## AQA Computer Science GCSE

### Data Representation – Binary Numbers

Computers are, at their heart, very complex machines which use a very simple way of storing information. It all comes down to Binary numbers – 1s and 0s.

Binary Numbers – an introduction

There are some questions to try:

#### Converting Binary to Decimal and Back Again

You need to be able to convert from binary to decimal.

Binary Numbers – converting from binary to decimal method - how to do it

Binary Numbers – converting from binary to decimal questions

And you need to be able to convert from decimal to binary as well. Which is a little harder.

Binary Numbers – converting from decimal to binary method – how to do it

Binary Numbers – converting from decimal to binary questions

There's a set of questions on paper as well:

#### Binary numbers: largest, how many and range

The exam board likes to ask questions like:

- what is the largest number that can be represented using 6 bits?
- how many binary numbers can be represented using 5 bits?
- what range of numbers can be represented using 7 bits?

These are actually really easy questions, but you need to know what to do – it's really easy to get confused.

Largest/How many/Range and how it works

If you want more detail, these guides make answering this sort of questions a piece of cake.

Finding the largest binary number in X bits

Finding the number of binary numbers in X bits

Finding the range of binary numbers in X bits

#### Why Binary?

Absolutely everything that a computer does can only be stored using binary numbers. Every single thing has to be able to be reduced down to a series of 1s and 0s to get it inside a computer of any kind.

Just think of what that means:

- every instruction that a program executes has to be stored as binary numbers. So when you type Python code it gets translated into a set of 1s and 0s so that it can be executed
- a photograph, which shows thousands of different shades of colours, ends up as 1s and 0s. Every digital photo of a work of complete artistic genius ends up as 1s and 0s
- every piece of writing has to be stored as 1s and 0s. Whether it's a quick e-mail, the complete works of William Shakespeare or today's newspaper. It all becomes 1s and 0s once you get it typed and stored electronically
- music, if it's stored digitally, ends up as 1s and 0s. The most complex, richest, dynamic music you can imagine. If it's in a computer it's just 1s and 0s

The reason for all this is that computers just can't deal with anything else. A switch can only be on or off - it can be a 1 or a 0. Nothing else.

Why Binary? – some theory which reminds you why we need to use binary.

More Complex Why Binary? – this details some of the ways in which data storage has developed over time and some other ways in which data can be stored and transferred using alternatives to switches.

#### Number Bases – a Summary

We'll come back to the idea of number bases, but this is the first step in this knowledge.

Binary and Number Bases Summary

#### Binary Revision Questions

Some sets of revision questions, dealing with all of the binary stuff, for when you need them:

Binary Revision Questions 1 – everything binary only

Binary Revision Questions 2 – binary and hex

And some other questions, some of which cover other area of unit 3.