Data Representation and Number Systems
What you must know
Computers store data as binary (base 2). Be able to convert between binary, denary and hexadecimal, and explain why hexadecimal is used (compact, easy to read). Understand bits and bytes, character sets (ASCII, Unicode), image representation (pixels, resolution, colour depth), sound (sampling rate, bit depth) and file size calculations. Know the difference between analogue and digital data and the terms overflow and sign bit for negative numbers.
Traps candidates fall into
- Forgetting place values double leftwards: 128, 64, 32, 16, 8, 4, 2, 1 for one byte.
- Mixing bits and bytes when calculating file size - divide by 8 to convert bits to bytes.
- Confusing resolution (pixels) with colour depth (bits per pixel).
- Assuming higher sampling rate alone improves quality - bit depth matters too.
- Writing hexadecimal digits wrongly (A=10 … F=15).
Rule of thumb
Image file size (bits) = width × height × colour depth. Sound file size (bits) = sampling rate × bit depth × seconds × channels.
Worked example
A 200×100 pixel image at 8-bit colour: 200 × 100 × 8 = 160,000 bits = 20,000 bytes ≈ 19.5 KB. Convert denary 13 to binary: 8+4+1 = 1101. Convert 1101 to hex: group as 1101 = D.