Key Idea: Everything inside a computer is a pattern of bits. Number bases let those patterns be written compactly, and logic gates are how the machine acts on them.
Paper 1
- Short answers and structured questions.
- Define, state, describe — one precise line per mark.
Paper 2
- Applied, scenario-based.
- Calculations — conversions, capacities, transfer times.
Both
- Explain wants the mechanism AND its consequence.
- Show every step of a conversion — method marks survive a wrong answer.
🔢 Converting between bases
Conversions appear on both papers and they are free marks — provided you show the working.
| Conversion | Method |
|---|---|
| Denary → binary | Divide by 2 repeatedly, read the remainders upwards |
| Binary → denary | Add the place values where a 1 appears |
| Binary → hex | Group into 4 bits from the RIGHT, convert each group |
| Hex → binary | Expand each hex digit into exactly 4 bits, keeping leading zeros |
Place values to have by heart
- 128 · 64 · 32 · 16 · 8 · 4 · 2 · 1 — eight bits, and their sum is 255
- One hex digit is exactly 4 bits, which is the whole reason hex is used
- Hex digits run 0–9 then A=10, B=11, C=12, D=13, E=14, F=15
n bits give 2ⁿ different values. To represent V values you need the smallest n with 2ⁿ ≥ V. So 8 bits = 256 values = 0 to 255.
Important: If a result needs more bits than the register holds, the top bits are lost — the answer wraps round rather than growing. Adding two 8-bit numbers whose total exceeds 255 is the standard example.
🖼️ Storing different kinds of data
| Data | Size calculation | Watch out for |
|---|---|---|
| Text | characters × bits per character | ASCII 7–8 bits; Unicode more |
| Image | width × height × bit depth | Answer is in bits — divide by 8 |
| Sound | sample rate × bit depth × channels × seconds | Stereo means × 2 |
Forgetting the two channels in a stereo sound calculation halves the answer, and forgetting to divide by 8 multiplies it by eight. Write the unit on every line.
🔌 The logic gates
| Gate | Output is 1 when… |
|---|---|
| NOT | the input is 0 (it inverts) |
| AND | both inputs are 1 |
| OR | at least one input is 1 |
| NAND | not both are 1 (the opposite of AND) |
| NOR | neither is 1 (the opposite of OR) |
| XOR | the inputs differ |
A table for n inputs has 2ⁿ rows — 2 inputs give 4, 3 inputs give 8. List the input combinations in binary counting order so none is missed.
Reading a logic diagram
- Work left to right, labelling the output of every gate as you go
- Add one column per intermediate output, not just the final one
- Two diagrams are equivalent if their truth tables match — not if they look alike
📝 Exam-style questions
Convert the denary number 205 to binary and then to hexadecimal.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A stereo recording lasts 90 seconds, sampled at 48 000 samples per second with 16 bits per sample. Determine the file size in megabytes, taking 1 MB as 1 000 000 bytes.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Construct a truth table for the expression (A AND NOT B) OR C.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
✅ Quick check
Cover the answers and work left to right.
How many values can 6 bits represent? 2⁶ = 64 (0 to 63).
Why is hexadecimal used at all? One hex digit is exactly 4 bits, so converting needs no arithmetic — just grouping.
A 3-input truth table has how many rows? 2³ = 8.
Which gate outputs 1 only when its inputs DIFFER? XOR.
An image is 800 × 600 with 24-bit colour. Size in bits? 800 × 600 × 24 = 11 520 000 bits (divide by 8 for bytes).
Exam tips
- Show the place values or the division remainders — a wrong answer with correct method still scores.
- Group binary into fours FROM THE RIGHT when converting to hex.
- n bits give 2ⁿ values; to hold V values you need 2ⁿ ≥ V.
- Image and sound sizes come out in BITS. Divide by 8 for bytes, and remember stereo doubles it.
- Give every intermediate gate its own truth-table column — they carry marks.
- Equivalence is proved by matching truth tables, never by the diagrams looking similar.