1. Information Processing
Lecture 6A
Hexadecimal Notation

2. The Hexadecimal System
The Hexadecimal number System had 16 separate characters:
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
The extra letters are so that the numbers can be written using one character each. This means that A7BC is a number written in Hexadecimal code

3. Hexadecimal
Dec Hex
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
These numbers are written in base 16, so that a number like 9E means
the 9 is 9 x 16 = 144
the E is 14 x 1 = 14
Altogether this would be 158
Slide

4. Hexadecimal Numbers
Normally in the context of computers, we will only be considering two-digit Hexadecimal numbers like A3 or 4E
When the numbers have more digits we tend to split them up into two-digit pairs.
This makes interpretation a lot easier

5. Hexadecimal to Decimal
For example:
The number 4E in Hexadecimal, is:
4 E
That is 4 x 16 =
and E (= 14) x 1 = 14
Total : (Decimal Notation)

6. Challenges Convert F2 from Hexadecimal to Decimal
Convert 8B from Hexadecimal to Decimal

7. Challenges F2 F x 16 = 15 x 16 = 240 …and 2 x 1 = 2 Total = 242 8B
B x 1 =
11 x 1 = 11
Total = 139

8. Converting Decimal to Hexadecimal
Two digit Hexadecimal numbers lie in the range 0 – 255
We will only consider numbers in this range.
The answer will always be a two-digit hexadecimal number

9. Converting Decimal to Hexadecimal
Example:
Convert 181 to Hexadecimal
181  16 = 11 remainder 5
In Hexadecimal 11 = B
In Hexadecimal 5 = 5
This means: = B5
Decimal Hexadecimal

10. Challenges Convert 100 from Decimal to Hexadecimal

11. Challenges 239 100 239  16 = 14 rem 15 100  16 = 6 rem 4
14 in Hex is E
15 in Hex is F
So the Hexadecimal number is: EF
100
100  16 = 6 rem 4
So the Hexadecimal number is:

12. Hexadecimal to Binary
The easiest way to convert Hex to Binary is by using a ‘look-up’ table to find the Binary equivalents for the Hex digits 0 to F
For example, the Binary for 6A would just be:
6 = 0110
A = 1010
6A =
Hex Binary
0  0000
1  0001
2  0010
3  0011
4  0100
5  0101
6  0110
7  0111
8  1000
9  1001
A  1010
B  1011
C  1100
D  1101
E  1110
F  1111

13. Challenge
Convert E8 to Binary

14. Challenge E8
E = 1100
8 = 1000
This means that E8 =

15. Binary to Hexadecimal
Binary Hex
0000  0
0001  1
0010  2
0011  3
0100  4
0101  5
0110  6
0111  7
1000  8
1001  9
1010  A
1011  B
1100  C
1101  D
1110  E
1111  F
Converting Binary to Hex can be done in exactly the same way, by using a look-up table
For example the binary number will be:
1001 = 9
1011 = B
So that = 9B

16. Challenge
Convert to Hexadecimal

17. Challenge 11000011 This can be split: 1100 = C 0011 = 3
0011 = 3
So that = C3

18. Summary Hexadecimal is just a shorthand way of writing Binary Code.
Each of the numbers 0 – 15 is written as an individual character.
This means that we can represent each of the decimal numbers with two digits
Every one of the 8-digit binary numbers can be represented by a two-digit hexadecimal number.