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

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

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

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

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

build out the decimal number
that needs to convert it into

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

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

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

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

which way you learn to convert
binary numbers. Whatever method

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

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

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

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

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

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

remember that the place values
were due to the 0.

2 to one. Two to two.

Two to three.

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

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

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

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

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

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

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

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

Into binary.

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

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

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

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

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

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

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

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

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

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

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

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

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

and smallest place value that I
need to use.

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

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

important. These are the secret
place Holder zeros. Remember

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

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

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

placeholder, zeros are extremely

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

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

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

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

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

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

in binary is 110.

1.

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

And the exit decimal
numbers as well.

And then look at another
decimal example.

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

much bigger number than the
previous example, and looking at

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

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

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

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

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

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

nice and simple number.

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

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

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

the four and here on the one.

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

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

binary numbers starting with
zeros, unless this is something

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

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

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

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

the one to be 0.

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

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

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

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

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

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

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

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

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

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

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

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

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

sufficient. So if I'm using up

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

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

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

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

answer is 1001011.

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

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

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

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

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

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

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

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

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

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

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

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

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

-- 6 is 5.

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

The remainder in this
case will be 26.

26 that can take
a 16 out from it.

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

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

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

one. So the binary equivalent.

Of 122 in debt.

Symbol
is

1111010.

The final example on
converting decimal numbers

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

with the place values.

1248

1630 Two, 64128 and
256. The next one

would be 512.

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

that this number is actually
bigger than my place value,

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

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

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

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

number system. I only have got

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

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

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

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

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

here, your remainder should
always be smaller than the last

place where you've used.

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

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

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

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

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

after I've used the 64.

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

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

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

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

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

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

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

convert decimal numbers to
binary numbers using the place

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

minute, you will have some
opportunities to practice

these questions yourself and
you will have the answers

after.

So these are the practice
questions.

And here are the answers.