No, I want to continue building up and introduce the binary system, binary is something like a one
o zero.
We have already introduced a bit, which is a one or zero.
And this is what binary is.
Actually, it's nothing more than something is on or something is off.
That is what is binary.
So so they figured out that if they can create some kind of arithmetic to this one's or zero's, maybe
they can create something like a calculator.
Right.
So they invented the binary system and then they tried to get this binary system and implement it and
digital circuits and gates like the Aldgate and Aldgate.
And by putting this bunch of transistors together, they're going to get some useful devices.
Know the numbers you have in the binary systems is just zero.
And one, you have nothing more than that.
So let us put all the operations that we can do with these two bits if we have zero below zero.
Well, they said, OK, the sum is going to be zero.
If they put one plus zero, well, they're going to get something like just one, and that makes sense.
Now they said, OK, what if we have one plus one?
They said, OK, the thing here, it's going to be zero.
And we have one as a carry.
It's the same thing as adding nine and one.
We're going to get ten, which is one zero, which is repeating the old system.
029 one more time.
Same thing here, because the number of zero zero one right in the decimal you have from zero to nine.
So when the finishes, well, you're going to start over and roll over and then you're going to get
one zero which is ten.
But here, well, whenever you add one plus one, you're going to roll over again, which is zero,
and you're going to put one next to it.
So you can say one plus one is actually ten.
This is how the new system works.
Actually, you just have these three operations, zero zero zero one zero is one one plus one is ten.
As simple as that, it's not really 10 zero and one in the car.
We're going to say, what does this mean later?
So they thought, OK, let's design some circuit that looks like this.
I'm going to have two bits right here, two switches.
I'm going to have a bunch of end and all gates connected together.
And there is a result at the output and they carry.
So they said, OK, if I put zero zero, I want to get to zero here.
If I put one zero, I will not get the one here.
If I say one plus one, I want to get one here and I want to get one in the carry as simple as that.
No, this is the representation for this and they called it have add or we're going to see later why
it's not called Full Adder and half either.
Because it's all this something to bits right here.
So this is the black box representation, you just have a box with two bits, but we don't know what's
inside.
There's another representation, which is we're going to see how it looks like if we put an X, Aldgate
and Aldgate.
No, there is many type of gates which we're going to introduce later.
Here we have an X or gate and then end.
If we connect them together, we're going to get a half or so here.
040 you're going to get the zero and you're going to get a zero zero plus one or 1.0.
You're going to get the one here and a zero here.
This is the carry and this is the Z or the some same thing.
If you have a one here and one here, well, you're going to get one here and one here.
So we are summing now in the binary system, and that's great.
That's a huge progress that we can create a lot of asthmatics and a lot of mathematics just using this
simple circuit.
Now, if we open up this if we open it up and see what the electronics looks inside it, we're going
to see transistors that are connected in this way.
So this side right here, the S looks like this.
This is the some this is the A and B, same thing here.
If you look at the carry, its circuit looks like this.
Right.
So right here, if we have some electronics and we connected exactly like that and we have an input
A and B, well, you're going to be having, like an adult, a circuit adder, which can later be represented
to create a real calculator, which is the basis of the CPU.
We're going to see that also later, as you can see here, there's a bunch of inputs like a had to be
had a B, so don't get yourself confused.
We're not going to talk about this level here.
But that's really not that complicated.
It's just that you get all the A's and connected them together, all the arhats and connect them together
to one terminal B and B as well, separately each to a terminal.
And then you execute them in a certain way and you just get this half ago.
And that's, as I said, a huge invention because you're starting with simple switches.
You can turn them to a transistor.
You turn these transistors to some kind of logic gates, and then you represented some binary system.
And you combine this together and now you have something that can do real math for, you know, next
is we can do the same thing for subtraction, for multiplication, for division.
We can create circuits that do this exact job.
So if we have all of this operation and we have these four boxes right here that, well, we can do
any operation in math we want at least as a binary operations, that's huge.
Now, if we multiplex all of these together, the multiplication, addition, the subtraction, the
division, we multiplex all of these circuits together.
And here we have some operation input, like we say, OK, if I answer some zero here, I want you to
perform an addition.
If I insert a one here, I want you to perform a multiplication.
Let's assume that this op has two wires.
If you put zero here and one here, maybe you will be able to perform division.
If you put one here and one on the other applier, then you will be able to perform some other mathematical
operation.
So by multiplexing the circuits together, you have something called Arithmetical Logic Unit or an eight
of you.
This is the basis of a CPU.
Now your computer has the CPU, any electronic device has some kind of microcontroller or CPU which
has this Aliu your calculator.
He has an alibi.
So as you can see from simple switches, you can create a whole mathematical logic calculator.
Right.
You now we are building up, as you can see, and later we are going to see more stuff and we are going
to connect them until we have a full embedded system.