A number system is just a way of representing amounts of something. For example, most humans represent amounts with 10 individual numbers from 0-9, before repeating by starting over and adding another to the left. When thinking of number systems, it's easy to fall in to the trap of thinking that the way we count is the only way. But why? Wouldn't it be just as easy to only have 6 numbers before adding another one to the left? What about 13? 24? The number system we use is called DECIMAL (although for some reason, exam boards like to use the term DENARY so we'll use that from now on.) Because it uses 10 different numbers, denary is known as BASE-10

Each individiual number in binary is called a BIT. 8 bits make up what we call a BYTE. You might be wondering why we use 8 bits together. Each individual number in the sequence is called a bit and 8 of them together is called a byte. Computers seperate binary up in to bytes because a byte is the single smallest string of bits which can make up a text chatacter like A or L.

Computers only understand one number system- BINARY. In fact, this is the only thing they understand at all. You may be able to communicate with a computer in several programming languages, but even these complex systems of communication eventually it all gets converted in to the only language a computer understands. You'll have heard of binary before and probably seen it. It's a series of 0s and 1s which look something like this:

The binary number system only uses 2 numbers, 0 and 1. You may think this is quite limiting but it's not. Using 0s and 1s a computer can create any number you can with your 0-9s. It just works slightly differently. Because it uses 2 different numbers, binary is known as BASE-2

The reason computers can only speak in binary is that a computer is just a series of switches, each which are either in an on (1) or off (0). The sequence in which these switches are either on or off make up things you see on the screen and the calculations that a computer performs. It may seem difficult to imagine, but we're speaking about billions of switches here, not just a few.

For the exam, you will need to know how to convert different number systems between each other. First we'll take a look at how to convert binary to denary. Each number position in binary has a value, just as it does in denary. The values look like this:

This means that the binary number 00000000 has the denary value of 0, since none of the positions are 1. What about this one:

We have now put a 1 in the 8 position. This means that the binary number 00001000 is the equivalent of 8.

One more:

This time we have a 1 in the 2 position and a 1 in the 32 position which makes 34. Therefore the denary equivalent of the binary number 001000010 is 34.

If you've not yet learned what hexadecimal is, then go to the hexadecimal page before reading here, as it won't make much sense.

Converting binary to hexadecimal is easy if you can convert binary to denary.

STEP 1: Take a binary string and split it in to two

STEP 2: Work out the decimal equivalent of the two new strings

STEP 3: Use the conversion chart above to work out the hexadecimal equivalents of 9 and 10:

As you can see, 9 is 9 and 10 is A. Therefore 10011010 in hexadecimal is 9A

In the exam they may give you a bigger binary number of 2 bytes (16 digits). Don't worry, just split it up in to 4 and do the same.

This one is just as easy once you understand the basics. Let's take the number 4A3B as an example

STEP 1: Work out the binary equivalent of each individual number. Write each of them with 4 numbers even if they start with a zero.

4 = 0010 |

A = 1010 |

3 = 0011 |

B = 1011 |

Now just write them together starting with the top one first:

0010 1010 0011 1011

Therefore, 4A3B in hexadecimal is 0010101000111011

Simple!

1) Convert the following binary number in to denary: 01100110

2) Convert the following hexadecimal number in to denary: E7