Yeah, I'm relieved that I don't have to do more multiplications of eight here.

Let's stop and so this is my number in octal.

Just a reminder, where that one came from,

that 1 there became that 1 there, okay.

Let's look at hexadecimal next.

Just a reminder, hexadecimal place values are powers of 16. We'll write them.

So we have 1, 16,

and then 16 squared which will remind yourself 16

squared is 256,16 cubed 4,096.

Those the integer one,

so that's 16 to the power of 0,

16 to the 1,

16 squared, 16 to the cube.

We are going to need the fractional parts with the negative parts of 16 for this bit,

so we're going to divide by 16,

so 16 to the minus 1,

which is 1 over 16 that writes down as a decimal as 0.625.

Next, 16 to the minus 2,

which is 1 over 256.

Calculator says we get 0.00390625 and just carry on like that,

16 to the minus 3,

and so on, you get the picture.

So these are the place values.

So for fractional numbers in hexadecimal,

we are going to work with these place values here.

Let's look at an example, right.

Let's transform this number here,

0.9B which is a hexadecimal number.

Let's remind ourselves what these B's and A's and so on mean.

The digits in hexadecimal,

we have 16 digits to work with and those are 0,

1, 2, 3, 4, 5, 6,

7, 8, 9 and then A for 10, B for 11.

So 10, 11, 12,

D for 13, E for 14,

F for 15. That's it.

Now, I recommend that when you do your work,

write at the top of the page the digits so you don't confuse what A,

B, C, and D and so on are worth.

So, there we are on top-line.

So we're going to write what the place values

are and we're going to work out what this number is in decimal that way.

So we just did this.

The 9 stands for the 1 over 16 and that B is on

the position for the 1 over 256.

That means that this number is 9 times 1 over 16

plus 11 times 1 over 256.

Just a reminder again,

this 11 here is because of the B,

and this 9 here is the other digits on the original number.

So calculated to the rescue,

adding up these numbers,

it comes out to a 155 over 256 which is no more no less than

0.60546875

and that is in decimal.

Now, if your number had an integer part and a fractional part,

we'll work out what the integer part is in

hexadecimal during the division by 16 and take the remainders algorithm.

Workout the fractional part

using the algorithm I'm going to show you now which is the other way around,

multiply by 16 and take the integer parts as digits.

So the example I've got for us is 0.96875,

that's a decimal number we want to write this in hexadecimal.

We're going to start by multiplying by 16,

because that's the base, it's base 16.

Multiply that and we get 15.5 precisely and this is the integer part.

This is going to be our first hexadecimal digit.

Now remember, 15 in hexadecimal is F. So,

we're going to write it here, 0.F,

that F from that 15.

From 15.5 here, we're going to take away the 15 and just work with the fractional part.

So 0.5 and then we multiply by 16 and that is 8.

Eight is going be the next digit,

going to be there, and we stop because 8 is an integer.

There's no fractional part to continue.

Yeah, we're still happy, cool.

So that means that fractional number in decimal is written as 0.F8 in hexadecimal.