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Welcome to the third video on
binary numbers. In this video,

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we're going to look at how to
convert decimal numbers to

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binary numbers, and in this
particular video I'm going to

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show you the place value table
or addition method. In this

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video. Our goal is to find out
what place, why you combinations

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build out the decimal number
that needs to convert it into

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binary. I can only use once for
any of the place values.

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As in the binary number system,
I only have the digit one and

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zero in a further video I'm
going to show you a different

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method called the division
method, so it doesn't matter

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which way you learn to convert
binary numbers. Whatever method

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you feel more comfortable with,
just stick with that and then

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your answer will be just as
correct. If you are doing it

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with the other method. So the
table method, it's called the

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place value table method because
we are going to use the binary

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place value. To convert decimal
numbers for that again, let's

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look at what the binary place
value table looks like. So

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remember that the place values
were due to the 0.

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2 to one. Two to two.

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Two to three.

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2 to 4, two to five etc. You can
continue this as long as you

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want it to, but these numbers
also translate back down to

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normal decimal numbers without
the power form. So 2 to the

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power of 0 would be 1. Two to
the power of 1 would be 2. Two

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to the power of two would be 4.
To do a power of three is 8 to

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two power of four is 16 and 2
two power of five is 32. So if I

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have got. Decimal number, such
as the teen? How am I going to

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use my knowledge of the place
values to convert this number?

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Into binary.

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So what I'm going to do, I'm
going to look at how many 30

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twos would I need to use? Use to
make the 13 while it's too big

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because 13 is much much smaller
than 32, so I'm not going to use

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any of that. How many six teams
am I going to need? I'm not

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going to need any of the
sixteens either, because 16 is 2

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big 413, so the biggest place
value I can use is 8 because

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eight is the bigger out of the
place values, which is smaller.

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Done 13 so now if I'm used
eight, what's the difference

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between 13 and eight? What is
the remainder that I still need

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to build up from the rest of the
place? Values so 13 -- 8 makes 5

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and five can be built up from 4
an one, which means that I'm not

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going to use any of the tools
and here is an important thing

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that any of the place values
that are in between the biggest

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and smallest place value that I
need to use.

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All the way up to to the power
of 0, which is one I need to

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place zeros in between. Because
these errors are very, very

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important. These are the secret
place Holder zeros. Remember

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that in decimal numbers 502 and
52 are very, very different. So

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if I forgotten this placeholder
0 here and I'm just writing them

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52, I'm altering the value of
the number. So these places were

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placeholder, zeros are extremely

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important. Now. O's I could put
in here but so far it's not

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important because I'm just
telling by placing zeros in here

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that I'm not using this place
values. But these zeros are

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don't really carry any essential
information, so these kind of

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zeros at the frontier the so
called unnecessary 0 so I don't

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have to write them out.
Therefore I can conclude that 13

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in binary is 110.

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1.

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So again, just quickly right up
the place value table.

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And the exit decimal
numbers as well.

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And then look at another
decimal example.

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42 in decimal, what would that
be in binary? Now this is a much

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much bigger number than the
previous example, and looking at

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42. Is 32 the biggest place
value I can get out from 42 or

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can I use the next place value
up while the next place value up

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would be 64? 'cause remember,
these numbers are always double

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up if I'm going from right to
left, which means that 64 is too

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big for my 42. So yes, 32 will
be the biggest place value that

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I can use now. What's the
remainder? 42 -- 32 gives me a

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nice and simple number.

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10 and again, when I'm looking
at this place values, 10 can

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easily build up from 8 and two
again. Don't forget about the

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placeholder zeros, so I need to
place a 0 here under 16 here on

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the four and here on the one.

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Whether to put a base value on
the 64 or not, it's usually your

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choice, but in practical
examples you don't really see

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binary numbers starting with
zeros, unless this is something

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called like the fixed length
place value table is like the 8

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bit binaries, but at the moment
we're just looking at general

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binary numbers. Therefore, 42 in
decimal is 101010 in binary, and

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again 42 is an even number.
So I'm expecting my last digit,

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the one to be 0.

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Let's up our game and look at a
much, much bigger number.

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75 in decimal, what would that
look like in binary? Now I don't

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know about you, but I'm getting
a little bit tighter writing out

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all the powers and they don't
really give me that much extra

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information. So what I'm going
to do from now on just write out

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the decimal place value
equivalent, the one the two, the

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four, the eight, the 16, the 32,
the 64, and the next one is 120.

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8 now as soon as you went over
the number in question with

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place values, then you know that
that place where you will not be

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used and the biggest place value
that you can use to make 75 will

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be 64. So again, what is the
remainder? So what's the

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difference between 75 and 64?
Well easily calculated at 11.

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That means 32 is too big. 16 is
too big for eight will be

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sufficient. So if I'm using up

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an 8. What else do I need to
difference between 8:00 and

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11:00? Is 3 and three can be
built up from two and one.

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Again four, I haven't used so I
need to place the zero down to

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indicate that that place value
is not used, so the final binary

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answer is 1001011.

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And I'm indicating that this
is a binary number here.

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Next example 122 in decimal.
What does it look like in

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binary? So again, start with the
place values 124, eight, 1630,

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two 64128, now 120. Just a
slightly too big. But it means

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that it's still not place value
that I'm going to use.

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So the biggest place for you I
can use to build up 122 it's 64

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again. So 64 will definitely be
used. So what's the remainder?

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How much more do I need to take
out from this place values?

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So 122 -- 64 four is too big
for two to be taken away from.

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So I need to borrow from here.
Therefore one stays here and

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then 12 appears. Here the
difference between 12:00 and

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4:00 is 8. Again, I will need
to borrow because six is too

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big for one, so zero will be
here. 11 will be here and 11

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-- 6 is 5.

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So 58 is the remainder 58. I can
take 32 out from it.

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The remainder in this
case will be 26.

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26 that can take
a 16 out from it.

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The remainder is 10 and I
remember at 10 can be built up

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from 8 and two there are two
place values that I need to fill

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up with zeros because these are
placeholders, the 0, four and

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one. So the binary equivalent.

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Of 122 in debt.

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Symbol
is

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1111010.

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The final example on
converting decimal numbers

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to binary numbers in this
video is 249. Again, start

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with the place values.

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1248

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1630 Two, 64128 and
256. The next one

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would be 512.

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But that is too big and so is
256. I just needed to make sure

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that this number is actually
bigger than my place value,

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because if I start with a place
where you that is slightly too

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small, then I will run out of
digits that together. And don't

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forget you can only put ones and
zeros in here, so I can't say

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that I'm using two of the 32
because two is not part of my

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number system. I only have got

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one and 0. So the biggest place
value I can take out is the 128,

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so I'm going to use one of the
128 and I need to see what's my

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remainder. 9 -- 8 is one 4 -- 2
is 2 and 2 -- 1 is 1. So I

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still got quite a big number,
but that number is smaller than

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128 so I'm on the right track.
Anytime when you got a remainder

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here, your remainder should
always be smaller than the last

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place where you've used.

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But 121 is less than 128, so I'm
on the right track. So 64 I will

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definitely use. But what's the
remainder? Again? So four is too

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big for one to be taken away
from DEF running to borrow again

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11 -- 4 makes it 7 again six I
can take away 6 from 1 so need

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to borrow again. 11 -- 6 gives
it 5 so I've got 57 as remainder

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after I've used the 64.

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The next place why is 32? So
take away 32 gives me 7 -- 2

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gifts, five, 5 -- 3 gifts two,
so I'm using that after the 32

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I'm going to use the 16 as well.
So the difference here now 25 --

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16. Is 9 an? I remember
the nine can be easily build up

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from 8:00 and 1:00, so I'm going
to need two placeholder zeros in

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here, so 249 in decimal is
11111001. In binary. This was

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our last example. I'm hoping
that you understand how to

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convert decimal numbers to
binary numbers using the place

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values. And that you probably
find it easy in the next

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minute, you will have some
opportunities to practice

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these questions yourself and
you will have the answers

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after.

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So these are the practice
questions.

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And here are the answers.