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Hexadecimal

The Hexadecimal system is a Base 16 system.

The digits used : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E and F.

Some examples of hexadecimal numbers........ 3B47, 17, DEAF.

Consider the hexadecimal number 15CA.

To convert it into denary....

Place the number under the appropriate headings....
(Multiplying by 16 for each heading number)....

4096 256 16 1
1 5 C A

So the hexadecimal number 15CA represents the denary number

(1 x 4096) + (5 x 256) + (12 x 16) + (10 x 1) = 5578

Note :

Remember that A=10, B=11, C=12, D=13, E=14, F=15.

Hexadecimal numbers are indicated by a subscript of 16.

Eg 11016 is a hexadecimal number.

 
 

Hexadecimal has come to be a short-hand notation for binary number patterns. It is easier to work with smaller hex numbers than with large binary numbers.

Fewer errors will occur as it is easy to incorrectly read a large binary number!

 

Converting between Binary and Hexadecimal.

Each digit in a hexadecimal number represents a 4-bit binary number.

The conversion table needed is ...

Denary Binary Hex
0 0000 0
1 0001 1
2 0010 2
3 0011 3
4 0100 4
5 0101 5
6 0110 6
7 0111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F

Example:(hexadecimal to binary)

The hexadecimal number 4AC2

4AC2 in binary is 0100 1010 1100 0010

 

Example (binary to hexadecimal)

The binary number 001101011101.

First step...start from the right and split into 4-bit blocks...

0011...0101...1101

Convert each 4-bit block into hex....to get 35D