1. Topic 3: Data
Hexadecimal

2. Hexadecimal We’ve looked at two number systems
Denary (a.k.a. decimal): Base 10
Binary: Base 2
There are all kinds of number systems out there, but there’s one more useful one
Called hexadecimal
Data: Hexadecimal

3. Hexadecimal Hexadecimal is a base 16 number system
First, let’s look at the values for a possible digit:
then A-F
There’s a reason why we look at hexadecimal
To do with its relation to binary
Hexadecimal 1 2 3 4 5 6 7 8 9 A B C D E F
Denary 10 11 12 13 14 15
Data: Hexadecimal

4. Hexadecimal Let’s look at the same values
But this time we’ll include the binary values
Notice how the denary value 15 fits into 4 binary bits, but 1 hexadecimal digit?
Hexadecimal 1 2 3 4 5 6 7 8 9 A B C D E F
Denary 10 11 12 13 14 15
Binary
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
Data: Hexadecimal

5. Hexadecimal This nice ‘coincidence’ makes representing binary easy1 2 3 4 5 6 7 8 9 A B C D E F
Denary 10 11 12 13 14 15
Binary
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
This nice ‘coincidence’ makes representing binary easy
Instead of using 4 binary digits, we can use 1 hexadecimal digit
It’s worth noting that this easier representation is purely for us
Computers will still use binary
Data: Hexadecimal

6. Converting to Hexadecimal
As we have another number system, we’ll need to know how to convert
From denary to hexadecimal
From binary to hexadecimal
From hexadecimal to denary
From hexadecimal to binary
Luckily, the best way to convert between hexadecimal and denary is to go through binary
So we only need to work out how to go between hexadecimal and binary
Denary Binary Hexadecimal
Data: Hexadecimal

7. Converting to Hexadecimal
Binary and hexadecimal neatly come together in a 1:4 ratio
Converting binary to hexadecimal is easy
We separate the binary number into groups of 4
Adding most-significant zero’s as needed
Then translate each group into a hexadecimal digit
Finally, we write those digits in order
Example
We have: (2510)
First we make the groups
and add 0’s as needed
We get the denary value of each group (and get their hexadecimal value)
00012 = 110 = = 910 = 916
Then we write the digits in order
1916
Data: Hexadecimal

8. Convert the following denary values into hexadecimal28 11 39
150
200
255
ANSWERS
From top-left to bottom-right:
1C B 27
96 C8 FF
Data: Hexadecimal

9. Converting from Hexadecimal
Converting from hexadecimal to binary works in the exact opposite way
We split the hexadecimal number into its digits
We find the denary value of each digit
We convert that denary value into a 4-bit binary number
Finally, we write the binary numbers in order
From left-to-right
Example
We have: A516
First we split the number into its digits (and convert each one into denary)
A16 = = 510
Then we convert each number into 4-bit binary
1010 = = 01012
Then we write these numbers on after the other
Data: Hexadecimal

10. Convert the following denary values into hexadecimalB1 CD D7
ANSWERS
From top-left to bottom-right:
Data: Hexadecimal

11. Some Uses of Hexadecimal
There are two common uses of hexadecimal
Colours
Some systems use 1 byte per colour (red, green, and blue)
Makes 24-bits in total
Can be shortened to a 6-digit hexadecimal number
Memory Addresses
Come in 32-bit or 64-bit binary values
Can be shortened to 8- or 16- digit hexadecimal numbers
Useful Note
In programming languages:
10: a denary value 1010
0x10: a hexadecimal value 1610
Data: Hexadecimal