Hello, guys, and welcome back.
In this lecture, we're going to talk about half and full.
Now, if you remember in the overview, we have talked about half Addas and we have seen how I have
add or is the main component in any Aliu which will be composed later your whole C.P.U.
So it's a very important topic to understand how arithmetic is being done in digital design.
So let us get started.
Well, in order to create a circuit, actually we need to create its own truth table.
So it's very simple, actually.
We have input and B and we have two outputs, the sum and we carry.
Right.
This is all we that we had.
So if you remember, we are trying to sum A and B, right?
So when a zero and a zero, it's like something A and B and both are zero zero and the carry will be
zero.
Right next if I have a zero and B one, well the addition of zero and one in binary is one and the error
is zero.
Same thing when A is one and B zero.
Well, we're going to get a sum of one and we have zero.
Now, if you remember, if we are adding one plus one, right.
We're going to get a ten minute summation is zero and the carry is going to be one.
So let us design the circuit.
This is how it will look like as a black box.
And now, since we have two outputs, we need to work on every output individually.
So let us first work on this column because we're trying to figure out what is the output for the summation.
Now we are going to check the columns where we have ones, right?
So we have this column here and this column here.
So either of these will give us one right?
Meaning we need an or gate of two inputs.
Now, we're going to take a look at every case individually.
Let's take a look at the first one when A zero, B is one and the summation is one.
So we need an and gate rate of two inputs.
And remember, for every zero, we're going to put another gate.
So here at the A. we have a not gate.
Right.
And by that, we are done from this gate.
Now, let's go to the second case again.
We have two inputs.
We need one, Edgard, and how many zeros we have.
We have one zero at the B. So the B will have another gate in front of it.
Now, let us check the output gap, which is this one one one zero one.
Now, Viqueira is one only at this case, right at this one one zero case.
Right now, the carrier is one only one, A is one and B is one.
So we need one headgate gate.
And this is literally the end gate, right?
One one eight is one and B is one.
And we have an output of one.
This is just an end gateway.
So we just create an and gate right here and then we just connect our carry and we can connect ourself
and that's it.
So let us recap.
We have two outputs.
We take it one at a time.
We take the sum first of the cases where we have one.
It's this case and this case.
So we have an object of two inputs.
Next, we take every case individually.
First one is when A zero and B is one.
So we have an end gate right here with two inputs for the and the B and we put not gates at every zero.
So in this case, at the we do the same thing for the second case where A is one and B zero, and we
put another gate at the B because it's a zero and then we interconnect the gates with the and gates
and the output of the gate is actually the sum we have because we have two cases that can give us one,
this case or this case, either of them, meaning we have an O gate, will give us the summation of
one for the three we have on the one case, which is this one.
When A is one and B is one, we have a copy of one.
In order to satisfy this condition, we put an end gate.
There is no zero.
So we have no not at all.
Do it here.
And we just connect it directly to the.
Well, you might ask why don't we have an all gate for the Kawi like the sum.
Well, because it's very simple for the sum.
We have two cases.
Either of them would work, but for the Kerry, we have only one case which has one, which is this
one.
So we don't have any multiple options.
Right.
They would just have one option.
So we don't need any object.
Now, what I want you to know that the XOL gate that we have talked about looks exactly like that from
inside.
We did not talk about the internal circuitry of the gate, but it is exactly this.
So if you take a look at the through a table right here, you will see that when AMPE are different,
we are getting a one.
See this case zero one.
We are getting one and again, one zero.
We are getting a one.
So whenever you see a table like that it is exactly the orgeat right because it shoots a one whatever.
Two signals are different so we can replace this short circuit with an or gate like that.
That's a great next, how about we showed the A's and B's together, I mean, we don't have to have
our inputs like that.
I mean, this is still a here and here and it should still be here and here.
So if we shot them together so that the aid is distributed to this guy, then this guy tempting for
the B we will get that has added.
That looks like that.
So this is a half ADUT.
So if you have a circuit that looks like this, you can just reduce it to something like this.
Now we know what they have other looks like and what it does consist of.
No, let us talk about the full address.
A full adder consists of two 1/2 addas connected to each other.
Now, assume I want to add zero plus one and one plus one.
Well, I want to add the one here and the one here, right?
So this is a zero and this is a one.
This is B zero and this is B one.
So this is a zero.
And this is A one.
This is B zero.
And this is B one.
In order to add these, I want to add a zero plus p0.
Right.
So this is what we're going to do is you go plus B zero.
It is one plus one.
So the summation is zero and the carry is one.
Right, because one plus one is zero.
And this one.
No, since I am adding two bits, I need to continue additions in the second half, either because I'm
going to add a B one, right.
So this is A1 and this is V1.
And you want to add them, but I have one in the Kawi.
So this has added.
Right?
You is missing the Kawi because I need to add it as well.
So what we're going to do, we're going to add one more input here, which is called the carry.
This is the Kawi output, and here I want to add this Kawi output.
So here we are adding A one and B one, and we are adding givee Kerry.
So we are adding one plus zero plus one.
Here we have one plus zero and the carry coming from the previous edition, which is the one.
So right now, if we continue the summation, we are assuming one plus zero plus one.
Right.
So one plus zero is one, plus one is zero and carry one.
Right.
So we are going to get here in the circuit as you go at the summation and the carry right here is going
to be one.
Is that correct?
So we are here some one plus three, it should be four and this is four.
So right now the result is this is some zero.
This is someone and they carry.
So it is zero zero one.
Right.
Here, this CEO right here, this scary that we are seeing right here is actually going to be an internal
signal, right?
So it's not part of the output.
This is just an internal signal that is going to connect.
These two have addressed together.
So they're really the result is one zero and zero right here.
And by that, we have explained full address and now we know that the main difference between her father
and Fullagar is that the full order contains a way to add to Carrie as well to the final rizzle.