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
• You already know about base 10
(Decimal/Denary)
x10
x10
x10
1000
100
10
1
1
2
3
4
• And you’ve just learnt about base
2 (Binary)
x2
x2
x2
8
4
2
1
1
0
1
1
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!
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)
Hexadecimal
x16
x16
x16
4096
256
16
1
0
1
2
3
As we move
left, the
column headings
increase by a
factor of
sixteen
This number is:
1 x 256 + 2 x 16 + 3 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?
http://www.advanced-ict.info/interactive/hexadecimal.html
Hexadecimal
• Hexadecimal uses the digits 0-9
and the letters A-F to represent
the denary numbers 0-15
Den Hex
Den
Hex
0
0
8
8
1
1
9
9
2
2
10
A
3
3
11
B
4
4
12
C
5
5
13
D
6
6
14
E
7
7
15
F
Notice how 0 is
classed as a
digit, so there
are 16 numbers in
total from 0 to
15
Making bigger numbers
• You do it in exactly the
same way
16
1
Den
1
0
1x16
16
1
1
1x16 + 1x1
17
1
A
1x16 + 1xA(10)
26
A
0
A(10)x16
160
2
B
2x16 + 1xB(11)
43
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
111111110000000011101110100110
01.
• http://www.advancedict.info/interactive/colours.h
tml
255
• Denary
– 255
• Binary
– 11111111
• Hexadecimal
– FF
• 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.
You convert denary to hex
in the same was as binary
16
2
1
D
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
Let’s do another one
16
C
1
7
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!
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.
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.
Hex
Denary
Binary
1
1
D
B
13
11
0
1
1
0
1
1
• So DB in hexadecimal is 11011011 in binary.