Spec & Goals 3 min
AQA Spec 3.3 · Fundamentals of data representation (whole unit)
By the end of this lesson you can:
- Revise and self-check the whole of spec 3.3, spotting your weak topics.
- Answer exam questions that span the unit, for the marks on offer.
- Make a focused revision plan that targets the topics you got wrong.
Warm-Up — command words & the paper 5 min
This is the last lesson of Unit 3. First, know the exam you are sitting.
Command words tell you what to do
Read the command word first — it sets how much to write.
| Command word | What it demands |
|---|---|
| State | A word or short phrase. No explanation. |
| Describe | Say what something is, or the steps, with detail. |
| Explain | Give reasons — the how or the why. |
| Calculate | Work out a value; always show your working. |
Key Concept — your Unit 3 spec checklist 14 min
Tick each spec point. If you cannot do one, that is a topic to revise tonight.
| Spec point | You should be able to… |
|---|---|
| Number bases | State that humans use denary (base 10), computers use binary (base 2), and hexadecimal (base 16) is a shorthand for binary. |
| Binary ↔ denary | Convert an 8-bit binary number to denary using place values (128, 64, 32, 16, 8, 4, 2, 1), and back again. |
| Hexadecimal & conversions | Convert between hex and denary, and between hex and binary, by grouping bits into nibbles (4 bits). |
| Units of information | Order bit, nibble, byte, kB, MB, GB, TB and convert between them using 1 kB = 1000 bytes. |
| Binary addition | Add two 8-bit numbers, carry correctly, and identify an overflow error when the result needs a 9th bit. |
| Binary shifts | Apply a left shift (multiplies by 2 per place) and a right shift (divides by 2 per place). |
| Character encoding | Describe ASCII (7 bits) and Unicode (more bits, more characters), and link a character to its code. |
| Representing images | Define pixel, resolution and colour depth; calculate file size = width × height × colour depth. |
| Representing sound | Define sample rate and bit depth; calculate file size = sample rate × bit depth × seconds. |
| Data compression | Explain why we compress; compare lossy and lossless; describe RLE and Huffman coding. |
Worked Example — a full multi-part question 12 min
Here is one question with three parts. We earn the marks aloud.
Part (a) — Convert the binary number 0110 1010 to denary. [2 marks]
Write the place values above the bits, then add the ones that are set.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |
Add the set place values: 64 + 32 + 8 + 2 = 106 (method 1, answer 1).
Part (b) — Convert that number to hexadecimal. [2 marks]
Split the 8 bits into two nibbles: 0110 and 1010.
0110 = 6, and 1010 = 10 = A. So the answer is 6A (one mark per correct nibble).
Part (c) — A bitmap image is 100 pixels wide, 50 pixels high, with a colour depth of 4 bits. Calculate the file size in bytes. [3 marks]
Size in bits = width × height × colour depth = 100 × 50 × 4 = 20 000 bits (1).
Convert to bytes: 20 000 ÷ 8 = 2500 bytes (1 for ÷ 8, 1 for the answer).
Try It Yourself — timed mini-paper 12 min
Give yourself 12 minutes. Show all working; check your answers with your teacher.
Convert the binary number 1001 0011 to denary. [2 marks]
Convert the hexadecimal value 3F to binary. [2 marks]
State the result of a left shift of one place on 0001 0110, and what it does to the value. [2 marks]
Calculate the file size, in kilobytes, of a 5-second sound clip sampled at 8000 Hz with a bit depth of 16. [3 marks]
Explain why a photographer might choose lossless compression rather than lossy. [2 marks]
📝 Exam Practice 10 min
These questions span the whole of Unit 3. Match your answer to the command word and the marks.
Convert the binary number 1010 1100 to denary. Show your working.
Mark scheme
- Set place values identified: 128 + 32 + 8 + 4 (1).
- Total = 172 (1).
A file is 4 000 000 bytes. State its size in megabytes (MB), using the AQA convention. Show your working.
Mark scheme
- Divides by 1000 twice / uses 1 MB = 1 000 000 bytes (1).
- 4 MB (1).
Add the 8-bit binary numbers 1100 1010 and 0110 0001. State whether an overflow error occurs.
Mark scheme
- Correct addition working with carries (1).
- Result needs 9 bits:
1 0010 1011(1). - Overflow occurs — the answer will not fit in 8 bits (1).
An image is 200 pixels wide and 150 pixels high with a colour depth of 8 bits. Calculate the file size in kilobytes (kB).
Mark scheme
- Size in bits = 200 × 150 × 8 = 240 000 bits (1).
- ÷ 8 = 30 000 bytes (1).
- ÷ 1000 = 30 kB (1).
Describe the difference between lossy and lossless compression.
Mark scheme
- Lossy removes / discards some data (1).
- The original cannot be fully restored / quality is reduced (1).
- Lossless keeps all the data / is reversible (1).
- The original is restored exactly, but the file is usually larger (1).
Recap & Key Terms 3 min
Use your mini-paper marks to plan tonight's revision.
- Slipped on number bases or binary ↔ denary? Redo CS-L3-02.
- Hex conversions confusing? Redo CS-L3-03 and practise nibbles.
- Muddled the units? Redo CS-L3-04 — remember 1 kB = 1000 bytes.
- Lost marks on binary addition or overflow? Redo CS-L3-05.
- Unsure on binary shifts? Redo CS-L3-06 — left ×2, right ÷2.
- Forgot ASCII vs Unicode? Redo CS-L3-07.
- Image file-size wrong? Redo CS-L3-08 and learn the formula.
- Sound file-size wrong? Redo CS-L3-09.
- Mixed up lossy and lossless? Redo CS-L3-10.
- Binary
- Base-2 number system using only the digits 0 and 1.
- Denary
- The everyday base-10 number system, digits 0 to 9.
- Hexadecimal
- Base-16 shorthand for binary; each hex digit is one nibble (4 bits).
- Nibble
- A group of 4 bits; two nibbles make one byte.
- Byte
- 8 bits. Larger units: 1 kB = 1000 bytes, 1 MB = 1000 kB, 1 GB = 1000 MB.
- Overflow
- An error where a result is too large to fit in the available bits.
- Binary shift
- Moving bits left or right; left ×2 per place, right ÷2 per place.
- ASCII
- A 7-bit character set covering English letters, digits and symbols.
- Unicode
- A larger character set that can represent characters from many languages.
- Colour depth
- The number of bits used per pixel; more bits means more colours.
- Sample rate
- How many sound samples are taken per second, measured in hertz (Hz).
- Lossless compression
- Compression that keeps all data and can restore the original exactly.
- Lossy compression
- Compression that discards detail to shrink more; the original is not restored.
- RLE
- Run-length encoding — stores repeated values as a value plus a count.
- Huffman coding
- Lossless compression giving common symbols shorter binary codes.
Homework 1 min
Task (≤ 15 min): Revisit your weakest topic from the mini-paper. Open that lesson and redo its Exam Practice section.
Bring one question you still find hard to the next session, so we can work through it together.