Now we have to understand how to represent this logic.
I'm going to have an AND A B and they're going to go into this.
That's a.
And that is to say A and B if I were to draw like this A B and a half this my drawings are not perfect
but that's an OR that would represent a or b a not if I had an A is represented like this.
So that's a nice k.
Now that would be a.
And it's not.
So if you had a zero it becomes a 1.
In this case if we had a 1 in a zero and you add it that becomes a zero.
If we had a 1 in a 0 over here and this or it becomes a 1.
Those are the logic cases.
Now we can extend these and say things like do in ands and then not it's sometimes just that symbol
is given.
Sometimes when you have the and with the not you put like the whole triangle thing in front.
Either way this is a knot and or what we would say a man.
And a and D.
And just as much as we can have a knot and we can also have a knot or so you can put the little dot
in front or you could say with the triangle in that would be 8 knots or is 8 nor So we have and or not
we have NAND and nor in our last symbol.
Now we really need is a X or.
Which looks like bad.
It's similar to the OR.
Except it has the little line in front.
And if you remember this is the symbol.
The plus with the circle around them for the X or a plus with the circle around that is the symbol for
the X or it's still not very neat but reasonable.
So now we can build these logic gates together and build things together.
So if I had a statement P and Q and I'm going to put parentheses or not P and NOT Q Let's do p and q.
Well we'll start with a P in a Q and we'll do an end.
We have a not P and A not q.
So let's bring this down.
I have to not them both
that's the not P and Q and I am ending them.
So I get this.
Now it says Take this which is here and take this which is there and or them together.
So let me or them
in that's what I get out.
So if I were to trace some number going into this for instance for the trees as 0 and 1 let's see what
happens.
Zero and that with one is that here.
It is also going to be zero because we not them the 0 becomes a 1.
And this one becomes a 0 and then that becomes a zero as the and in a week or two zeros you get a zero.
That's what I get.
In that case let me do it for the other case when I have one and one for instance.
So if I have one in one one and one is one if they're not dead they become zeroes and that's zero.
But now one in 0 1 or 0 because this is here or over here is one.
So you get that as an output.
So we can follow this out and we can look at the diagram to explain how this is working in any diet.
Many many diagrams can be built.
The idea is you work on each parts separately.
You work on this part and this part and then you put them together.
So that would be the diagram for the circuits sequential circuits.
We could also just to understand the logic.
So we do.
I could have something that's going to have a circuit and perhaps it's going to have
something that's a choice about where to go.
What would a choice be.
Well it could either go this route or it could go that route.
So if either one of them is down.
In other words if it comes down that would be an or because one or the other would make it valid.
And then the and then the electricity could go through.
So that would be or or service if you had something like this where it would need to get past both of
these.
That would be in and because we need both of them in order to be true.
So that's what the circuits look like.
You know inside the computer.
But this is the laad the diagrams that we're going to use to do it.
Let's do another quick one in order to make sure that we're OK with this.
I'm going to say not p or q x or not P or P and not q.
So I'm going to draw those in order to see it.
Now this could be simplified probably but we'll ignore that for now.
Let's just get our P's and Q's.
We have a not p with my ored with the Q.
So let me do my Or there's my or so this is not P Ord with Q.
Now I have to X or that with a not p.
So I have to X or this output with n p.
So I'm going to take my p ok and I'm going to X or it's
with this not a very neat diagram but OK.
So this not-P are going to take that an X or it's with the output of the not P or Q All right again.
C and then we have two or this with pure Q..
So I'm going to come down draw this like this and I'm going to have a P and I'm going to have a not
q necessary.
And now we have to add them.
So and then and I have two or those two.
The output of this and this is ored with that.
And so I will or it may doing my Misi or diagram.
That's an or in case you're wondering about one zone or and this is an X or in this one is ns and the
others are non-SS.
So not very clear.
Not very clean but you know that's essentially how the idea is going to work.
There you go.