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Computers and data representation
This topic includes the way in which computers represent data internally. This requires an understanding of the way in which the computer manipulates data using the binary number system. As this tends to be difficult for people to read, other different systems have been used. The most used is the hexadecimal system. To demonstrate understanding students need to be able to convert between the different number systems and do basic arithmetic in the binary system.
Syllabus outcome
H1.3 A student describes how the major components of a computer system store and manipulate data
This topic allows students to investigate further how the basic arithmetic processes and storage of data is performed by electronic circuitry (SDD Syllabus, p 52).
Representation of data within the computer
A computer-based system is made up of electronic circuits. These circuits carry two states, a low and a high charge. Manipulating the charges so that they can do something of use is what the computer does. The binary number system is well suited for this manipulation because it is a two state number system. It can be used as a model of the computer's circuits with a '0' representing a low charge and a '1' as a high charge. By manipulating the circuits of the computer system to behave like the binary number system, the computer is able to perform calculations, the basis of all its operation. Other number systems can be used, but the difficulty of creating more than two states makes them impractical.
Clicking on the hyperlinks below will take you to the notes and activities for the different sections of this topic.
Number systems
- binary
- decimal
- octal
- hexadecimal
- Using the base conversion Java applet
A general discussion of number systems related to computers, specifically binary, octal and hexadecimal may be viewed in http://www.mackido.com/General/Binary.html 
Character representation
Integer representation
- sign and modulus
- one's complement
- two's complement
- Practise your skills in representing negative numbers using a Java applet
Representation of fractions
Binary arithmetic
- addition
- subtraction using two's complement representation
- multiplication, shift and add
- division, shift and subtract
This work was prepared by Ellen Sheerin
All notes and activities, including the
Java applets were prepared by Mark Watson.
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