data representation computer science revision

Teach Computer Science

Data Representation

Topics include binary, decimal, and hexadecimal numbers, and the conversions between them.

Computational Thinking

We may think that computers “think” and that they outsmart humans “just like that”. However that’s not the case, computers do exactly what we humans tell them to do, or better said, what we program them to do. Once programmed a computer can only execute problems and produce solutions more efficiently than humans. Computational thinking …

For Data Units, candidates should be able to: define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte understand that data needs to be converted into a binary format to be processed by a computer. Data units in computer systems Bit This is a single unit of memory and can only store 2 possible binary …

Image Representation

For Image Representation, candidates should be able to: explain the representation of an image as a series of pixels represented in binary explain the need for metadata to be included in the file such as height, width and colour depth discuss the effect of colour depth and resolution on the size of an image file. …

Sound Representation

For Sound Representation, candidates should be able to: explain how sound can be sampled and stored in digital form explain how sampling intervals and other considerations affect the size of a sound file and the quality of its playback. How can sound be sampled and stored in digital form? A microphone converts sound waves into …

Number Systems

For Number Systems, candidates should be able to: convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa add two 8-bit binary integers and explain overflow errors which may occur convert positive denary whole numbers (0-255) into 2-digit hexadecimal numbers and vice versa convert between binary and hexadecimal equivalents of the same …

Character Sets

Candidates should be able to: explain the use of binary codes to represent characters explain the term character set describe with examples (for example ASCII and Unicode) the relationship between the number of bits per character in a character set and the number of characters which can be represented. How are binary codes used to …

Computer Instructions

In regards to computer instructions, candidates should be able to: explain how instructions are coded as bit patterns explain how the computer distinguishes between instructions and data. Computer Instructions: How are program instructions coded? Machine code instructions are binary numbers and are coded as bit patterns, for example, a 16 bit machine code instruction could …

Converting Decimal to Binary

Converting Decimal to Binary: The Decimal Numbering System Decimal is a base 10 numbering Binary Numbering System Binary is a base 2 numbering system that is made up of two numbers: 0 and 1.  0 means OFF and 1 means ON.  The computer’s central processing unit (CPU) only recognizes these two states – ON and …

Converting Hexadecimal to Decimal

Hexadecimal Numbering System Hexadecimal is a base 16 numbering system that is made up of 16 digits: 0 – 9 and six more, which is A through F. Uses of Hexadecimal The hexadecimal numbering system is often used by programmers to simplify the binary numbering system.  Since 16 is equivalent to 24, there is a …

Converting Hexadecimal to Binary

Converting Hexadecimal to Binary Hexadecimal Numbering System Hexadecimal is a base 16 numbering system which is made up of 16 digits: 0 – 9 and six more, which is A through F. Uses of Hexadecimal Hexadecimal numbering system is often used by programmers to simplify the binary numbering system.  Since 16 is equivalent to 24, …

Converting Decimal to Hexadecimal

Converting Decimal to Hexadecimal: The Decimal Numbering System Decimal is a base 10 numbering system that is made up of 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.  It is the most commonly used numbering system.  The reason behind that is convenience.  We have 10 fingers that we use for …

Uses of Hexadecimal

Hexadecimal Numbering System Hexadecimal is a base 16 numbering system that is made up of 16 digits: 0 – 9 and six more, which is A through F.The table below shows how the hexadecimal system works and its equivalent decimal number: Hexadecimal Decimal   Hexadecimal Decimal 0 0   11 = (1 x 16) + …

Converting Binary to Hexadecimal

Binary Numbering System Binary is a base 2 numbering system which is made up of two numbers: 0 and 1.  0 means OFF and 1 means ON.  The computer’s central processing unit (CPU) only recognizes these two states – ON and OFF.  It is the foundation for all binary code, which is used in computer …

Converting Binary to Decimal

Converting Binary to Decimal: The Binary Numbering System Binary is a base 2 numbering system that is made up of two numbers: 0 and 1.  0 means OFF and 1 means ON.  The computer’s central processing unit (CPU) only recognizes these two states – ON and OFF.  It is the foundation for all binary code, …

Bitmap Image and Colour Depth Quiz

Further Readings: Bitmap Color depth

Colour Depth Gap Fill Exercise

Further Readings: Color depth

Data Units Gap Fill Exercise

Further Readings: Units of information

Data Units Multi-Choice Quiz

Colour mapping and direct colour.

Pupil Resources – EXTENSION TOPIC What is the difference between Colour Mapping and Direct Colour? Colour mapping With low colour depths (up to 8-bit) it is practical to map every colour to a binary code. 1-bit colour mapping – (2 colours) monochrome, often black and white. 2-bit colour mapping – (4 colours) CGA – used …

Instructions

Candidates should be able to: explain how instructions are coded as bit patterns explain how the computer distinguishes between instructions and data. How are program instructions coded? Machine code instructions are binary numbers and are coded as bit patterns, for example, a 16-bit machine code instruction could be coded as 001010101101001011. In machine code, the …

Sound – Quality, Size & Storing Solutions

Candidates should be able to: How can sound be sampled and stored in digital form? A microphone converts sound waves into voltage changes. If a microphone is plugged into a sound card then the voltage can be sampled at regular intervals (the sample rate) and each value converted into a binary number. This digitising of …

On a mission to end educational inequality for young people everywhere.

ZNotes Education Limited is incorporated and registered in England and Wales, under Registration number: 12520980 whose Registered office is at: Docklands Lodge Business Centre, 244 Poplar High Street, London, E14 0BB. “ZNotes” and the ZNotes logo are trademarks of ZNotes Education Limited (registration UK00003478331).

Computing, Computer Science, and Information Technology resources for GCSE, IGCSE, IB, and GCE A-Level

Teach computing.

Revision notes, activities, lesson plans, teaching ideas, and other resources for GCSE, A-Level, and IB Computer Science teachers and students.

Examples of Local Cryptocurrencies

Digital Money for Local Communities covers three examples of country-wide c...

Hash function A hash function takes arbitrary sized input data (e.g. a fil...

Cryptocurrencies vs regular currencies

What is Bitcoin and How Does it Work? is a high level overview of the Bitco...

Examples of Cryptocurrencies

Bitcoin is by far the most well known cryptocurrency. The Bitcoin website w...

Practice paper 3 exam questions

One of the drawbacks of the yearly case study is that there are no past p...

Emergency Management System Explainer Video

This short video gives an overview of some EMIS features. It includes many ...

Geographic Information Systems (GIS)

For some functionality, an EMIS may also be connected to a GIS (Geographic ...

Programming languages - from Scratch to machine code

The CS Field Guide has a very comprehensive guide to different types of pro...

Assembly language simulators

There are several assembly language simulators available for use online. Si...

3.2 Data Representation

Lesson resources.

3.2.1 Understand how computers encode characters

Characters, Symbols and the Unicode Miracle

Characters, Symbols and the Unicode Miracle explains how ASCII arose from the need to communicate data in a compatible manner between computer systems, and the problems that arise with this apparently simple task. It then discusses the creation of the Unicode system.

Unicode Table

Unicode table is a nice scrollable web page which lists all of the unicode characters. The title and a brief description of each section is presented while you scroll. This page is useful for helping students realise just how many different characters need to be represented by computer systems, and the problems this would cause with a standard like Unicode.

Lesson - Data representation - text

This download contains all lesson resources necessary to teach students how ASCII is used to representation text in a computer system. The download includes several fun activities where students have to uncover 'secret' messages using their understanding of binary and ASCII. There are different worksheets for students of different levels.

This lesson is one of the many excellent resources provided under CC-NC-SA by Mr Colley .

Text representation worksheets

Gary Kacmarcik at the excellent cse4k12 site has created a set of sheets for a lesson activity on text representation. The first sheet is an ASCII table and the other two sheets ask students to encode a text message and decode a message respectively. Note that students are expected to encode and decode using hexadecimal rather than binary (although they could easily be asked to use binary instead).

CS Field Guide - Data representation

CS Field Guide is an absolutely fantastic resource filled with material that is well written, clear,and accessible. Each section comes with highlighted key points, extension points, and even interactives to help understand the concepts. The interactives are excellent as teaching resources (many of them are linked here), while the notes themselves make excellent revision resources - particularly for GCSE.

This section covers all aspects of data representation - numbers, text, images, and instructions.

Spot the mistakes exercises

The slides in this presentation present basic 'facts' about computing fundamentals: input, output, binary, hexadecimal, and data representation. Each slide contains a number of basic mistakes (highlighted on the following slide). Students simply need to read through the text, spot the mistakes - and correct them. These activities work well as quick lesson starters or plenaries to check understanding.

Representing Text in Binary

This video clearly explains the two main ways of representing text in binary - ASCII and Unicode, plus the advantages and disadvantages of each. The limitations of ASCII, which led to the development of Unicode, are also clearly explained.

3.2.2 Understand how bitmap images are represented

B&W Pixelation

There are three versions of this excellent applet, designed for the University of Chicago's Introduction to Computer Science course to help students understand image representation in computers. In the first version , students simply enter binary digits to represent black or white pixels. In the second version students are introduced to the concept of a very basic file format, with the first two bytes representing the image dimensions. Students can also enter the data in binary or hexadecimal. The final version is even more complex, allowing students to specify the colour depth of the image, and requiring them to enter the appropriate number of bits for each pixel.

Overall this site is an excellent introduction to data storage and image representation, and makes a complex subject quite entertaining.

Bitmaps Activity

These activities involve students converting between bitmap images and numeric representations of them in binary and hexadecimal. This is a great way to see how relatively complex information can still be represented as binary. You can download the worksheet with guidance and an additional blank worksheet .

The activities were created by Gary Kacmarcik at the Computer Science & Engineering for K-12 site, which contains an excellent range of activities. They are licensed under the Creative Commons Attribution-Share Alike 3.0 Unported License .

Hexadecimal colour codes

Section 5.5.2 of this much bigger page on data representation covers the uses of hexadecimal numbers to represent colours in images. It explains the correlation between the hexadecimal digits and the number of bits available, and the effect the bit depth has on the appearance of the image. The excellent interactives really make the concept come alive and visually highlight these differences to students. A highly recommended resource.

Pixel colour code viewer

This pixel viewer can help students understand how images are created and represented. Zooming right into the image reveals the RGB values of each pixel, shown in decimal.

Image bit depth comparison

This is a great little resource for demonstrating the effect of bit depth on images. The same image is displayed at various colour depths from 24 bit to 2 bit. It is also possible to upload your own images and have them displayed in the same way.

RGB Colour matcher

A colour matching tool that asks users to play with the RGB sliders to match a specified colour. This is a great way to help students understand how red, green, and blue are mixed to produce colours. What makes this colour matcher stand out is that it also represents the colour values in binary (24 bit) at the bottom. This makes it a useful companion for tools like Pixelization (see elsewhere on this page).

3.2.3 Understand how analogue data is represented in binary

Lesson - Data representation - sound

This download contains all lesson resources necessary to teach students how sound is represented in binary. It includes PowerPoint presentations, worksheets, and sample sounds for students to play.

3.2.4 Understand the limitations of binary representation of data

Data Representation: Storing Sound

Basics of sound representation.

• Sound is a form of energy that we perceive through our ears.
• In computing, sound is represented digitally as binary data .
• Sound can be stored in several formats, with the most common ones being .wav, .mp3, .ogg, etc.

Analogue and Digital Sound

• Analogue sound is how humans hear it in nature, continuous and fluid.
• Computers, however, represent sound by collecting many small samples and stitching them together, this is called digital sound .

Sound Sampling

• Digital representation is done by a process known as sampling . It involves measuring the sound wave’s intensity at fixed intervals.
• The rate at which this measurement is done is called the sampling rate .
• Higher sampling rate results in better sound quality but also requires more space to store the data.

Storing Sound

• Once the sound data is sampled, it is quantized and then encoded into binary to create a digital sound file .
• In a sound file, each sampled sound is stored as a binary number representing the amplitude of the sound wave at that moment of sampling.
• Larger binary numbers yield a better representation of the original sound, but also take up more storage space.
• This space-saving versus quality trade-off is often managed by sound file compression.
• Bit depth is the number of bits used for each audio sample.
• Greater bit depth allows for a wider dynamic range and better sound quality.

Sound Compression

• To reduce the size of digital sound files, compression algorithms are used.
• Two main types of compression are: lossy compression (e.g., .mp3) and lossless compression (e.g., .flac).
• Lossy compression significantly reduces file sizes by permanently removing certain sound frequencies that are less important or less likely to be detected by human ears.
• Lossless compression reduces file sizes without any loss of quality, however, it doesn’t reduce sizes as drastically as lossy compression.

Stereo and Mono Sound

• Stereo sound uses two channels (right and left) to produce sound, giving a sense of depth and directionality. Each channel is stored and processed separately.
• Mono sound uses only one channel, making it less spatially complex than stereo sound but also less storage-intensive.

Importance of Sound Representation Knowledge

• Understanding the basics of how sound is represented and stored is essential for working with audio files in programming, sound design, and other applications. It’s also needed to understand and manage sound file storage and quality.