# 4.2 Representing data

But if all the data and computer instructions within a computer are represented by 1s and 0s, how can this limited set of conditions be used to represent, for instance, every letter of the alphabet that might be typed into a computer from a keyboard? Activity 4 showed that there are four possible combinations of 1s and 0s in a 2-bit binary code. So if you had only two bits available you could only represent four different letters, e.g. ‘a’ could be represented by 00, ‘b’ by 01, ‘c’ by 10 and ‘d’ by 11. This shows that a 2-bit binary code can only represent four items of data.

## Activity 5 (Self assessment)

Write down all the possible combinations of a 3-bit binary code and state how many items of data three bits can represent.

### Answer

The possible combinations of a 3-bit binary code are 000, 001, 010, 011, 100, 101, 110, 111. Hence the three bits can represent 8 items of data.

Interestingly, a pattern can be deduced for the relationship between the number of bits and the number of items they represent.

2 bits can represent 2 × 2 = 2

^{2}= 4 items3 bits can represent 2 × 2 × 2 = 2

^{3}= 8 items and following on with the same pattern4 bits can represent 2 × 2 × 2 × 2 = 2

^{4}= 16 items.

Study note: If you are unsure of the use of the mathematical notation 2^{2}, 2^{3} etc., you will find it helpful to refer to the Numeracy Resource below.

Click on the 'View document' link below to open the 'Numeracy resource'.

View document [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

A group of eight bits is called a **byte**, so an 8-bit binary code is 1 byte long, a 16-bit binary code is 2 bytes long and a 64-bit binary code is 8 bytes long.

## Activity 6 (Self assessment)

How many bits are there in 4 bytes?

How many items of data can be represented by 1 byte?

### Answer

Four bytes contain 4 × 8 = 32 bits.

Since one byte contains 8 bits, the number of items that can be represented by one byte is 2

^{8}= 256. (Note that if you had to work out the number of items that eight bits could represent by writing down all possible combinations of 8 bits it would be very tedious and there would be a strong possibility of making an error. Using the calculation 2^{8}= 256 is much easier way of finding the answer, as would be 2^{16}= 65 536 for the number of combinations of a 16-bit binary code.)

In general, computers that perform more complex tasks at higher speeds use a larger number of bits to represent their data and instructions. The very simple central heating controller, which only has to do a limited amount of processing, may use an 8-bit representation. More powerful computers will use 16-, 32- or 64-bit representations.

When a computer is running a program a lot of data is being passed around the various elements within the system. The data received by the input subsystem(s) must be passed to the processor in a form it can use, and the processor in turn must present data to the output subsystem(s) in the required format. Even more fundamentally, the processor must be able to recognise each instruction within the program and execute it.