Fundamentals of data representation — AQA A-Level Computer Science

Fundamentals of data representation covers how computers store and interpret data using binary, including number systems (binary, denary, hexadecimal), character encoding (ASCII, Unicode), images (bitmap, vector), sound (sampling), and compression. Understanding these concepts is essential for AQA A-Level Computer Science as they underpin all data processing and storage.

Fundamentals of data representation is a core topic in AQA A-Level Computer Science that explains how all data, from numbers to text, images, and sound, is stored and processed by computers. It begins with the binary number system, which is the foundation of all computing, and extends to hexadecimal as a shorthand for binary. You will learn how to convert between number bases and perform binary arithmetic, which is essential for understanding how processors work.

Beyond numbers, this topic covers character encoding systems like ASCII and Unicode, which allow text to be represented digitally. You will also explore how images are stored as bitmaps or vectors, and how sound is digitised through sampling. Understanding these concepts is crucial for calculating file sizes, which is a common exam question, and for appreciating the trade-offs between quality and storage space.

Finally, data compression techniques, both lossy and lossless, are introduced to show how files can be reduced in size for efficient storage and transmission. This topic is not only examinable in its own right but also underpins many other areas of the specification, such as data structures, networking, and the internet. Mastering it gives you a solid foundation for the rest of the course.

• →Binary, denary, and hexadecimal number systems and conversions between them.
• →Binary arithmetic: addition, subtraction, and shifts (logical and arithmetic).
• →Character encoding: ASCII (7-bit) and Unicode (variable length, e.g., UTF-8).
• →Bitmap images: resolution, colour depth, and file size calculation.
• →Vector graphics: primitives, attributes, and advantages over bitmaps.
• →Sound representation: sampling, sample rate, bit depth, and file size calculation.
• →Compression: lossy vs lossless, and common algorithms like run-length encoding (RLE).

• Award credit for correctly identifying the sign bit appropriate to the number.
• Award credit for accurate conversion of the mantissa to a normalised form.
• Award credit for applying the correct exponent bias and storing the exponent in biased form.
• Award credit for recognising and handling edge cases such as zero, denormalised numbers, infinity, and NaN.

• 💡Always begin by identifying the sign bit before proceeding with conversion.
• 💡Memorise the exponent bias values for single (127) and double (1023) precision.
• 💡Clearly show intermediate steps including normalisation and bias application in your working.
• 💡Check for special representations such as all-zeros or all-ones in exponent fields to avoid common pitfalls.
• 💡Always show your working in calculations, especially for file size questions, as method marks are awarded even if the final answer is wrong.
• 💡Use the correct units: bits, bytes, KiB, MiB, etc. Know the difference between decimal (MB) and binary (MiB) multiples.
• 💡When comparing lossy and lossless compression, always mention the trade-off between file size and quality, and give a specific example (e.g., JPEG vs PNG).

• Omitting the exponent bias when converting to stored format.
• Failing to normalise the mantissa correctly, leaving leading zeros.
• Confusing the bit allocation between single and double precision fields.
• Assuming floating point arithmetic is exact, neglecting rounding errors.
• Misconception: 'Hexadecimal is a different type of data.' Correction: Hexadecimal is just a different way of representing binary numbers; it is not a separate data type.
• Misconception: 'Higher sample rate always means better quality sound.' Correction: While higher sample rate improves frequency capture, the bit depth also affects dynamic range; both must be considered.
• Misconception: 'Vector images are always smaller than bitmap images.' Correction: Vector images are resolution-independent and can be smaller for simple graphics, but complex vector images may be larger than a simple bitmap.

1. 1Week 1, Days 1-2: Revise number systems – practice converting between binary, denary, and hexadecimal. Use flashcards for quick recall.
2. 2Week 1, Days 3-4: Focus on binary arithmetic and shifts. Work through past paper questions on addition and logical shifts.
3. 3Week 1, Days 5-6: Study character encoding (ASCII and Unicode) and image representation. Create a summary table of key terms.
4. 4Week 2, Days 1-2: Learn about sound representation and file size calculations. Practice with different sample rates and bit depths.
5. 5Week 2, Days 3-4: Understand compression techniques. Compare lossy and lossless with examples.
6. 6Week 2, Days 5-7: Consolidate by doing mixed exam questions under timed conditions. Review mark schemes to understand command words.

• 📋Multiple-choice questions on conversions or definitions (e.g., 'What is the hexadecimal representation of 1111 0010?').
• 📋Short-answer questions asking to explain a concept, such as 'Explain the difference between lossy and lossless compression.'
• 📋Calculation questions requiring file size or binary arithmetic, often with 'Show your working'.
• 📋Extended response (6-mark) questions evaluating the suitability of a representation method for a given scenario, e.g., 'Evaluate the use of vector graphics for a company logo.'