## 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.

How computers deal with numbers

Binary Numbers - binary and denary - an introduction

#### Converting Binary to Decimal and Back Again

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

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 denary 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

#### 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.

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

The slides summarise how the three numbers bases (binary, decimal and hexadcimal) work. This is probably best left until you know about all of them and might be helpful for revision.

#### 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

Here are some summary questions that you can do at this stage.