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.