Converting between number bases

Quick links

3.3.1

Number bases

3.3.2

Converting number bases

3.3.3

Units of information

3.3.4

Binary arithmetic

3.3.5

Character encoding

3.3.6

Representing images

3.3.7

Representing sound

3.3.8

Data compression

Syllabus content

Content   Additional Information
Understand how binary can be used to represent whole numbers.   Students must be able to represent decimal values between 0 and 255 in binary.
     
Understand how hexadecimal can be used to represent whole numbers.   Students must be able to represent decimal values between 0 and 255 in hexadecimal.
     

Be able to convert in both directions between:

  • • binary and decimal
  • • binary and hexadecimal
  • • decimal and hexadecimal.
 

The following equivalent maximum values will be used:

  • • decimal: 255
  • • binary: 1111 1111
  • • hexadecimal: FF

It is common for the first question on the paper to be a straightforward binary to decimal conversion. If you are confident then the rest of the paper may not seem to be so much of a struggle.

Exercise

There is a worksheet that you can use to help with lerning to convert between the most commonly used number bases in Computing, base 2, base 10 and base 16. (We use Octal (base 8) as well but we'll leave that for another time.)

Here is a useful website that shows how you can convert between a number of different number bases. On the other hand here is a page.

 

Finally, a number base joke! Why do programmers confuse Christmas with Halloween?

Progress

Do you feel comfortable with the various number bases used so far? Binary and Hexadecimal.

3.1 Fundamentals of algorithms

3.2 Programming

3.3 Fundamentals of data representation

3.4 Computer systems

3.5 Fundamentals of computer networks

3.6 Fundamentals of cyber security

3.7 Ethical, legal and environmental impacts of digital technology on wider society, including issues of privacy

3.8 Aspects of software development

Glossary and other links

Glossary of computing terms.

AQA 8520: The 2016 syllabus