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

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

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

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

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

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

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3 to the power of two is 3

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

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

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in here, the power.

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

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

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

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

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

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

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draw your attention to the first

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

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one. For example.

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

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

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

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number itself for example?

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

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

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By definition, the decimal

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number system. Is a
base 10 positional.

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Number system.

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Which uses 10 digits.

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

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digits plus zero, which makes

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

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

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

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positional number system because
if you place digits at different

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positions they represent
different values. The former

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mathematics is representing each
of the place values tend to zero

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10 to the one.

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

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

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

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It might seems a little bit
overcomplicated when you think

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

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

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

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

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

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

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

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different order? So what happens
if I say 735?

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Well, as I was reading out the

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

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

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depending on which place value
and placing or which position

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and placing the digits, they
will represent different values.

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

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

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the second number.

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E 310 switches 30 and the
seven in the first number

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

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is 700 which is 700.

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

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

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

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For example? What's the
difference between 1007?

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Andseventeen well without having
the zeros in the number I end

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

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so-called place value holders.

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

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

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

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

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

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or the ones and I'm using one of

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

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

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number without using the in
between place values, I always

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had to place a 0 here.

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

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

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the heading you have got the
powers and the equivalent

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

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this to position different
numbers in that? Now we talked

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

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in the place where you table so.

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

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

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about 735, we mix up the order.

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

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

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seven over the units.

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

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

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

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

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gets 10 times bigger.

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

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

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another important feature of the
place values themselves, which

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

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introduce smaller numbers.

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Now we have got all the
conceptual understanding that we

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

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important for computer science
because binary numbers are

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basically the way to communicate
to the computer. Remember that

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the computer at a very basic
level will type up small

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electrical circuits, and you can
either turn on electrical

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

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electric circuits you can tell
the computer to do different

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instructions. So depending on
what kind of binary number

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

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carry out different calculations
or different instructions.

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By definition, the binary
number system is base

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two positional number system.

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We using 2 digits.

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And these two digits are
zero and one.

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

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

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

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

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

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

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

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

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

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

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

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

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

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So when we look at the place
values themselves compared to

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

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

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

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

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

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

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number system because there are
other different number systems.

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

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get multiplied by the base.

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

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divided by the base.

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

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

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

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

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

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

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So. A binary number is
nothing else but a string

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of ones and zeros.

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

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

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

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the corresponding place value,
so the placeholder property of

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the zero becomes really
important and comes up a lot

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more often than in decimal
numbers.

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

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

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

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

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

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

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

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how can we make a distinction
between binary and decimal?

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So there is a very common
notation to distinguish between

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

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

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

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

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

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

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

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

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difference between the number
itself and the notation of

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signaling which system working
in this letter notation, the

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

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long as the calculations go.

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

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

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

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as the calculations go, you
can leave this number.

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So I hope that you have a
better understanding of the

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binary and the decimal number
systems in the next few

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

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numbers.