1. Lesson Objectives Understand the hexadecimal numbering system
Convert numbers between hexadecimal and denary, and vice versa
ALL students be able to count in hex from 1 to 16
MOST students will convert hex numbers into denary
SOME students will convert numbers between hex, denary and binary

2. 1 2 3 4 1 You already know about base 10 (Decimal/Denary)
And you’ve just learnt about base 2 (Binary) 1 2 3 4 10
1000
100
x10 1 2 8 4 x2

3. Why do we need binary numbers?
Because computers work on the principle of 2 states, that something is either ON/TRUE or OFF/FALSE.
This can only be done with base 2 (binary)
If it was done with decimal/base 10 there would be 10 different states!

4. The problem with binary…
There is one big problem with binary…numbers can become VERY long!
In order to make it easier for a human programmers to work with binary numbers, they use the hexadecimal system (like a binary shortcut)

5. Hexadecimal
As we move left, the column headings increase by a factor of sixteen
x16
x16
x16 1 2 3 16
4096
256
This number is:
1 x x x 1 = 291
It’s still two hundred and ninety-one, it’s just written down differently
How can there be sixteen possible digits in each column, when there are only ten digits?

6. Hexadecimal
Hexadecimal uses the digits 0-9 and the letters A-F to represent the denary numbers 0-15
Den
Hex 8 1 9 2 10 A 3 11 B 4 12 C 5 13 D 6 14 E 7 15 F
Notice how 0 is classed as a digit, so there are 16 numbers in total from 0 to 15

7. Making bigger numbers You do it in exactly the same way 16 1 Den 1x16
1x16
1x16 + 1x1 17 A
1x16 + 1xA(10) 26
A(10)x16
160 2 B
2x16 + 1xB(11) 43

8. Where is it used?
When have you seen numbers being represented as letters?
Hex is often used for 32-bit colour values, especially on web pages
FF00EE99 instead of

9. 255
Denary
255
Binary
Hexadecimal FF

10. Large binary numbers are hard to remember
Programmers use hexadecimal values because:
each digit represents exactly 4 binary digits;
hexadecimal is a useful shorthand for binary numbers;
hexadecimal still uses a multiple of 2, making conversion easier whilst being easy to understand;
converting between denary and binary is relatively complex;
hexadecimal is much easier to remember and recognise than binary;
this saves effort and reduces the chances of making a mistake.

11. You convert denary to hex in the same was as binary16 1 D 2
Convert the denary number 45 into a hex number
Step 1: How many times does 16 go into 45?
45 / 16 = 2 (with 13 remaining)
Step 2: How many times does 13 go into 1?
13! 13 in hex is D

12. Let’s do another one 16 1 7 C
Convert the denary number 199 into a hex number
Step 1: How many times does 16 go into 199?
199 / 16 = 12 (with 7 remaining)
Step 2: 12 in hex is C
Step 2: How many times does 7 go into 1?
7! 7 in hex is 7!

13. Lesson task: Complete the denary to hex conversions in your workbook.
Extension: If you complete, have a go at the cross word task in your booklet.

14. Hex to binary
To convert from hexadecimal to binary treat each digit separately. It may be easier to go via denary to get a binary number.
So DB in hexadecimal is in binary.
Hex D B
Denary 13 11
Binary 1