Hello, guys, and welcome back.
In this lecture, I want to talk to you about Multiplex's.
And we're going to see how useful and important these circuits are and the logic design worked.
Now, let me give you an example of a use case where we really need a multiplexed assume that you have
a receiver device.
It has only one input.
However, you have four transmitter devices.
How can we send from these four devices to this receiver device?
We cannot really connect all of this for here because, well, we have only one input right here.
And if we connect this together, we are going to have some electrical problems and we cannot really
send messages.
What we want to do is to put an intermediate which called the multiplication, which is a small router
that is going to load the data from every device individually.
So I have a multiple mixer.
It has four input.
Every input is connected to one transmitter device and I have one output.
So I tell the multiplex here, OK, I want the data from input zero and it's going to take all the data
from input zero.
Let's take a look how we can do that.
There is something called the select line.
Now, this select line is going to select if it's going to connect this input to this output or this
input to this output or this one to this or this one to this, it can connect only one input at a time
to its output.
Right.
So multiplexing has inputs and outputs one at a time.
We can connect one input to the output we have.
So let us assume that we have selected zero, so the must control all the markets, select you is equal
zero meaning input zero, meaning I zero is going to be connected to the output.
So the data will come from transmitter device to zero to the output and then to the receiver device.
Now assume that I have said, OK, now the selection is at one.
So much control equals one.
Meaning now that transmitter device number one, this one is going to be connected to one, then it
will be connected to the output, then it will go to the receiver device.
See here, by changing the selection, we can choose which data to be received by the receiver device.
Now, if we have to I2 is going to be connected to the output when we have three, it is going to be
connected to the output.
Now let us see, what does this multiplexed looks like from the inside?
Remember, we like to see stuff in and and or and not form.
Right, because by that we can break it to its simplest form so that if we want to implement it in real
life, we know what we are doing.
We are not looking at just some black boxes that we have no idea what's inside it.
So first we drove the truth table.
Remember, that was table of inputs, which I zero I.
S the select a zero and one and s and we have an output.
OK, so we have three inputs.
I remember in order to put all the combinations we need to say, OK, two to the number of inputs or
two to the power three meaning eight.
So we have eight possibilities that we need to fill right next.
Now, the logic here is very simple.
If my transmitter if my transmitter device is standing zero here and I am selecting year zero, it means
that I zero will be connected to the output.
So whenever the select is zero, right.
The data will come from Israel, is that correct?
Israel, meaning I am taking the data as it is from zero to the output.
So right now my eyes zero has.
Zero here, zero here, one here, one here, it will go directly as it is, does the output, right?
As you can see here, it has moved to the output, so I zero here is now at the output.
Izawa is that the output is the output and here it is at the output right now.
Let us take the case where my deselect here is what.
So if my select right now is one meaning one will move to the output.
So we have case one here, one case here, one case here and one case here.
So the zero will move here.
As we can see, it moved here.
The one from the other one will move here to zero here will move here.
And the other one, it has a one.
It will move as it is as I want to the output.
See, the logic here is very simple as a zero, whatever we have at zero, whatever data we have, be
it a number, it won't be at zero, whatever it is, we will say that the output when we have our we
will take whatever I has to the output.
Now, do you remember that example of combination, of logic of how we can draw a circuit just by looking
at this table?
We take the cases where we have one.
How many cases where we have.
We have one case, two cases, three cases and four cases, so we need an OR gate right here with four
inputs because we can have either of these cases conducting one at the output.
OK, so we have four of them.
Next, we need Ed Gates right here for each case.
And lastly, we need to take whenever we have the zeros, we need to put, not gates at their input
right here.
So they're not Gates right here.
We are using just small dots were like that.
Instead of just drawing a not gates, we're just putting.
And I thought right here, because we have learned that a circle or dot is just another gate, right?
So let us check if this is correct, the first case is zero one, what we have on the one not gate,
right.
Which is at the input zero.
So this is zero.
It's going to end up gate No.
One here and s are just one.
So we can connect them directly to the end.
So this is this is connected directly to the end gate and this is the only one connected directly to
the that.
Now the second case is here we have two not gates at all, one at S. So this is s right here.
It's connected through a knob gate to the end.
And we have here and not gates that is connected directly to I1.
So this is correct.
Now, in this third case, we have only one the gate at the S, so we follow the S, the red one right
here and we put another gate to it and as you and I want, can be connected normally as we are seeing
right here.
Lastly, we have a case where all of them are once.
So we did not gates, which so we just connect them as they are.
And by that, this is what a multiplexed looks like from the inside.
It is as simple as that.
So if you connect the circuit like that.
We will have a multiplexed now, if you have zero right to hear whatever data you have at I1, you will
see that the output no, if the estimate is zero, you're going to get whatever that you have zero and
you are going to see that the output.
If this is one whatever that you have at Irun, you will see that the.
No, a multiplex, sir, could have multiple bids as well.
What does this mean?
Meaning that this icicle could be not just a zero or the one that could be a bunch of zeroes or ones
that will be rerouted to this output right here.
So if it's zero right here, you're going to get a 16 bit.
Rerouting their cells to the output.
Now, if it's one, you're going to get 16 bits rerouting from one to the output.
This is very important if your data is 16 or 32 bits.
Remember, in large numbers, which we are going to see later, are represented with the combinations
of bits.
So this is why we need a multiple multiplex.
Now, another thing to note is that if I have multiple inputs, remember, not multiple bits per input,
no multiple inputs like I zero.
I want to a three.
Well, I'm going to need to select lines and not one.
Right.
Because in order to cover all of these combinations, I need two lines.
Zero zero is going to give me this zero one is going to give me I want one zero is going to go with
it to one.
One is going to go with three.
So the more inputs I have, the larger the select line is going to be.
And again, don't confuse the number of inputs with the number of Pittsburgh input.
I mean, here every input could have sixteen bits and we have four inputs.
Right.
So this could be 16.
This could be 16.
This one and this one.
Nevertheless, case we have is the demarks or the multiplex or it works exactly the opposite way.
Now assume that I have one central device and I want to send different data to four receiver devices.
Well, and I want this message to specifically go for one of these receiver device.
I need a demarks right here at demarks is going to take the input and depending on the select line,
it's going to redistribute to one of these outputs.
So it's totally the opposite for Multiplex.
And Multiplex takes multiple inputs and map it to an output, but a demarks is going to take one input
and map it to multiple outputs.