Boolean Logic & Logic Gates: Crash Course Computer Science #3

Today, Carrie Anne is going to take a look at how those transistors we talked about last episode can be used to perform complex actions. With the just two states, on and off, the flow of electricity can be used to perform a number of logical operations, which are guided by a branch of mathematics called Boolean Algebra. We’re going to focus on three fundamental operations - NOT, AND, and OR - and show how they were created in a series of really useful circuits. And its these simple electrical circuits that lay the groundwork for our much more complex machines.

*CORRECTION* AT 1:27 the graph says "Quinary System" but then the graph shows 10 possible states - which is actually decimal. Technically, there should be only 5 possible values there, but the overall concept is still the same.

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[crashcourse]

*CORRECTION* AT 1:27 the graph says "Quinary System" but then the graph shows 10 possible states - which is actually decimal. Technically, there should be only 5 possible values there, but the overall concept is still the same. NOTE: Since we can't use annotations in our videos going forward if we find any smallish errors in our videos like this we'll leave clarifications in the episode description. Thanks all for the wonderful feedback! -brandon

[darkBender]

I am a third year majoring in computer engineering and this video explains transistors and logic gates better than a semester class.

[vlogbrothers]

Bit at the end made me wonder if I'm merely a computer. Great episode! -John

[BlankPicketSign]

My first real exposure and application of logic gates was in Minecraft with Redstone

[TheBrothersBlue]

Unlike most CS introductions, Crash Course does a great job in giving the student context, explaining how computers function at a fundamental level before applying layers of abstraction. Very well done -- As a Sophomore ComputerSci major, I'm excited to see more enriching content every week(:

[TheGenericNerd]

Oh my god, THANK YOU for clearly explaining how each logic gate is physically represented in an electrical circuit. A lot of that abstraction makes it really daunting and hard for dummies like me to get it through our thick heads.

[MFMegaZeroX]

A good video as always! As a CS major myself, this is actually finally a series where I can answer questions and stuff in the comment section! Just a pedantic note for people who want a little more info:

1) There are also not versions of all the gates. AND, OR, and XOR become NAND, NOR, XNOR, respectively. They are represented by adding a small circle to the end of the gate. While they can be formed just by adding a not gate at the end of the inputs, they are common enough that they get their own specialized parts. You often here people verbally NAND and XNOR when talking about logic, so I think it is interesting to note even though this isn't computer engineering.

2) While by convention in truth tables 1 is true and 0 is false, this is often not the case when we actually look at real components. Because of power usage, the opposite is often used. Generally, the more common output is set to 0.

3) 0 doesn't actually mean nothing is flowing through. For example, we may set our 1 to 5 volts, and our 0 to 2.3 volts. This allows for us to have an "off" state at 0 volts. We wouldn't want our computer to be calculating stuff with 0s when it is off! There are also other uses for this state, but this may be covered in a future video.

[deathdoor]

Just passing by to say that I'm loving her course and excellent diction.

[Outwars]

She is a VERY good teacher. How she breaks it down so you understand the details and then subtly tells you about application of abstraction helps you focus on whats important... she makes actual little building blocks for you as she speaks.

[SirCrest]

Just wanted to say I love the themed animations for this series. The computer UI, old Mac OS UI, etc. Always great work to the animators and team.

[comb]

As an Electrical Engineering Student who was always curious about how Boolean Gates worked, my life is now complete...

[HaydenH]

Minecraft Redstone is just like real life.

[BlackXxScopez]

I used to make cpus in minecraft, and it's amazing what it could teach about computers. It makes you feel like you understand exactly how computers work, and in a sense, you do. programming using only 1s and 0s, creating all of the logic gates/decoders etc from scratch, optimizing, and attempting to add a second core. I've moved on from Minecraft since then, but it's a great tool to make use of if you have the game and want to go deeper into boolean logic/logic gates and computer architecture.

The hardest part is creating an Instruction set that is powerful enough to let you program basic programs but easy enough to decode to keep you from ripping your hair out. generally, It would be a non-pipelined CPU running at about 0.7 hz, but some made optimised pipelines that allowed speed of up to 2.5 hz, which is amazing given that every transistor take 0.1 seconds to switch, and after a certain range, you must add a repeater, which re-strengthens the signal, which also takes 0.1 seconds.

[TheQballChannel]

That feeling when you literally have a test on this tomorrow

[eddiehimself]

I mean the fact that George Boole came up with Boolean Logic a century before it became a vital component of designing computers is pretty incredible. It just goes to show how the discipline of pure mathematics, that is studying mathematics not for a practical purpose that is known at the time, but just for the sake of expanding the scope of maths itself, can really pay dividends when the technology catches up with it.

[anti_MATT_er]

I was wondering where I'd heard Boolean before, then realized that I took a logic class last semester. :D

[lordkingsmanminecraft]

Minecraft redstone already taught me this

[Leyshire]

Physical basis of logic gates wonderfully explained!

[FewMinuteProgramming]

Wow! I love these videos. It's amazing how far we've come with computers.

[gdilzbl]

The feeling when you don't have any exams tomorrow, but are doing it for fun and now the whole new world of Computer Science has opened for you to learn and become a master of every computer you'll ever meet in your life.