nowadays should consider another job/hobby. Or c/p arduino-code.
Easily my favorite study in school!
Great video, as always. Can't wait for the video on Karnaugh Maps. I'd love to see something on sequential logic as well. Or maybe an explanation of CMOS, NMOS, TTL or maybe even older families like ECL, RTL (or MML if you prefer) or DTL. Perhaps about how the work on the component level, the differences in performance, the history or how/why one family replaced the other as the technology progressed. I dunno how useful it would be to talk about older logic families, but I think it would be interesting for the sake of curiosity if nothing else. Thanks for taking the time to make this video. Cheers.
The thumbs up sign though 🤣.. Anyways the vedio was great. Explained in detail
I want more!
If you're looking to reduce the number of 74-series logic chips for this, use a 7486 since this is a single XOR gate.
Sum-of-products is not a _method_, but rather a canonical form for boolean expressions. The missing explanation here is the concept that *any combinatorial logic circuit* can be expressed as a sum-of-products, and therefore can be drawn with ANDs, ORs and inversion bubbles.
As a programmer I sometimes use this technique. However in that context it's best to let the compiler figure out the optimal logic, as optimized logic is much harder to read. Sum-of-products logic is quite easy to express in natural language. This-and-this, or this-and-that, or such-and-such...
Inductive thumbs up! ROFL
Thanks for this sir! I was wondering what software is the digital blackboard you're using there? Looks pretty useful! Be well :)
boolean/digital logic is so fascinating and honestly interesting, but it also makes me want to rip my hair out literally all the time. fascinating, isn't it?
Ah, the good old stuff!
The example is an XOR gate!!!!
I was waiting for the XOR
TheWP It's all over the video.
Yes, that would have simplified it to a single gate. I was waiting for it as well. I saw it immediately when he modified the logic table.
Same. I was hoping Dave would mention that he was implementing the XOR function, given it is an educational video!
Maybe because of how much bigger it is to build. That's why my father likes NAND gates and runs like hell from them.
In real life if you were building a circuit and needed an XOR gate you would most likely implement it with NAND gates. On a modern chip you often don't pay for the logic gates; instead you pay for the area used, and you pay for each type of gate used. So if you add 1 XOR gate, that costs the same amount of money as adding 100000 XOR gates! And generally any sort of processor or IP block that you're using in the circuit will already be full of NAND gates; you'll pretty much always already have NAND gates in your circuit. So implementing it with NAND gates is way cheaper in most cases, because NAND gates are a universal gate; you can build all the other logic gates with them.
If you check bins of surplus parts at a makerspace or something, you'll find lots of discrete NAND gates, and very very few of the other gate types; for the same reason! It is cheaper to buy 1000 NAND chips than 200 XOR and 200 AND and 200 NOT, even though 1000 is larger than 600! It is just way better to have less types of chips in the circuit.
hey I just had a midterm on this in my assembly coding class and I didn't understand how to do the circuit part at all until now
I need to wind a tesla coil over to my thumb to give you inductive thumbsup
lol that thumbs up... should become the next industry standard symbol for a thumbs up
Gosh. Back in the '70s... lets see you explain how to do a 7 segment display... 😅
I really loved Karnaugh mapping. When my prof explained to me I nearly wet my pants.
I did a pseudo segment dot display in the PS3/PS4 game Little Big Planet. It was a segment display using LED "dots", but it was more than just a basic seven segment. It also does hex digits A-F It had the corners curved, on curved digits, and used stubby segments for things like the 3, 4, and the E and F.
if.lbp.me/img/ft/b9f79c9cef798c40278d5d0724bed5d3719a6dab.jpg
@EEVblog, could ya maybe check out this Multimeter in a future video? VeckDigi MD22V
Did this "thing" at the end eventually force the deep lerning TH-cam gates to decide for bad contents? I counld't open the mailed link in the announcement.
The Intel that I work at uses HDL and synthesis to create our billions of transistors, not k-maps. When I interview recent university graduates and ask them to create a solution in HDL they invariably try to create some monstrous combinational logic equation instead of busting out the case statement or a left shift operator. I always direct them away from that slow and impossible to maintain coding method.
Steve M For years, the HDL tools affordable to students weren't good at optimizing, and even if they were professors have to structure their exams to actually measure if the students understand the underlying theory not just how to punch the question into a computer. Neither favors letting the computer do the work.
Apparently the magical automatic pen eraser thing gets sluggish as soon as it has multiple pen strokes to erase.
At 5:05 can you just join the output leads instead of using an or gate?
Nope. Wiring two logic outputs directly won't act as an OR gate, obviously.
You can if the logic is inverted and the outputs are open collector / drain. (google 'wired or').
👍👍
Dave, I think you should have gone a little further and talk about PALS. This is where boolean algebra comes in real handy in particular when you only have so many AND, NAND, NOT and OR gates in a given device.
Chris Morton And those are specifically sum-of-product devices. Unfortunately hard to get good PLDs these days that aren't scaled down FPGAs not quite optimized for PAL like work.
Nice. I'd just use an XOR.
(yeah, I know the point was to learn the math.)
10 years of minecraft prepared me for this
Dave, y u no say this is an XOR gate?
Remember the Apollo Guidance computer, all NAnd gates.
Yes your are right, same idea other way round.
Got an add at the start, so... not sure how unsuitable it really is if advertisers are buying space.
This is very apt for what I've been doing for the past two nights.
(Attempting to reverse-engineer the gates / logic / registers in the main "ALICE" chip from the Amiga 1200.)
m.imgur.com/a/j1jNn
Isn't that 20 years old or so? Do people still use those?
Definitely! Amiga is still cult computer.
Brek Martin
Haha. :p
@cbm80audio - I can say with very high confidence that Brek is probably joking. :)
(he frequently sleeps with a CD32 under his pillow. lol)
Theres a recent A500 repair and refurbish video on YT
Paul T
Yep, Mr RetroManCave did a great job with both the restoration and vid.
By coincidence, I've just been seeing if I can display my A500 on the projector, using a cheap EasyCap USB dongle on the Android box. ;)
It's nearly working, but I think I left the keyboard and floppy drive unplugged inside the Amiga, so just got a white screen.
Is nand gate easier to make than inverter.?
Wikipedia says that CMOS NAND is 4 transistors whereas CMOS NOT is 2 transistors.
But NAND can be combined to make more useful things than NOT because it can compare operands.
First method: 1 OR (1x7432 chip), 2 AND (1x7408 chip), 2 inverters (1x7404 chip)
Second method: 5 NAND (2x7400 chip)
Best method: 1 XOR (1x7486 chip)
Thanks 🖒
I was thinking the same thing after he added the second 1. One XOR and your done. Of course that wouldn't have been terribly educational :)
A large gauge well veined inductor! :○
Wouldn't you just use an xor gate on there?
You can't select any particular bit with XOR gate, but there's no "just" about it because XOR isn't one of the formal gates. It's made of other formal gates and ends up looking the same as this.
Go look up what's inside an XOR gate ;-)
But to implement this circuit, using 1/4 of one 7486 is more efficient, no? And propagation delay etc will be better for a 7486 than wiring five separate NANDs together...
I think the video is about the way to do things like this and not "how to design xor" (it could be any other gate or some other logic).
Of course it is just a general example, but if you actually needed this specific function in reality, then a 7486 would be the most logical (haha) design choice. If the rest of the circuit needed a few spare 2-input NANDs then you could just add a 7400 and you'd still be using 2 ICs, but you'd have 3 spare XOR gates as well.
Speaking simplification, you've just forgot to point that you've used 5 NAND gates to build a single XOR.
It's very basic. Please make a video about solving a complex equation with only one type of logic gate
I will be the same. Dave replaced AND, NOT and OR gates with NAND, what more do you need?
... or you can use eeprom
Bob's your uncle 😹😹
So is your (?) brain an capacitor? :-) If I try to draw a thumb/hand, it is always bad.
I'm Colourblind, I couldn't see anything at all...
Could you please next time use another colour than red on a dark green background?!
It feels so weird hearing someone talking about logic gates outside of minecraft.
Ha, ha! Well Minecraft is teaching people about logic gates, I don't know any other mainstream game that can sneak "real life knowledge" like that...
Plus the way they did it doesn't feel like they were trying to sneak anything. It is more like building stuff is fun and we will give you something similar to electricity called redstone so you can build even better stuff.
If we're lucky, he'll make an Iron Farm walkthrough video too.
But my power is connected to ground! =P
If you play on Playstation, there's Little Big Planet, which has far more straight forward logic gates.
They actually implement the proper symbols and everything in the game, and you lay them out on "circuit boards".
i4.lbp.me/img/ft/3542817db70a04cabdd3c83584ff07301d1f293e.jpg
Digital logic is NOT only 1 or 0, it could be any discrete value out of given set (normally limited).
All integers can be expressed with a base 2 numeral system.
Yet statement about digital logic being ONLY 1 or 0 is not true.
For the purposes of this very basic discussion it can be taken as true. Don't throw newbs into the shark tank you arse.
It bugs me too, I hear people all the time claiming computers are "binary," and I keep trying to tell them "a 64 bit computer is base 64, it is not base 2" but nobody listens. Even on an 8-bit micro with single bit manipulating instructions, you still have to give the instruction two 8 bit arguments! It can only understand a single bit via an 8 bit mask!
64 bit computer is a marketing term, mostly, there is no such thing in practice, mostly. It means you make as much sense as them.
Many processors support different register sizes, and naming x86 16bit (yes, 16 bit processor can address terabytes of memory without problems, unlike the claims of some morons), 32bit or whatever is mostly a lie. It makes sense to claim that most operations are 64 bits, but not all of them. As you probably remember, "32 bit" Intel processors had 64 bit registers and operations, but for marketing reasons they didn't call them 64bit.
Base of Digital systems. Young ones: if you don't like this, then switch to Business degree now!
Next up: k-maps, using all NORs or NANDs, converting from NORs to NANDs (vice versa), basic VLSI design...
I think the *digital blackboard* lowered your video quality, Dave. I get that it is "new" but this would have been much better on your regular board. The colours on the black (grey) board just don't work well especially the red. The red on the video thumbnail alone didn't exactly make me rush to watch this. I think the old fashioned board works faster (faster to draw and much neater) and you can point with your finger instead of these goofy self erasing lines. The digital blackboard would be more suited to a low data rate connection than a YT video.
I find the content to be high quality in both cases, personally I think this is a small improvement!
i've figured this out myself using pen and paper xd
you are little late with this video
Sorry Dave, but your approaches are way overcomplicated.
First example, easier to use 2 NOR gates. Half a CD4001 for example. Invert the B line and then NOR them.
Second example is XOR, and can be done with a quad NAND such as CD4011.
I do realise that unification is an industry trend, but my aesthetic sense and optimizing behavior leans to make as few blocks as possible. So, you made a XOR element with FIVE NANDs... That's awful design for me.
This video was *not* about simplification, it was about getting a sum of products design from a truth table.
nihonam Look inside that XOR chip, and you'll find his circuit.
NAND gates the whole way down !
These vids ain't tee-bag...
Combinational NOT Combinatorial!!!!!