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.