This is a video on K maps a K map is a car no map.
It was named for a fellow named Karno.
K R and A U G H.
The carno map is just a way to get a simplified term.
It's it's quite a quick and easy way to do it.
You do have to have your table set up so we have a B and we have our output which is why we're going
to use the term first.
So this is A not B.
This over here is a B not and this over here is a B.
So if we were to have our main term we would just add all those together.
WE WOULD HAVE A not B plus a B not Plus a B equals Y.
Now if we add the max term that be easier for this.
But in this case we'll use a K map to show what that is.
So here's the setup for a K map you draw boxed box it should contain however many options there are
in this case there are four options so that's what we should have.
We're going to have a knot in an A will have a B not A B.
Just have to be consistent with this.
Now we'll put a one wherever something is the case so for instance we have a knot and a B.
So I'm going to put a one.
I have a and b I'm going to put a 1 and I have an 8 and B not going to put a 1.
Now the way it came up works is you have to just draw a circle around anything that's in a group of
1 2 4 8 x cetera.
In this case I have one group right here.
I have another group right here.
Now we cross off anywhere where there's an eight and a not are be in and b not in this case this group
right there has an 8 and a not and has a B so I could just get rid of that a not.
And that's just to be this groovey here is a B and B not.
And there's an A B and B not so.
So that is what I'm left with that in fact is exactly what the term is with the max term is which is
a plus b which is which will which would satisfy this as well.
So this is a K map and here's how it goes.
Let's now see an example with three variables.
Three very big example is no different.
We're just going to set everything up we'll look for the ones because we're doing the term.
So our men term in this case is we have an A not A B not in a C because that's what the word is.
Then we have the next one we have a.
That is not it.
We have a B and then we have a c that is not it.
And then the next one which is right here we have a knotted A B and they c we go to the next one which
is over here and that's in a with a B not and the C.
And then over here we have an AB and AC.
Now if we add them all together we get the mean term.
However I'm going to put them into my K map and see what this looks like.
So let's draw a map.
We're going in.
We'll just do it again it's two dimensional.
In this case so we can have it look like this
it within a and b not over here and I'll draw my graph
and I'm going to get 8 spots.
So this would cover eight spots.
And we'll have a c not in a C.
Now let's put a one wherever we have something we have an A not A B not an A C.
That's right there we have a we have all of these.
You have to check and see that what we have and we have all of these OK the rest are zeros.
Now let's highlight a group of two right there and we have a group of four over here.
Now this group of two has a serious illness of their cancer so we're left with an A not an a b in this
group of four over here has all the A's and B's and there are not.
And then the C is the only thing left.
So this is what we're left with a not B plus C and that would be equivalent to the what the term is
over there.
That would be equivalent in a midterm.
Let's now go and do another example.
OK let's do another example.
This next example is again we just have to get out of our own terms and set it all up.
So let's do that.
So we have a not a B not A C not b not c not right there.
We have an A not A B C not right there for this one.
We have a a b nodded and the C over here we have a B and C..
Now if we add all those together that will be our main term.
Let's draw the map to express this
one to three and I'm going to set it up the same way I did before.
So that we have in a knot with a B we have a knot Well it's do not be not over there we have our a knot
with a B.
We have our A B and we have are A with B not it.
The C nots in the C are over here and now is just to fill it in.
While we have an eighth we have that we have this we have an ABC and we have an AB not C over there.
Well it's highlight our groups.
This is one group this is group two.
Let's see what cancels.
In this case the A's in the B we have an A.
That's just an a not so I'll keep that with the B's can similarly have a c not in this group Nabby's
B's can so but we get a still so we have the A C and that's equivalent to r y.
Now there's no difference between doing something with three variables or four variables.
So we could look at this crazy thing and we can do with four variables.
It looks like it's actually quite hard but in fact it will simplified tremendously as soon as we start.
So as we start going now I'm not going to write down all the huge mid terms over here but instead I'm
just going to draw the graph over here.
So let's draw a graph.
It would be better if I can draw a straight OK and we're going to need 16 different spots so that's
going to be one to three and one to three.
Now we have 16 different spots and let's write out what we need.
We have an eight hour BNA.
I'll just write them out first them and fix it after a B B.
And this is going to be the AB night and this is the A B B then we're going to have R C and D over here
because we have C and D you know fix it in a second.
Just easier to write it out this way and then fix it so we're going to have r c d not c and then the
d not over here.
And now we just have to fill in where everybody belongs.
So we're going to fill in this term this term these terms.
This this this and that so we could just look at the first one for instance.
And so that's going to be not a not be not C and D.
So not a not B is right they're not C or C not and D is going to be right there.
And so therefore we can get there so let's draw this out.
If you fill it in you get all of your terms.
OK so we could fill it in and get all of our terms one two three four and we're going to get this.
OK.
So let's highlight what we have.
Well here's a big one this is 8.
That's perfectly fine.
That's 8.
And this is another two.
Now in this age the A's and B's canso and the C's in the C's can.
So the only thing left is the in that eights.
That's nice.
And then this over here the DS can see it.
So we're left with plus a lot with the B with the C and that is equal to Y.
So that's your for which is really just as easy as anything else.
Let's do another example of the four Kate.
Let's do another example.
Here is another why again we just have to find our ones and do that.
So let me get my ones.
There's a 1 1 ones ones.
OK.
So let's do our graph.
We make a big table and it's going to be 1 2 3 1 2 3 and again we just have to fill in all of these
things so baby baby baby baby cane.
So we'll fill it in with Amy.
Not a not be not see the CDC the C The C-notes and we're good.
OK so now let's find out where everybody belongs.
So we have to we're going to have one two three four that's six ones and let's if we can put them in
that's going to be one of them.
That's the first one.
We have those two.
Then we'll have to be here like this and we can highlight them then we circle them and you can check
them for yourself to see that those are the correct terms.
And over here what can cells.
Well the bees can sew.
So we're going to be left with something that isn't as beautiful as we had before but that's OK.
We're going to have this what we're going to have an a knot with the babies canso a c not an A D not
Plus in this case these can so we're left with a C that the babies can sew so we have an A and A C left
so we have a C and that is our main term over there so we could use max term as well and do that.
Now I would warn you that there are some special cases that can be used with this.
So for instance if you have a map that looks like this let's give you some special cases.
This is really it really goes around.
So for instance if you had one in the corner over here like this that is a group in fact that is a group
because those in the corner would be a group and that would be before if you know you had 16 spots right
there.
Same thing if they had something like this if they had one zide there.
This is a group of four right there that's a group of four.
Same thing.
If you had just ones like this that would be a group of ones and same thing if we had ones like this
that would be a group of four.
So you could go to the edges and it's kind of thought of like if you put it around the circle or more
accurately around the Taurus then you can consider those a group will do max term in the next video.