# Information representation

> CIE A-Level Computer Science · CIE 9618 A-Level
> Source: https://www.owlsprep.com/study/cie-9618-u1-overview/
> Weight: n/a

This unit explores how all types of digital data (numbers, text, images, sound) are represented as binary for computer storage and processing, forming the foundational knowledge for all computer science topics.

**Prerequisites:** No prior specialized computer knowledge is required

## Learning objectives

- Understand that all types of digital data are represented as binary sequences in computer systems
- Convert between different number bases and binary formats for all common data types
- Calculate file sizes for text, images and audio based on encoding parameters
- Compare and contrast lossy and lossless data compression techniques and their use cases

## Unit at a glance

This unit follows a logical, progressive learning arc: we start with core number system concepts, then move to encoding for different data types, and end with techniques to reduce data size for storage and transmission. The core theme here is simple: all data that computers process is ultimately just sequences of 0s and 1s.

Each sub-topic builds directly on the previous one: understanding number bases is required to work with binary integer representation, which in turn supports understanding real number and multimedia encoding. Mastering these fundamentals will make every other topic in the course easier.

Below are all sub-topics in this unit:
- [Number bases](https://www.owlsprep.com/study/cie-9618-u1-number-bases/) — Learn to convert between binary, decimal, and hexadecimal number systems.
- [Binary representation of integers](https://www.owlsprep.com/study/cie-9618-u1-binary-representation-of-integers/) — Explore unsigned, two's complement, and binary arithmetic for whole numbers.
- [Binary representation of real numbers](https://www.owlsprep.com/study/cie-9618-u1-binary-representation-of-real-numbers/) — Understand fixed-point and floating-point binary for non-integer values.
- [Character encoding](https://www.owlsprep.com/study/cie-9618-u1-character-encoding/) — Learn how text is encoded using standards like ASCII and Unicode.
- [Binary representation of images](https://www.owlsprep.com/study/cie-9618-u1-binary-representation-of-images/) — Understand bitmaps, resolution, colour depth, and calculate image file size.
- [Binary representation of sound](https://www.owlsprep.com/study/cie-9618-u1-binary-representation-of-sound/) — Learn how analogue sound is digitised and calculate audio file size.
- [Data compression](https://www.owlsprep.com/study/cie-9618-u1-data-compression/) — Compare lossy and lossless compression and their practical applications.

## Common pitfalls

- **Wrong:** Confusing colour depth for images with sample rate for sound
  - Why it fails: Mixing up these parameters leads to frequent errors in file size calculations
  - Correct: Remember: bit/colour depth describes bits per sample/pixel; sample rate only applies to audio sampling frequency
- **Wrong:** Assuming all real numbers can be stored exactly as binary floating-point
  - Why it fails: Students often forget that limited bit size creates rounding errors for many values
  - Correct: Recognise that floating-point binary only stores approximations of most real numbers
- **Wrong:** Converting hexadecimal to decimal first when converting to binary
  - Why it fails: This extra step introduces unnecessary calculation errors
  - Correct: Convert each hex digit directly to a 4-bit binary sequence for fast, accurate conversion

## Cheatsheet

| Concept / Formula | Description |
| --- | --- |
| Image file size | $\text{Size (bits)} = \text{width} \times \text{height} \times \text{colour depth}$ |
| Sound file size | $\text{Size (bits)} = \text{sample rate} \times \text{duration} \times \text{sample bit depth}$ |
| 1 byte | 8 bits |
| Two's complement negative | Flip all bits, add 1 to the result |
| Hex to binary | 1 hex digit = 4 binary digits |
| Lossless compression | Original 100% of data can be reconstructed |
| Lossy compression | Permanently removes data to achieve much smaller file sizes |

## What's next

We recommend working through the sub-topics in order, as each builds on concepts from the previous topics. Start with the first sub-topic, Number Bases, to master the core fundamentals needed for all later topics in this unit. Once you complete all sub-topics here, you can move on to the next core unit for CIE 9618: Communication and Internet Technologies.

- [Number bases](https://www.owlsprep.com/study/cie-9618-u1-number-bases/)
- [Unit 2: Communication and Internet Technologies Overview](https://www.owlsprep.com/study/cie-9618-u2-overview/)
- [Binary representation of integers](https://www.owlsprep.com/study/cie-9618-u1-binary-representation-of-integers/)

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