This video we'll discuss binary in terms of numbers past the binary points and X or we'll start with
numbers that are past the binary point in decimal where we have base 10.
We have something called a decimal point.
However in binary we have a binary point.
So this number right here 1 1 0 1 points 1 0 1 0 1 1 the beginning of it is just like before we have
in this spot we have a 1.
We have nothing in this but we have something in the forest but we have something to spot.
So it's eight plus four plus one that's 13.
So on this side we get 13.
However what is on this side of this of the of the binary point.
Well if this number if the first number if we have this number that means that we're taking a two to
three one times two to three plus one times two to the two could be fixed plus one times two to the
two plus zero times 2 to 1 plus 1 times 2 to the 0.
That's what that number represent.
So if we go past the binary point that number is 1 times 2 to the negative 1 which has won over to the
next number is plus 0 times 2 to the negative 2 which is 1 over 4 and we keep going.
These are the numbers 1 times a half that represents the 1 0 is 0 times 1 to the fourth one is one times
one to the eighth plus plus zero times one to the 16.
So that's two to the negative one negative tuning of three to four etc..
This is what that is true to the negative.
One is that half to the negative two is a quarter.
This is an eighth a sixteenth a 30 second etc..
These are the only numbers that we could add together to get something passed the binary point.
In other words we could get the number of points 7 5 and that would be represented by having these two
numbers we could get several other numbers.
But at the end of the day there are many numbers where no matter how small we made these numbers point
five point five point twenty five point sixty five etc. We cannot get something like Point 3 3 repeating
because that cannot be represented in binary because there is no way to get that because there was no
combination of these numbers that could represent that.
So numbers pass the binary points.
Maybe feasible maybe unfeasable numbers before the binary points are all feasible.
So the key point is another point that we need to make is that if we're talking about binary There are
operations that we could do we said that we could take numbers for axes and we can add that we can subtract
them.
We could do other things as well we can do multiplication and division.
Let's just review an addition problem.
I'm just going to take some numbers.
I'll add that together.
I have one and one I have one I carry the one I've won and I have one I carry the one I that should
be a 0 rather 0 0.
This is one.
And now I do carry the one this is zero and it's 1 0 and that's 1 0 and that's what I have over there
which is 1 0 0
1 0 0 1 0 0 0 1 0 0 0.
OK.
So again because one plus one is 1 0.
So I carry the one that should be a 0 0 one plus one is what they are but one plus one plus one is this
plus one which gives me that.
And that's why I have that over there.
Now that's one operation.
We said there's two compliments where I can if I wanted a negative number if I wanted to represent negative
numbers then I just flip the bits now there's another thing that we can do and that besides addition
subtraction.
There's another type of logic that we can fulfill with when dealing with binary numbers are we dealing
with.
Yeah.
Well specifically by unary and that's called x or x or is an exclusive or some people say or what that
means is if I were to have all the different combinations
of the numbers and I do X or which has the plus with that that becomes a 0 0 1 0 1 0 when the same thing
is added together it's 0 and different things are added together.
It's a 1.
So if I were to have a number like this and I would to extorts with a number like this this would be
the same answer as 0 0 0 1 1.
Because those are different.
One presumes they are plus 1 1 0.
Now the nice thing about X or is that you can take this number and you can invert it by just multiply
by just ignoring it again with one of these numbers so if I X or add with this number the top number
that's the top number that I had over here meaning this and this are the same if I X or it's
Then I get out.
What was the other number right there.
So if I have this x or is invertible it's just a different operation.
But it's something that we should be aware of.