1. Which hexadecimal digit equals decimal 15?
- E
- F
- A
Check the answer and reasoning
F
Hexadecimal uses A through F for decimal 10 through 15.
CS / IGCSE
Data representation and compression
Binary and hexadecimal encode numbers; characters, bitmap images and sampled sound use agreed formats. Resolution, colour depth, sample rate and sample resolution affect storage and quality.
Learning objectives
- Explain data representation and compression using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Binary and hexadecimal encode numbers; characters, bitmap images and sampled sound use agreed formats. Resolution, colour depth, sample rate and sample resolution affect storage and quality.
Lossless compression permits exact reconstruction. Lossy methods discard selected information and may suit media, but are unsuitable when every original bit must be recovered.
Equations and relationships
bitmap bits = width × height × bits per pixel
Uncompressed pixel data only; excludes headers and metadata.
Worked example
A 10×10 monochrome image uses 1 bit per pixel. How many pixel bits?
Follow the solution
10×10×1=100 bits before headers or padding.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Use the prediction activity below; a local model appears only where it supports this topic.
Check your understanding
2. A 10×10 monochrome image uses 1 bit per pixel. How many pixel bits?
- 10
- 100 bytes
- 100
Check the answer and reasoning
100
10×10×1=100 bits before headers or padding.
3. Which compression must preserve program source exactly?
- Lossless
- Lossy
- Either always
Check the answer and reasoning
Lossless
A changed character may change program behaviour, so exact reconstruction is necessary.