1 Information representation
Represent numbers, text, images and sound in binary, then compare how compression changes storage and quality.
Mapped to Cambridge International AS & A Level Computer Science 9618, 2027–2029 Version 2. These original lessons and self-checks are independent study support; they are not Cambridge papers, official marks or grades. The course does not yet provide a timed four-paper simulation or a locked-down Paper 4 programming environment.
Before you begin
- Use the 2027–2029 syllabus for your exam year. AS candidates study Sections 1–12; A Level candidates study Sections 1–20. Paper 4 uses a programming language chosen from Python, Java or Visual Basic in console mode.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which unit is based on 1024 bytes?
What you will learn
- Explain the key representations, structures or processes in this syllabus section
- Apply the method to a new computer-science example
- Justify a design choice and check its limits
Numbers and text need an agreed representation
Binary place values are powers of two. Hexadecimal groups four bits per digit. BCD stores each decimal digit in a four-bit group; it is useful when decimal digits must be retained exactly, but it uses more bits than ordinary binary for many values.
For a fixed-width two's-complement integer, the most significant bit has a negative weight. With n bits the range is −2ⁿ⁻¹ to 2ⁿ⁻¹−1. Overflow occurs when a result lies outside that range; the stored bit pattern wraps and no longer represents the mathematical result.
Binary prefixes use powers of 1024: 1 KiB = 1024 bytes. Decimal prefixes use powers of 1000: 1 kB = 1000 bytes. ASCII, extended ASCII and Unicode assign codes to characters; Unicode supports a much wider range of characters.
Multimedia turns measurements into samples
A bitmap stores a colour value for each pixel. Its approximate uncompressed size is width × height × colour depth, in bits, before any header or metadata. Greater resolution or colour depth can improve detail but increases file size.
Sound is sampled at regular intervals. Approximate uncompressed size depends on sample rate × bit depth × duration × number of channels. A higher sample rate captures more frequent changes; greater bit depth gives more possible amplitude levels.
Lossless compression reconstructs the original data; lossy compression discards some information to reduce size. Run-length encoding (RLE) is effective when values repeat in sequences and can make irregular data larger.
Pause and explain
A 4-bit two's-complement value has what range?
Worked example
An image is 320 × 200 pixels at 8 bits per pixel. Estimate its uncompressed data size in bytes.
Show the worked solution
- There are 320 × 200 = 64 000 pixels.
- At 8 bits each, the data uses 512 000 bits.
- Divide by 8 to convert bits to bytes; headers and metadata are excluded.
Answer 64 000 bytes, before headers or metadata.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 1110 1011₂ to hexadecimal and explain the grouping.
Give me a hint
Group four bits from the right; convert each nibble separately.
Compare my reasoning
- The nibbles are 1110 and 1011.
- 1110₂ = 14 = E; 1011₂ = 11 = B.
- Keep the original order of the two groups.
EB₁₆.
Look for these in your work
- Correct nibble grouping
- Correct hex digits
- Order preserved
A mono sound clip lasts 12 s, sampled at 8000 samples/s and 8 bits/sample. Find its uncompressed size in bytes.
Give me a hint
Multiply duration, samples per second and bits per sample, then divide by eight.
Compare my reasoning
- Samples = 12 × 8000 = 96 000.
- Bits = 96 000 × 8 = 768 000.
- Bytes = 768 000 ÷ 8.
96 000 bytes, excluding any header.
Look for these in your work
- Sample count found
- Bit depth applied
- Bits converted to bytes
A bitmap's resolution is doubled in both dimensions while its colour depth is halved. How does its data size change?
Give me a hint
Compare the factors for pixel count and bits per pixel.
Compare my reasoning
- Doubling width and height multiplies pixel count by four.
- Halving colour depth multiplies bits per pixel by one half.
- The combined factor is 4 × 1/2.
It doubles, before headers or compression.
Look for these in your work
- Both dimensions counted
- Depth factor included
- Combined change stated
Common mistakes
- Mixing KiB (1024 bytes) with kB (1000 bytes).
- Using unsigned place values for a two's-complement value.
- Assuming lossy compression can restore discarded detail.
What can you explain now?
What does increasing bitmap colour depth do, if resolution stays constant?
Compare with the explanation
It increases the number of bits stored per pixel and the possible colours.
More bit-depth values allow finer colour representation but increase the image data size.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Which properties determine raw bitmap and sampled-sound size, and how do lossless and lossy compression differ?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.