1
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What if we needed to convert
a binary number that we're

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given in binary to decimal.

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00:00:07,220 --> 00:00:15,440
But let's say we were given
a binary number of 10100111.

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How do we convert
that to decimal,

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the decimal equivalent?

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Well, the answer is, we're
going to take everywhere there

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is a one, we're going to take
that value from the placeholder

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it's in and simply add them up.

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So we're going to add
up 128 plus 32 more

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plus 4 plus 2 plus 1.

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So we can do that longhand, 128
plus 32 plus 4 plus 2 plus 1.

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8 plus 2 is 10, plus 4 more
is 14, plus 2 more is 16,

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plus 1 more is 17.

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There's our 1, there's our 7.

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Then we have in this column
3 plus 2 plus 1 is 6.

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And in the hundreds
position, we have a 1.

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So that value of this binary
number right here is 167.

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And I put 167
equals 167, I guess

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that's a little bit redundant.

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So in converting from
binary to decimal,

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we simply look for the
1's and then add up

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the values of those positions
for our equivalent total value.

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So now it's time for your
exercise in converting binary

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to decimal.

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And what I'd like you to convert
is this, this number right

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here into decimal.

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So go ahead and pause me.

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When you're done,
go ahead and resume,

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and we'll confirm or answer.

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All right, welcome back.

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Let's see how we did.

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So for this answer, which we'll
call option number A here,

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we have 64 plus 32 more
plus 16 more plus 4 plus 2

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and that's it.

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So we add all of those up.

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There's 4, 5, 6.

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6 more is 12, plus 4 is
16, plus 2 more is 18.

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We'll carry the 1, there's an 8.

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So for the 10th position,
we have 6 plus 1 more is 7.

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Plus 3 more is 10, plus 1
more is 11, that would be 118.

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And if that's what you came
up with, congratulations.

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You have the ability to convert
from binary into decimal.

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Now let me give
you a couple more

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that I'd like you to
practice with as well.

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Let's take this one right here.

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Well, 00000000.

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I want you to use
that one if you would,

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as well as this one, 11111111.

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And one more, let's have you
go ahead and do 11110000.

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And we'll call those A, B, and
C. And what I'd like you to do

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is write out on paper what the
decimal equivalent of A, B,

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and C is.

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And if you're saying, Keith, I
think I've got the A, it's 0,

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you'd be absolutely right.

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It might take you a little
bit longer for B and C.

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So go ahead and pause me while
you do all three of those.

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Write out your answers
and then click on resume,

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and we'll compare notes.

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OK, welcome back.

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So let's take this first
one, option A first.

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And option A is 0 plus 0
plus 0 plus 0 plus 0, OK.

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So A equals 0.

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Now, this next one, we have
some more adding to do.

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So we have 128.

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And here's what I'd recommend.

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Don't just do it in your mind.

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If you're new to this, do
it as we have in this video,

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by writing out, like 128
plus 64 plus 32, which

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is what this is all about.

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So for answer B, it would be
128 plus 64 more which is 192.

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Plus 32 more, which is 224.

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Plus 16 more, which is 240.

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Plus 8 more, which is 248.

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Plus 4 more, which is 252.

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Plus two more, which is 254.

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Plus 1 more is 255.

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So B equals 255.

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And you might say, well, Keith,
you did that in your mind.

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You didn't even write that out.

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And that's because this
is one of those values

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that you're going to
see a lot, of 255.

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And it's just because of raw
practice with these numbers

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that they can do
that in my head.

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Otherwise, I'd be
writing it out.

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So 128 plus 64 plus 32 plus
16 plus 8 plus 4 plus 2 plus 1

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equals 255.

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And for answer C, we have
128 plus 64 plus 32 plus 16.

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And if we add all that up
the long way, the short way,

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use a calculator
or what have you,

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it's going to end up to be 240.

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If those are the three values
that you got before we compared

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notes, my hat's off.

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If you didn't get
these three numbers,

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I would ask you to
go back, manually,

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like we did right here and here
and add them up once again,

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just to confirm
that you're doing

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the conversion from binary
into decimal correctly.

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Also, the valid range, if
you will, for any octet,

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any number in IP version 4 is
going to be between 0 and 255.

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It can't be any lower
than 0 because then we're

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going into negative numbers.

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And it can't be any
higher than 255.

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Because in an octet, if every
single binary number is on,

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the maximum it can
ever get to is 255.

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But I also-- just with
a little caution also,

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I want to point out
that 0 through 255

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is actually 256
different numbers.

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Because 0, indeed, is a value.

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But the numerical high number
you're ever going to see

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is going to be 255.

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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.