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Binary and Hexadecimal

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Converting Between Binary and Hex


The CPU works using binary. Electronically this is done with electronic switches that are either on or off. This is represented on paper by noughts and ones. A single BIT or binary digit requires one wire or switch within the CPU. Usually data is handled in BYTES or multiples of bytes. A Byte is a group of eight bits. A byte looks like this

01001011

This is inconvenient to read, say and write down so programmers use hexadecimal to represent bytes. Converting between binary and hexadecimal is not difficult. First split the byte into two nybbles (half a byte) as follows

0100    1011

Then use the following table

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

 

EXAMPLE

Split the byte into two halves

01001011 becomes 0100    1011

Using the table above

0100 is 4
1011 is B

The answer ...

0100    1011 is 4B in Hexadecimal.

 

To convert the other way take a hexadecimal such as E7.


Look up E in the table. It is 1110.
Look up 7 in the table. It is 0111.


E7 is 1110    0111.


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© C Neil Bauers 2003