Number Systems – Hexadecimal

We’ve already looked at the basics of binary and denary in the previous lesson, but this not the on;y number system that we need to be aware of.

hexadecimal

If Denary is Base 10 (10 digits) and Binary is Base 2 (2 digits), then our third number system, Hexadecimal is in Base 16 (16 digits) as Hex = 6 and Dec = 10. But we don’t have 16 digits!

Not to worry! What we do have are letters:

0=0
1=1
2=2
3=3
4=4
5=5
6=6
7=7
8=8
9=9
10=A
11=B
12=C
13=D
14=E
15=F

Now, where have we seen the use of numbers and letters between A-F before?

Most likely you have seen them used in colour codes on the internet. Consider the terrible programmer Christmas Joke: “May all your Christmases be #FFFFFF” – not only is this awful, but the #FFFFFF is the code for white, but translated is actually 3 8bit binary numbers, so 24 digits long!

How do we know this?

F = 15 

15 in Binary = 1111

4 bits x 6 = 24

 

It’s not just numbers up to 15 that we can represent using hexadecimal and part of the GCSE syllabus is showing that you understand the relationship between Denary, Binary, and Hexadecimal. The gif image at the top of the page shows the steps used to convert – try your own version using the following algorithm:

  1. Convert the denary number into an 8 bit binary number

  2. Split the binary number in half (into two nibbles)

  3. Convert each of the nibbles into a denary number

  4. IF either numbers are >=10 convert into a letter

  5. Combine the hexadecimal digits to make the number

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