https:/.../emt061080p.mp4

Hello and welcome to the 6th
video in the binary series. So

you more or less now understand
how you can convert a binary

fraction into a decimal
fractions. But how can we do it

the other way around? So let's
say I have got a fraction, say 4

3/4. How can I convert that

into? A binary fraction. Again,
let's call up on the place value

table. So the rate explained

is here. 1248 and
on this side,

half or quarter.

And an 8 now what happens in
here when it comes to the whole

part, the four. I know that I
can build up from using one for

an nothing else, so I will need
the place value holders.

And then the radix point now 3/4
by the obvious thinking would be

always just to put the three in
here. Don't forget that we are

in the binary, so we can only
use ones and zeros, so we can't

use a 3, but there are quarters.
So what happens if I take out

one of those quarters? So if
I've got 3/4 and I take away 1/4

from it, I am going to left with

two quarters. But hold on, two
quarters is exactly the same as

a half. Well, that solves my
problem, because then I can just

put a digit here. So you might
have spotted this by knowing the

half and a quarter makes up 3/4.
But this means that four and

three quarters in decimal is the
same as 100 radix .11.

In binary. Let's look
at another example.

3 and 5

eights. Place values again.

1. 24 Radix
point half a

quarter. And an 8.

Now three is 2 + 1, so I'm going
to use G of this place values

Radix point here, but when it
comes to 58 again, I'm going to

be in a little bit of a trouble
to find out what combinations

going on in here, and therefore
you need to have quite a good

understanding of manipulating
fractions, adding and

subtracting them. So if you're
not sure, please do recap days,

so don't forget that there are
loads of very good online

resource is that you can recap

on. Had to add and subtract
fractions, so let's see what

happens with the five 8 now.

I can use up one of the AIDS,
but I can use up only one of

them. So what happens if I take
an 8 away from the 458? So I've

got 48 left now that Tendai,
because remember any function

that has got twice as much as
the bottom is at the top, always

cancers down to half, so the
remainder here is just half.

That means I need a place for
the zero here, so three and five

eights in decimal is the same

as. 11 radix .101.

In binary.

Let's look at a slightly
different decimal equivalent, so

6.25 in decimal. What does it
look like in binary? Now for

this particular format, it's
good to know the fraction and

decimal fraction equivalent, so
again, the whole part of the

table will be 1248, etc. Radix

point. And then we would have
half a quarter and an 8 here.

Now.

This part of the table is the
same, but beyond the radix point

because I have got the decimal
fractions. Now I would need to

look at the decimal fractions
here, so half is 0.5, a quarter

is 0.25. Well, that tells you
something that and then eight is

0.125. So Luckily this is a
rather simple function to

convert into binary fraction
because six will be the sum of.

Four and two. So I need
a placeholder zero for

the one radix point 1/2.
I'm not using because all

I'm using is .25 so 6.25
in decimal is the same as

110 radix .01 in binary.

Let's look at a
somewhat more complicated

example, so 5.3125.

In decimal, what is it equal to
in binary? So again, right down

the place values. So on the left
hand side of the radix point

everything is the same as it
always has been.

And on the right hand
side now I have got

0.5 zero, .25, zero, .125
and then I have got

0.0625.

So let's see which one of these
I need to use to make up my

#5 is 4 and one and on the
other side of the radix point.

Now 0.5 is too big because the
0.3125 is less than 0.5, so I'm

not going to use this. What
happens if I take 0.25 out from

my decimal fraction part? So if
I've got the 0.3125?

And I need to take away the 0.25
from it. What do I left with? So

first of all to carry out this
obstruction I need to fill in

the zeros 5 -- 0 is five 2 -- 0
is two 1 -- 5. I cannot do so I

need to borrow.

11 -- 5 is Six 2 -- 2 is 0.

.0 -- 0 is zero. Well that
seems rather lucky because the

0.3125 is just simply the sum of
0.25 and 0.0 sixty five. So

that's another place value. Hold
up there for.

5.3125 in decimal is
equivalent to 101 radix

point. 0101
in binary.

Now, I hope that seeing these
examples will give you a good

idea about how to go around
converting binary fractions to

decimal fractions or decimal
fractions into binary fractions.

Also, you probably have a little
bit of an idea about how

difficult or hard inconvenient
converting decimal fractions

into binary functions can be not
to further add to this

difficulties, what if I would
need it to convert, such as

simple fraction? S3 and 4 /. 5
now there are no fifths in the

binary place value table because
these place values are just

halves of Hobbs, etc etc. So
there are no 15 that so you can

sit around there quite a bit of
time to sort of think about what

I can do. How can I be that
forfeits out of.

Hop hop squatters, 8 entrance,
etc. Another rather simple

example that could be also
problematic. Let's say if I

wanted to convert 5.4 again, .4.
What combinations of 0.5, zero,

.25, zero point 25, etc would
make up the .4 bit. This sort

of draws your attention to the
limitations of the binary

fractions. While not every
single decimal fractions.

Can be expressed as a finite
binary fraction. We can always

extend the system to use more an
more digits to express the

fractions, but unfortunately
this is an inherent property of

the binary system.

In the next video I will show
you how we can try to come

about these problems and see a
different method of converting

decimal fractions into binary,
which can make things slightly

easier. But for now I'm going
to leave you with some

practice questions and you
will find the answers to these

after the questions.

So these are the practice
questions.

And here are the answers.