CAMBRIDGE COMPUTER SCIENCE TOPIC 1 DATA REPRESENTATION

DATA REPRESENTATION

DESIGNED FOR CIE GCSE EXAMINATIONS

In this section, you’ll dive into how computers handle different types of data. By the end of this topic, you’ll understand the essential building blocks that allow computers to store, process, and display everything from numbers and text to images and sounds.

You’ll start by learning about number systems like binary, denary, and hexadecimal, and how to convert between them. You’ll also discover how computers add binary numbers and how overflow errors happen when there’s more data than an 8-bit system can handle.

Next, we’ll explore how computers represent text, sound, and images in binary. You’ll see how things like character sets, sample rate, and resolution play a role in file size and quality.

Finally, you’ll learn about data storage units and compression techniques, which help make files smaller for easier storage and faster transmission.

By mastering these basics, you’ll be well-prepared to understand more complex computer science concepts later on.

TOPICS
SECTION SUMMARY
WORKBOOK

TOPIC 1 | DATA REPRESENTATION
1.1 NUMBER SYSTEMS
  ☐ 1.1.1 WHY COMPUTERS USE BINARY
☐ 1.1.2 BINARY, HEX AND CONVERTIG BETWEEN NUMBER SYSTEMS
☐ 1.1.3 BENEFITS OF HEX
  ☐ 1.1.4 BINARY ADDITION AND OVERFLOW
  ☐ 1.1.5 BINARY SHIFTS
  ☐ 1.1.6 NEGATIVE NUMBER REPRESENTATION, TWO'S COMPLEMENT
1.2 TEXT, SOUND AND IMAGES
  ☐ 1.2.1 HOW COMPUTERS REPRESENT TEX
  ☐ 1.2.2 HOW COMPUTERS REPRESENT SOUND
  ☐ 1.2.3 HOW COMPUTERS REPRESENT IMAGES
1.3 DATA STORAGE AND COMPRESSION
  ☐ 1.3.1 HOW STORAGE IS MEASURED
  ☐ 1.3.2 CALCULATING IMAGE AND SOUND FILE SIZE
  ☐ 1.3.3 PURPOSE OF COMPRESSION
  ☐ 1.3.4 LOSSY AND LOSSLESS COMPRESSION
EXTRAS
  ☐ END OF TOPIC REVIEW | COMING SOON
  ☐ TOPIC 1 KEY TERMINOLOGY
  ☐ REVISION FLIP CARDS
  ☐ TOPIC 1 ANSWERS
  ☐ TOPIC 1 TEACHER RESOURCES (CIE)

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Welcome to your quick revision of Topic 1: Data Representation. Let’s dive in and review key concepts for your IGCSE Computer Science exam. First, let’s talk about binary – the base-2 number system that’s crucial to how computers work. Computers use binary to represent all data, whether it's text, images, or sound. This is because binary is processed easily with logic gates and stored in registers. Moving on to the different number systems you’ll need to know. There’s denary, which is base-10, like the numbers we use every day; binary, which is base-2; and hexadecimal, which is base-16. You should be comfortable converting between these systems. This includes converting: Denary to binary and vice versa. Denary to hexadecimal and vice versa. Binary to hexadecimal and vice versa. Now, you may wonder why hexadecimal is even necessary. Well, hexadecimal provides a shorter, more readable way to represent binary data, especially in areas like memory addresses and color codes. It’s more human-friendly! Let’s touch on binary addition. You need to practice adding two positive 8-bit binary numbers. Just be aware of overflow: when a result goes beyond the 8-bit limit of 255, the value can’t be fully represented, and an overflow error occurs. For binary shifts, remember that a left shift effectively multiplies the number, while a right shift divides it. With each shift, zeros are added to one end, and any bits that go past the limit are lost. Finally, there’s two’s complement – a way to represent both positive and negative integers in binary. Make sure you’re comfortable converting between two’s complement binary and denary, as it’s a helpful tool for representing a range of values. Text, Sound, and Images Let’s move on to how computers represent different types of media, starting with text. Computers store text as binary, using character sets like ASCII and Unicode. ASCII is limited, but Unicode allows for a wider range of characters, supporting different languages and even emojis. However, Unicode does require more bits per character than ASCII. When it comes to sound, a computer samples a sound wave and converts it into binary. The sample rate – the number of samples taken per second – and the sample resolution – or bits per sample – both impact quality and file size. A higher sample rate or resolution gives better quality but also increases file size. For images, they’re made up of pixels that are stored in binary. Resolution is the number of pixels in the image. The higher the resolution, the clearer the image but also the larger the file. The color depth represents how many bits are used for each color. A greater color depth improves quality but, again, increases the file size. Data Storage and Compression Now, let’s quickly review data storage units. You’ve got basic units like bit and byte, but it’s also useful to know larger units like kibibyte (KiB), mebibyte (MiB), and gibibyte (GiB). Practice converting between these units – for example, there are 8 bits in a byte, and 1024 MiB in a GiB. When calculating the file size of an image or sound, you’ll use factors like resolution and color depth for images, or sample rate, resolution, and length of track for audio. Lastly, data compression is essential. Compression reduces file size, saving storage space and reducing transmission time. There are two main types: Lossy compression removes data permanently, like reducing an image’s resolution or a sound file’s quality. Lossless compression reduces file size without data loss, such as through Run-Length Encoding, where repeated data is stored more efficiently. And there you have it – a quick but thorough recap of Topic 1: Data Representation. Use this summary to reinforce your understanding, and you’ll be well-prepared for exam day. Good luck!

Read Aloud

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SECTION 1 | 1.1 NUMBER SYSTEMS
Binary System

Computers use binary (base 2) to process all data.
Data is stored in registers and manipulated using logic gates.

Number Conversions
Denary (base 10), binary (base 2), and hexadecimal (base 16) systems are key. You need to convert:

Denary to Binary and Binary to Denary.
Denary to Hexadecimal and Hexadecimal to Denary.
Binary to Hexadecimal and Hexadecimal to Binary.

Hexadecimal

Useful for simplifying binary data, as it’s more readable for humans.
Used in areas like memory addresses and colour codes.

Binary Addition & Overflow

Practice adding two 8-bit binary numbers.
Overflow occurs if the result exceeds 8 bits, typically if it surpasses the value 255.

Logical Binary Shifts

Left Shift multiplies, Right Shift divides.
Only 0s are shifted in, and bits shifted out are lost.

Two’s Complement

Allows representation of both positive and negative integers.
Understand conversion between binary and denary using two’s complement.

SECTION 2 | 1.2 TEXT SOUND AND IMAGES
Text Representation

Text is represented in binary using character sets like ASCII and Unicode.
Unicode supports more symbols and languages than ASCII, but requires more storage.

Sound Representation

Sound is converted to binary by sampling the sound wave.
Sample Rate: Number of samples per second; higher rates mean better quality and larger files.
Sample Resolution: Bits per sample; higher resolution increases accuracy and file size.

Image Representation

Images are a grid of pixels each represented in binary.
Resolution: Total pixels in an image. Higher resolution means better quality and larger files.
Colour Depth: Bits per pixel to represent colour. Higher depth improves quality but increases the file size.

SECTION 3 | 1.3 DATA STORAGE AND COMPRESSION
Data Storage Units

Common units: bit, byte, kibibyte (KiB), mebibyte (MiB), gibibyte (GiB), etc.
Practice converting between units (e.g., 8 bits in a byte, 1024 MiB in 1 GiB).

File Size Calculation

Use resolution and color depth (for images) or sample rate, resolution, and length (for audio) to calculate file sizes.

Data Compression

Reduces file sizes for less storage space and faster transmission.
Lossy Compression: Permanently removes data (e.g., reduces image resolution, and sound quality).
Lossless Compression: Compresses without data loss (e.g., Run-Length Encoding).

COMING SOON