# 1.1 Data Representation

# Lesson resources

In the data representation topic students will study the use of binary and hexadecimal number systems. This includes their roles in computing systems, such as the use of hexadecimal in colour definitions (such as in HTML and CSS). The final part of section 1.1 studies different ways data can be represented and interpreted, covering common file formats for images and sound.

Note: CIE have made some minor changes to this section of the syllabus for the 2016 examinations: students will need to convert binary numbers to decimal numbers, and vice versa (for positive numbers only).

# 1.1.1 Binary systems

### Binary Tetris

Binary Tetris is a flash game designed to help teach students the binary number system. Players must flip bits to achieve the required number, or add up the bits to calculate the number being represented. I'd recommend asking students to turn their sound off before starting this!

*Updated: 2015-04-07*

### Binary conversion activities

These two worksheets help students with decimal to binary conversion and vice versa. The activities were created by Gary Kacmarcik at the Computer Science & Engineering for K-12 site and are licensed under the Creative Commons Attribution-Share Alike 3.0 license.

*Updated: 2015-04-15*

### Lesson - Data representation - binary

This download contains all lesson resources necessary to teach students binary. It includes explanations of the system and lesson activities.

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

*Updated: 2017-10-15*

### Counting in binary

This handy PDF serves as a good summary sheet for students learning to count in binary. It covers decimal numbers from 0 to 63 (5 bits). It is good for GCSE and younger students, although it can be useful for older students too.

The sheet was created by Gary Kacmarcik at the excellent cse4k12 site and is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported License.

*Updated: 2017-10-17*

### 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.

*Updated: 2017-10-24*

# 1.1.2 Hexadecimal

### Hexadecimal-binary matching game

This is a fun little matching pairs style game in which players must match decimal numbers with their hexadecimal equivalents. A good way of testing students' ability to quickly perform mental conversions. Click here to play.

*Updated: 2017-11-05*

### Binary to hexadecimal

A worksheet that explains the "divide into groups of 4" method of converting binary numbers to hexadecimal numbers.

This was created by Gary Kacmarcik at the Computer Science & Engineering for K-12 site - an excellent site which I recommend you visit. They are licensed under the Creative Commons Attribution-Share Alike 3.0 license.

*Updated: 2015-04-16*

### 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.

*Updated: 2015-06-03*

### Lesson - Data representation - hexadecimal

This download contains all lesson resources necessary to teach students base 16 (hexadecimal). It includes PowerPoint presentations that cover the number system and converting to denary and binary. There are also some nice hex table handouts for students who may be struggling to grasp the concepts. how sound is represented in binary.

This lesson is one of the many excellent resources provided under CC-NC-SA by Mr Colley. I've added PDF versions of the .pub versions found in the original download, for those who don't have Microsoft Publisher.

*Updated: 2017-10-15*

### Counting in hex

Similar to the binary sheet, this handy document covers decimal numbers 0 to 63. It is useful for teaching students who are new to binary, or as a quick recap for those revising it. The sheet was created by Gary Kacmarcik at the excellent cse4k12 site and is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported License.

*Updated: 2017-10-17*

### Binary and Hexadecimal starter activities

Two lesson starter, plenary, or homework activities are the binary crossword and the matching quiz. They test students' ability to read binary and hexadecimal, and convert between these systems and denary.

*Updated: 2017-10-17*

# 1.1.3 Data storage

### Image Representation - Flash activity

This Flash activity lets students draw a simple bitmap image and represents it using a simple run-length encoding (RLE) algorithm in real time. Students can also important text representations of the compressed data and the application will draw the corresponding image. The web page is not in English but the application is still perfectly usable.

*Updated: 2015-04-15*

### Image, audio, and text compression

This very comprehensive page from the Computer Science Field Guide has extensive but clear notes on lossless and lossy compression. The page is well written and designed for a high school audience, with easy to understand examples, video, and even interactive sections. There are also extension "Extra for Experts" sections. The page covers image compression, audio compression, and text compression.

*Updated: 2015-04-16*

### Parity and Checksums activity

The card flip 'magic' game is a great idea from Computer Science Unplugged. The teacher sets up a grid of black/white cards and asks students to turn over one card without the teacher seeing. Using parity rules, the teacher is able to 'magically' determine which card the students turned over. This is a really fun game which demonstrates how simple techniques like odd/even partity can be used to solve significant problems.

The Computer Science Unplugged page has a range of support material: instructions for teachers, videos of the activity being performed, and a PDF download with extension activities and details about check digits in ISBNs.

*Updated: 2015-05-02*

### 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.

*Updated: 2017-10-15*

### 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.

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

*Updated: 2019-03-19*

### 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).

*Updated: 2017-10-17*

### Run Length Compression (RLE) interactive

This activity shows how a computer would represent a simple image when using Run Length Compression (RLE). Students can alter the image to see how the compression data would change. This is a good resource for helping students understand how lossless compression does not always result in significant size reduction.

*Updated: 2017-10-24*

### JPEG Compression comparison

A simple interactive that compares a highly compressed JPEG image with a less compressed image. A slide lets you view different parts of the image. JPEG banding is particularly visible in the sky but less so in other areas - the reasons for this make for interesting classroom discussions.

*Updated: 2017-10-24*

### 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).

*Updated: 2017-10-24*