How do you convert denary to binary and hexadecimal?

To convert denary to binary, repeatedly divide by 2 and record remainders from bottom to top. For example, 13 in binary is 1101. To convert denary to hexadecimal, divide by 16 and record remainders (10=A, 11=B, etc.). For 13, it's D. For larger numbers, convert to binary first, then group into 4-bit nibbles to get hex.

What is the difference between ASCII and Unicode?

ASCII uses 7 bits (or 8 bits in extended ASCII) to represent 128 (or 256) characters, mainly English letters, digits, and symbols. Unicode uses up to 32 bits per character, allowing over a million characters from all world languages, emojis, and special symbols. UTF-8 is a common encoding that uses 1-4 bytes per character, backward-compatible with ASCII.

How do you calculate the file size of a bitmap image?

File size (in bits) = width × height × colour depth. Then divide by 8 to get bytes. For example, a 1024×768 image with 24-bit colour depth: 1024×768×24 = 18,874,368 bits ÷ 8 = 2,359,296 bytes ≈ 2.25 MB. Remember that metadata (like header) adds extra bytes, but exam questions usually ignore that.

What is the Nyquist theorem and why is it important?

The Nyquist theorem states that to accurately reproduce a sound wave, the sampling rate must be at least twice the highest frequency present. For example, human hearing up to 20 kHz requires a sampling rate of at least 40 kHz (CD quality uses 44.1 kHz). If you sample below this, aliasing occurs, causing distortion.

How do you represent negative numbers in binary?

There are several methods: sign-magnitude (first bit is sign, rest is magnitude), one's complement (flip all bits), and two's complement (flip bits and add 1). Two's complement is most common because it simplifies arithmetic. For example, -5 in 8-bit two's complement: 5 = 00000101, flip to 11111010, add 1 → 11111011.

What is normalisation in floating-point representation?

Normalisation adjusts the mantissa so that it has no leading zeros (for positive numbers) or leading ones (for negative numbers in two's complement). This maximises precision. For example, 0.00101 × 2^3 becomes 1.01 × 2^1 after normalisation. The exponent is adjusted accordingly. In exams, you may be asked to normalise a given floating-point number.

Fundamentals of data representation

AQA

A-Level

This topic covers the fundamental principles of how data is represented within a computer system. It encompasses number systems, units of information, binary arithmetic, character coding, and the digital representation of images, sound, and other data types including compression and encryption.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

Topic Overview

Fundamentals of data representation is a core topic in AQA A-Level Computer Science that explores how data is stored, interpreted, and manipulated inside a computer. You'll learn about binary, hexadecimal, and how different data types—like integers, characters, images, and sound—are encoded. This topic is essential because it underpins everything from memory addressing to file formats, and it's a foundation for more advanced topics like data compression and encryption.

Understanding data representation is not just about memorising conversion methods; it's about grasping why computers use binary and how trade-offs (like range vs. precision) affect real-world systems. For example, you'll see how floating-point numbers can represent very large or small values but at the cost of accuracy. This knowledge is directly tested in exams through calculations, explanations, and comparisons of different representation schemes.

This topic fits into the wider subject by linking to computer architecture (how data moves through registers and buses), networking (packet structures), and programming (data types and type conversion). Mastering it will give you confidence in handling binary arithmetic, understanding error detection, and appreciating the limitations of digital storage.

Key Concepts

Core ideas you must understand for this topic

→Binary and hexadecimal conversions: Be able to convert between denary, binary, and hexadecimal fluently, including binary-coded decimal (BCD) and two's complement for negative numbers.
→Character encoding: Understand ASCII (7-bit and extended 8-bit) and Unicode (UTF-8, UTF-16), including why Unicode is needed for global text representation.
→Bitmap images: Know how resolution, colour depth, and metadata affect file size. Be able to calculate file size using: (width × height × colour depth) / 8 (in bytes).
→Sound representation: Understand sampling rate, bit depth, and the Nyquist theorem. Be able to calculate file size: sampling rate × bit depth × duration × number of channels.
→Floating-point representation: Know the structure (sign, exponent, mantissa) and how to normalise a floating-point number. Understand the trade-off between range and precision.

What You Need to Demonstrate

Key skills and knowledge for this topic

Conversion between decimal, binary, and hexadecimal number bases.
Understanding of binary prefixes (kibi, mebi, gibi, tebi) vs decimal prefixes (kilo, mega, giga, tera).
Two's complement representation for signed integers.
Fixed point and floating point representation of fractional numbers.
Calculation of storage requirements for bitmapped images and sound files.
Understanding of lossless vs lossy compression techniques.
Application of Caesar and Vernam ciphers for encryption.

Marking Points

Key points examiners look for in your answers

Conversion between decimal, binary, and hexadecimal number bases.
Understanding of binary prefixes (kibi, mebi, gibi, tebi) vs decimal prefixes (kilo, mega, giga, tera).
Two's complement representation for signed integers.
Fixed point and floating point representation of fractional numbers.
Calculation of storage requirements for bitmapped images and sound files.
Understanding of lossless vs lossy compression techniques.
Application of Caesar and Vernam ciphers for encryption.

Examiner Tips

Expert advice for maximising your marks

💡Always show your working for number base conversions to gain method marks.
💡Ensure you can clearly distinguish between the character code of a digit and its pure binary value.
💡Practice calculating the range of values for a given number of bits using two's complement.
💡Be prepared to explain why Unicode was introduced compared to ASCII.
💡Memorize the definitions of lossless and lossy compression and be ready to provide examples of each.
💡Always show your working in binary/hexadecimal conversions. Even if your final answer is wrong, you can get method marks. Use a systematic approach like dividing by 16 for hex or using place values.
💡When calculating file sizes, check units carefully. Questions often ask for answers in bytes, kilobytes, or megabytes. Remember: 1 KB = 1024 bytes, 1 MB = 1024 KB. Don't forget to divide by 8 when converting bits to bytes.
💡For floating-point questions, normalise the mantissa so it starts with 0.1 for positive numbers or 1.0 for negative numbers (in two's complement). This maximises precision. Also, remember that the exponent is usually stored in excess-N notation (e.g., excess-127 for 8-bit exponent).

Common Mistakes

Pitfalls to avoid in your exam answers

Confusing binary prefixes (powers of 2) with decimal prefixes (powers of 10).
Incorrectly performing two's complement conversion for negative numbers.
Failing to account for metadata when calculating image storage requirements.
Misunderstanding the difference between bit rate and baud rate.
Confusing the roles of ADC and DAC.
Misconception: 'A higher sampling rate always means better sound quality.' Correction: While a higher sampling rate captures more detail, the Nyquist theorem states you only need twice the highest frequency. Beyond that, there's no audible improvement, but file size increases.
Misconception: 'Colour depth is the number of colours in an image.' Correction: Colour depth is the number of bits used per pixel, so 8-bit colour depth allows 2^8 = 256 colours. It's not the number of colours directly, but the number of bits.
Misconception: 'Two's complement is just for negative numbers.' Correction: Two's complement is a way to represent signed integers; it also makes subtraction easier by using addition. The most significant bit indicates sign (0 = positive, 1 = negative).

Frequently Asked Questions

Common questions students ask about this topic

Before You Start

Prior knowledge that will help with this topic

•Basic understanding of number systems (denary, binary) from GCSE Computer Science.
•Familiarity with powers of 2 and simple arithmetic (addition, subtraction) in binary.
•Basic knowledge of how computers store data (bits, bytes) is helpful.

Likely Command Words

How questions on this topic are typically asked

Convert

Calculate

Describe

Explain

Define

Compare

Ready to test yourself?

Practice questions tailored to this topic

Fundamentals of data representation

Topic Overview

Key Concepts

What You Need to Demonstrate

Marking Points

Examiner Tips

Common Mistakes

Frequently Asked Questions

Before You Start

Likely Command Words

Ready to test yourself?

Related Topics in AQA A-Level Computer Science

Big Data

Consequences of uses of computing

Fundamentals of algorithms

Fundamentals of communication and networking

Topic Synopsis

Key Concepts & Core Principles

Exam Tips & Revision Strategies

Common Misconceptions & Mistakes to Avoid

Examiner Marking Points

Fundamentals of data representation

Topic Overview

Key Concepts

What You Need to Demonstrate

Marking Points

Examiner Tips

Common Mistakes

Frequently Asked Questions

How do you convert denary to binary and hexadecimal?

What is the difference between ASCII and Unicode?

How do you calculate the file size of a bitmap image?

What is the Nyquist theorem and why is it important?

How do you represent negative numbers in binary?

What is normalisation in floating-point representation?

Before You Start

Likely Command Words

Ready to test yourself?

Related Topics in AQA A-Level Computer Science

Big Data

Consequences of uses of computing

Fundamentals of algorithms

Fundamentals of communication and networking