Hello and welcome to the first
video of the binary numbers. In

this video. I would like to
introduce you to the binary

numbers and the binary number
system, but for us to understand

that we need to look at what the
decimal number system is and we

need to look at the powers
because powers are at the heart

of every number systems. So
let's start with the powers.

3 to the power of two is 3

* 3. And for example, 5
to the power of four is 5

* 5 * 5 * 5. So
there are two important concepts

in here, the power.

And the base, they both can be
any different whole numbers.

So the power tells us how many
times we need to multiply the

base together. So in this
particular case, four tasmac 2

multiplied the base 5 by itself
four times, and in the example

of three, the two tags need to
multiply the three by itself

twice. Now there are two
important powers that we need to

draw your attention to the first

one. Is any number to the zero
power is by definition is always

one. For example.

7 to the power of 0 is 1
two to the power of 0 is one

and 10 to the power of 0 is
also one another important

power. Is any number raised
to the first power is just the

number itself for example?

7 to the first power equals to
7, two to the first power equals

to two and 10 to the first power
is equal to 10.

By definition, the decimal

number system. Is a
base 10 positional.

Number system.

Which uses 10 digits.

And these 10 digits are 012 all
the way up to 9. So that's the 9

digits plus zero, which makes

them 10. Now what does it mean
based on and positional the base

10 taskview that using 10 digits
and every place value or every

position is represented by
powers of 10 and it's a

positional number system because
if you place digits at different

positions they represent
different values. The former

mathematics is representing each
of the place values tend to zero

10 to the one.

1:50 2:50 and so
on now what they mean as

numbers? 10 to 0 as we said
before, it's 110 to the one

Eastern tented it too, is 100
and 2:50 is 1000.

It might seems a little bit
overcomplicated when you think

about the decimal numbers, but
it is already built into the way

that we read our numbers. For
example, if you read out 573

just the way you say the number
you talk about decimal place

values 573, so the hundred 500
tells you that five is at the

hundreds place. The 70 tells you
that 70s at the 10s place and

three tells you that three is at
the units place. Now, what

happens if I use the same 3
digits but in a slightly

different order? So what happens
if I say 735?

Well, as I was reading out the

number. You probably notice that
now is 7 at the hundreds place,

three is at the 10 space and
five is at the units place. So

depending on which place value
and placing or which position

and placing the digits, they
will represent different values.

The five in the first number is
105 in the second number is just

five units. The three in the
first number is 3 units, but in

the second number.

E 310 switches 30 and the
seven in the first number

is seven 10s, which is 70
and in the second number

is 700 which is 700.

Now I would like to draw your
attention to the rule of the

zeros because so far I just
picked out any digits which is a

non 0 digit. But what happens if
I have good zeros in my number?

For example? What's the
difference between 1007?

Andseventeen well without having
the zeros in the number I end

up with a very much smaller
number, so the zeros are

so-called place value holders.

So today telling me that at this
place value I'm not using any of

the place value by placing the
zero. So in this case I'm using

seven of the units, not using
any of the 10s an I'm not using

any of the hundreds and I'm
using one of the thousands

without the zeros here. I'm just
telling you that I'm using seven

or the ones and I'm using one of

the tents. You will agree with
me that the two numbers are

very, very different, so every
time I need to build up a bigger

number without using the in
between place values, I always

had to place a 0 here.

Now we can build up a decimal
place value table and the former

place value table would look
like this. It's just basically

the heading you have got the
powers and the equivalent

decimal values. Now how can you
use a place value table like

this to position different
numbers in that? Now we talked

about a few different numbers,
so let's see what they look like

in the place where you table so.

573 you put a five in the
hundreds, seven in the Times

Seven in the 10s, and three in
the units column. If we talking

about 735, we mix up the order.

Of the digits 17. One of the
10s. Seven of the units and 1007

one of the thousand. None of the
hundreds. None of the 10s and

seven over the units.

One thing I'd like you to notice
is when you look at the place

value table. If you're going
from right to left, you can spot

that the numbers from place
value to place while you get 10

times bigger, so the values
themselves, the place where used

gets 10 times bigger.

Now if we reverse the order and
we going from left to right, the

place values themselves get 10
times smaller, so this is again

another important feature of the
place values themselves, which

will help us to extend the place
value table in a later video to

introduce smaller numbers.

Now we have got all the
conceptual understanding that we

need to build up the binary
numbers. Binary numbers are very

important for computer science
because binary numbers are

basically the way to communicate
to the computer. Remember that

the computer at a very basic
level will type up small

electrical circuits, and you can
either turn on electrical

circuits on or off, and in the
different combinations of these

electric circuits you can tell
the computer to do different

instructions. So depending on
what kind of binary number

instructions you're giving to
the computer, the computer will

carry out different calculations
or different instructions.

By definition, the binary
number system is base

two positional number system.

We using 2 digits.

And these two digits are
zero and one.

So what does the place where you
table look for the binary

numbers? But because it's a base
two number system, every place

value is a power of two. So what
are these powers?

2 to the power of 0 two to the
power of 1 two to the power of 2

to the power of. 3 two to the
power of four. 2 to the power of

5 and I can go on forever. As
you see the differences now.

That instead of base 10, I'm
just replacing the Terminator 2,

but the powers themselves stay
the same. Now what does it mean

for the actual values? What is 2
to the zero? While remember any

number to the Zero power is 1
two to the one, any number to

the first power itself, so it's
2 two to two 2 * 2 is 4, two to

three 2 * 2 * 2 is 8, two to
four is 16 and two to five.

He's 32 and I can go
on for higher values.

So when we look at the place
values themselves compared to

the decimals, Now when I go from
right to left, the place values

get doubled. So from one we can
get to 2 from 2 began get to 4

from 4 we can get to 8, they
double up and if I go from left

to right the opposite direction
they get halved from 32 to 16 I

get by having it and from 16 to
8 I get by having it again so.

This is a common feature of the
place where you tables any

number system because there are
other different number systems.

Every time when you go from
right to left, the place values

get multiplied by the base.

And when you go from left to
right, the place values get

divided by the base.

So when we look at the binary
place value table, it's like the

numbers I showed you before, but
put into a nicer format.

So what happens in the here in
the decimal place value table?

We had quite a lot of different
digits that we could play around

with. We had the digits from
zero to 9, but what happens in

binary? Which 2 digits can we
use here? Just the zero and one.

So. A binary number is
nothing else but a string

of ones and zeros.

For example, this is a binary
number. What it means then for

the place values is that with
one I'm saying that use the

corresponding place value and
with zero I'm saying don't use

the corresponding place value,
so the placeholder property of

the zero becomes really
important and comes up a lot

more often than in decimal
numbers.

Let's look at a few more binary
numbers. So basically I can just

use any ones and any zeros and
place them in any order whatever

to build upon binary number. So
let's say 1011001 it's a binary

number, 100001 is also binary
number, or 1011. Again a binary

number. Now you probably notice
that because we only using ones

and zeros. Every single one of
them could also be a decimal

number. For example, the last
one could be 1011 in decimal. So

how can we make a distinction
between binary and decimal?

So there is a very common
notation to distinguish between

binary and decimal numbers. So
if you see a number which only

uses ones and zeros to make sure
that this is a binary number,

you put a little two in
subscript. And if you want to

indicate that this is a decimal
number, you put a little

subscript of 10, indicating that
this is a decimal number.

So if it's not clear enough from
context, always look for the

subscript. It is a binary
number. Or is it a decimal

number? Now it's very, very
important that you are making

difference between the number
itself and the notation of

signaling which system working
in this letter notation, the

number 2 and here the number 10
are not part of the number. As

long as the calculations go.

This is just a way of telling
me or you or anybody ask that

this is a binary number. Once
we are aware of that, this is

a binary number. This two
becomes redundant, so as long

as the calculations go, you
can leave this number.

So I hope that you have a
better understanding of the

binary and the decimal number
systems in the next few

videos. I will show you what
we can do with the binary

numbers.