As you start working more with networks
and doing more IP subnetting, you'll
need to do more binary math.
And in this video, I'll show you how
to convert to and from the binary format.
Binary, of course, means a single bit
that can either be 0 or 1.
It's either on or off.
And we usually represent this as a 0 for off and a 1 for on.
When we put 8 of these bits together,
we have what's called a byte.
We often refer to this byte as an octet
to show that it is 8 bits that we
are using in this calculation.
To be able to perform all of the conversions we'll do today,
we need to make a conversion chart.
And this is our conversion chart that we
will use to be able to perform our binary calculations.
We'll start on the right side and put the number 1,
and then we'll double it.
If we double 1, we have 2.
If we double 2, we have 4.
4 times 2 is 8.
8 times 2 is 16, 32, 64, and 128.
This allows us to perform any type of binary calculation.
And this will be very handy when we
start doing more IP subnetting.
I put in 8 different slots for this binary conversion chart,
but depending on how many bits that you
need to have in your conversion, you
can keep extending this out by simply doubling the number
and extending it out over a very long distance.
You may find yourself using these longer charts when
you do some additional IP subnetting,
but the majority of what you're working with
will be 8 single bits made up into a byte.
Using our conversion chart, let's do a binary calculation.
This first question asks, what is binary 00000010 in decimal?
The first thing we'll do is write out this particular byte
in this bit form--
0, 0, 0, 0, 0, 0, 1, 0.
And of course, we want to know what the decimal equivalent is
of that binary value.
What we'll do is put our conversion chart right
on top of those numbers.
We'll start with the 1, 2, 4, 8, 16, 32, 64, and 128.
Every place there happens to be the binary 1,
we're going to bring down the number from our chart.
Every place there's a binary 0, we're going to bring down a 0.
And if we do that, we're bringing down
0 plus 0 plus 0 plus 0 plus 0 plus 0 plus 2 plus 0.
Since that second bit is the one that has the 1 associated
with it, we're bringing down the 2 from our conversion chart.
And if you perform that complicated math,
you'll find that the answer is 2 decimal.
So 00000010 in binary is equal to 2 in decimal.
Let's do another one.
Let's calculate 10000010 in binary
and convert that to decimal.
Same process occurs, we put down all of the bits.
And we put our conversion chart right on the top.
Every place there is a 1, we're going
to bring down the number from our conversion chart.
In every place there's a 0, we bring down a 0.
And if we perform this calculation,
it's 128 plus 0 plus 0 plus 0 plus 0 plus 0 plus 2 plus 0,
meaning that binary 10000010 is 130 in decimal.
And let's take it to the natural extreme
and determine in decimal, what is
the binary value of 11111111.
Same process occurs, we'll put down that binary value of all
1's.
We'll put our conversion chart right on the top.
And now we're adding together every single part
of that conversion.
So we need to calculate 128 plus 64 plus 32 plus 16
plus 8 plus 4 plus 2 plus 1, meaning that all 1's in binary
is the equivalent of 255 in decimal.
To do this the other direction, we
need to perform a number of additional steps.
If we want to take the decimal value of 154
and convert that to binary, we're
going to follow the same conversion chart.
So we don't know what those binary equivalents are yet,
but we do know what our conversion chart looks like.
The decimal 154 has a single combination
of 1's and 0's that this could possibly be.
So what we'll do is start with the 128.
So is 128 less than or equal to 154?
We know that 128 is less than or equal to 154.
So we'll put a 1 in that binary slot and bring down the 128.
Now, we'll perform the same calculation,
except now we know that 128 is part of this calculation,
so we'll add that to the next value in our conversion chart.
So is 128 plus 64, which is 192--
is that less than or equal to 154?
It's not because 192 is more than 154.
So we'll put a 0 in the slot with the 64.
Now let's perform the same calculation with 32.
128 plus 32 is 160.
Is 160 less than or equal to 154?
It certainly isn't.
So we'll put a 0 in that slot.
Now, we move to 16.
Is 128 plus 16, which is 144, less than or equal to 154?
It is, so we'll put a 1 and bring down the 16.
Next on our list is the 8.
We'll add up the 128 plus 16, which is 144, add 8 to that,
which is 152.
That is less than or equal to 154, so we'll put a 1
in that slot and bring down the 8.
Now, we've got 128 plus 16 plus 8.
We're all the way up to 152.
We'll add 4 to that, which is 156.
That is not less than or equal to 154,
so we'll put a 0 in the slot with the 4.
Next on our list is the number 2.
Is 152 plus 2 less than or equal to 154?
Well, that is equal to 154.
So we'll put a 1 in that slot, bring down the 2,
and since it's now equal to the number we were looking for,
we know the 1 slot can't be used.
Therefore, 154 decimal is equal to the binary value
of 10011010.
Although this is a few extra steps when you're performing
the decimal to binary conversion,
it works for any type of decimal number,
and you can easily calculate what
the binary equivalent would be.
Of course, you could write out charts
that had all of this information in it.
If those charts were only dealing with 2 bits,
then you'd only have 4 values that you could choose from--
0 through 3.
If you had 3 bits, then you can extend that out
to be 8 different values.
4 bits would be 16 values, and so on.
You can start to see a pattern as you begin extending out
the number of bits, and this pattern
is based on the powers of 2.
This same chart we created before
is really a powers of 2 chart.
2 to the 0 power is 1.
2 to the 1 power is 2.
To the 2 power is 4, and so on.
This is the chart that you'll be using
to perform all of your binary calculations, all of your IP
subnetting, and you'll use it any time
you need to make a conversion between binary
and any other numerical format.