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I'd like you to imagine
that you and I have

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walked into a showroom floor.

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It could be cars or
boats or what have you,

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and on one of the items
that we're looking at,

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it has a price tag, and
it says this 45,239.

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And I want to ask
you, how much is that?

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I'm talking about the
actual number itself.

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Now you might be saying, well,
Keith, this is really obvious.

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It's 45,239.

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That's the number.

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And how did you get
that so quickly?

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And the reality is
is because we've

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been using base 10 numbering
system for all of our lives.

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It goes something like this.

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We have several positions here.

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For example, the nine
is in the ones position,

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and the three is in
the tens position,

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and the two is in
the one hundredths

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position, the five, right
here, is in the one thousands

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position, and therefore is in
the ten thousands position.

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And all we're doing, because
we use a base 10 numbering

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system, is a first
number is always a 1,

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and then the next position
is times 10, and times 10,

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and times 10, times 10.

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In fact, we could go
all the way down just

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continuing to multiply that
placeholder by 10, by 10,

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by 10.

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It was four 10 thousands,
it was five one thousands,

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it was two one hundreds, it
was three tens, and nine ones.

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But this is so
second nature to us,

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we didn't have to
break it out like that.

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In fact, when we
count, for example,

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our numbers go
through 0 through 9.

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So we have 10 distinct numbers
to play with, 0 through 9.

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And when we count, we do
0, 1, 2, 3, 4, 5, 6, 7, 8,

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9, and what do we do next?

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We simply carry the one
into the next position,

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and we put a 0 here.

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So 1, 0, in decimal represents
one 10, and no ones,

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for a total of 10.

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And then we go to
11 and then 12.

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And then, if we get all
the way to, for example,

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999 by continuing counting,
and we need to go one more,

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we carry that one again,
and we have 1,000.

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Now you might be asking, OK,
Keith, I totally get this.

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This is base 10.

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The numbering system
most humans on the planet

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have been using our
entire lifetimes.

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So what does that got to do
with this thing called binary?

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Well, binary is simply
a different type

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of numbering system.

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Instead of using base
10, binary uses base two.

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So with base 10,
we had numbers of 0

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through 9, which are 10
individual separate numbers.

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And with base 2, we
have 0 through one.

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With a base 2 numbering
system, the first position

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over here on the
right is a value of 1.

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And then, as we move
left, this next position

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is simply this first
number times the base.

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So in the case of
binary, it's base 2,

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this would be 1 times 2.

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I'll put that right here,
and that would be 2.

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And this next position over
here, this next placeholder

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is going to be this number
times 2, so that would be 4.

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And as we go left, it
would be this number

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times 2, which would be 8.

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And then, times 2,
16, and times 2, 32.

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And times 2 again,
which would be 64.

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And times 2 again would be 128.

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So with a base 10
numbering system,

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it went one, and then times 10,
times 10, times 10, et cetera.

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With base 2, we start with
one, and it's times 2, times 2,

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times 2, times 2, et cetera.

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It's also important to
note that although we could

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go a really long way left
here, we really only need

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to worry about eight positions
at a time when we're dealing

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with things like IP version 4.

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I want you to write out these
value positions for binary,

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and again, the way
to do it is you

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start on the right
with a number one,

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and then you simply
take that number

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and multiply it by the
base as you go left.

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So please take a
moment and make sure

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that you can write
this out on-demand.

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So let's take a
look at an example

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of how a binary number works.

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Now in binary, there's
only two numbers

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that we get to play with,
and they are a 0 and a 1.

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In decimal, we had 0 through
9, 10 different positions.

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In binary, we have two.

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We have 0 and 1.

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It's sort of like
a light switch.

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Either it's off or on.

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That's our only two choices.

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So if we had a binary
number like this,

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that's 1, 0, 0, 0, 0, 0,
1, 1, 0, holy schnikers.

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What exactly is the value of
that number to us as humans?

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And the way to figure that out
would be saying OK, well, we

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have a 1 in the 128 position,
so that's 128, plus 0,

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because we have no 64's,
plus 0, no 32's, plus--

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OK.

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How many 16's are we going
to add to this equation?

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If your saying, well, Keith,
it's like a light switch,

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right?

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It's either on or off.

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Because this is a
0, it's off, which

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means we don't have any 16's,
so we're going to say 0 there,

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plus 0.

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And here we go.

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In this third
position, we have a one

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on in the position
that's worth four.

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So we'd add 4 there.

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And how about the 2?

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The answer is yep,
we have one of those.

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So we'll add a 2 as
well, and then 0.

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And then, it's simply
a game of adding.

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All we're going to do,
if we want to find out

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the actual value of this
binary number, all we simply do

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is add these up.

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So it's 128 plus 4
plus 2, and that's it.

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So 8 plus 4 is 12
plus 2 more is 14.

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We'll carry our decimal
one right there.

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That's a 4.

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2 plus 1 is 3, and
then we have a 1.

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And so the actual value
of this binary number,

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1, 0, 0, 0, 0, 1, 1, 0, is 134.

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I hope this has been
informative for you,

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and I'd like to thank
you for viewing.

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