https:/.../emt021080p.mp4

Welcome to the second video. In
the binary series. Today, we're

going to talk about how to
convert binary numbers to

decimal so when we see a binary
number, something like.

10110 then we know that this
place value is 2 to the power of

0. This place values to the
power of 1 to do a power of

three to two power of four and
two to power of five. So how can

we use this information to find
out what this binary number is

in decimal? What we can do
right? Every place value under

each digits? So two to zero do

today 1232. 223

224

and these numbers
mean this is

1248.

16

now that means we've got 1 * 2
to the power of 4.

Plus 0 * 2 to the power of 3.

Plus 1 * 2 to the power of 2 +
1 * 2 to the power of 1.

Plus 0 * 2 to power
of 0. This also means that

we've got 16 * 1 +
8 * 0 + 4 *

1. Plus 2 * 1.

Plus 1 * 0 Now zero times any
number always gives you 0, so

these numbers are equal to zero
that we don't really need to

take them into account when we
adding up, so the numbers that I

need to just add up 16 + 4 + 2
and that is 22. Now if we wanted

to be really precise what I
should be doing, I should write

a letter to in here to
indicating that this is a binary

number. And the letter 10 in
here indicating that this is a

decimal number, so.

10110 in binary
is 22 in

decimal. Let's have a look
at another example so you

can see clearly hard binary
numbers work.

Let's start with a slightly
smaller number 1101. This is our

binary number and we want to
find out what it is equivalent

to in decimal.

Now we can again start talking
about the place values and then

find out each at each place
value what is equvalent to.

However, there is a slightly
faster way. You might have

noticed that when we were
looking at the binary playplace

values, what happened to the
place values they all doubled as

we went from right to left, so
we can use that information

instead of remembering always to
the powers so I can start with

just writing one on top of the

first. Place value then double
of that two to the next place

value up, then double of 2 four
to the next place value up and

then AA 48 to the next place.
Value up again. Every time I see

a zero. I know that zero will be
multiplied by that place value

which also tells me that I don't
necessarily have to take that

place value into account so
another quicker way of doing the

conversion. Is I'm only taking
into account the place values

which has got ones under them,
so this number will be 8 + 4

+ 1. Now 8 + 4 makes 12
+ 1. This is 13 in decimal.

You would say that it's a rather
faster way of doing it.

So another example.

11010
to make sure that everybody

knows is a binary number, I'm
just going to put down the

letter to that and again look at
the place values. So the

smallest place value here is 1.
Then I'm just doubling up all

the different digits to get to
all the place values. And again,

I'm only picking out the place
values which have got ones under

them. So 16 + 8 four has zero
100, so that's not going to be

used. And to use that has got
one under it. The last place

value the one place where you
again is not used.

So adding these together
again, I can pick and choose

which numbers are merging
together and I can notice

that 8 + 2 adds up to 10
quite nicely, and 10 + 16 is

easier to add together that
16 + 8 + 2. So whenever you

have numbers here you can
pick and choose which one to

add together, especially if
you're not allowed to use a

Calculator. So 8 + 2 makes
1010 + 16 makes 26, so this

number is 26 in decimal.

Next example 11101. Again,
this is a binary

number. Place values.

124 eight 16. So which are the
ones I'm adding together

everything except the two. So
this is 16 + 8 + 4 +

1. Again I can pick and choose
which numbers to add together.

16 and four nicely adds up
together to 20 and I've got 8 +

1 which gives me 9. So
altogether this number is 29.

In decimal.

OK, now you can see three
different examples here in front

of you. And when you look at the
three different numbers, the

decimal equivalents that you
see, we can spot that two of

them are odd and one of them is
Even so how can I quickly and

easily just see if a number is
odd or even in binary? Now look

at all the place values, every
single place value is an even

number except for the very last
one. OK, so the smallest place

value is the one.

Everything else is even now we
know in mathematics that if I'm

adding even numbers together,
the answer always going to be

even. We also know if I'm adding
an even an odd number together.

The answer will be odd, so this
is a quick way to check if

you've made any calculation
mistakes or not. If the last

digit in the binary number is 1,
then you know that you used one,

so your answer has to be an odd
number, but if your last digit.

O, you know that you haven't
used any odd numbers in your

sum, so everything added
together there is even there

for your final number has to
be even. This is just

curiosity to help you if
you're not very familiar with

the binary numbers to see if
your answer is right or not.

I'm hoping that you started to
get an understanding of the

binary numbers, but let's look
at some slightly longer and

therefore a little bit complete.
More complicated examples. So if

I have got a slightly longer
number, such as 10101010 Now as

I mentioned before, I'm
expecting to have an even

answer. But what exact number
lies behind this binary number?

So again, start putting the
place values on top of the

digits 124, eight, 1630, two
64128. Now you don't need to be

quite good at doubling, but
doubling isn't overly

complicated, so you should be
able to carry out these

calculations relatively simply
even without a Calculator. So

what are the digits I'm using
here? Remember, anything

multiplied by zero always gives
you 0, so these digits.

Here we are not add any extra to
the number value that I have

here, so I only have to pick out
128 + 32 + 8 + 2. So again

I can pick and choose which
numbers to add together and by

looking at it I would say the
adding together 128 and two

gives me nice an easy number
which is 130 and adding together

32 + 8.

Gives me 40, so this
number is 170 in decimal.

I could have chosen a different
combination of adding the

numbers together. I could have

added 32. And 128 and 8 +

2. Ending up with 170 again, but
I think he would agree with me

that adding 128 + 2 together.

Slightly simpler than adding 128
and 32, although it's not

that much more complicated and
the last example for today's

video is 11001101 in binary.
Again, a nice and quick

way of putting the exact
place values on top of

the numbers one 248-1632.

64128 and again, remember
anything which has got zero

under 8 will just get
multiplied by zero.

Therefore that number
doesn't add to the value,

so I'm just picking out the
place values which has got

the digit 1.

So 128 + 64 + 8 + 4
+ 1. Now unfortunately, when I'm

looking at this some there isn't
anything that is nice and easy

to add together, so I will have
to think about this addition and

slightly different way. So what
I'm gonna do I'm going to add

together these smaller digits.
So 8 + 4 makes 12 + 1

makes 13, so these three.

Makes the team and I've got
64128 left. I'm going to leave

128 for now because I can see
that 64 an hunnan 13 can add

together quite simply so that
together makes 77. And now I'm

just going to copy 128
underneath and 7 + 8 makes 5

carried A one. 1 + 7 makes 8
+ 2, makes 10 carry the 122.

So this number is 205 in
decimal, and again I'm expecting

to have an odd number because I
have got a digit one in here.

And at this video was about how
to convert binary numbers into

decimal numbers. I hope you have
got a better understanding of

the process now and in the next
minute you will see some

practice questions that you can
try yourself and I will supply

the answers as well.

I suggest that you post the
video while you are carrying out

the calculations and then you
move on to the answers. So these

are the practice questions.

And here are the answers.