Fundamentals of data representation — AQA A-Level Computer Science

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.

• →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.

• 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.

• 💡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).

• 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).