A reliable Paper 2 question: almost every paper asks you to draw a circuit, complete a truth table or write a logic expression.
1. Logic gates and their symbols
A logic gate takes one or more binary inputs (0 or 1) and produces one binary output. You must draw the standard symbols below. NOT has one input; all the other gates have two.
2. Truth tables
A truth table shows the output for every possible combination of inputs.
| A | B | AND | OR | NAND | NOR | XOR |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 |
| A | NOT A |
|---|---|
| 0 | 1 |
| 1 | 0 |
Try it: logic gate playground
3. Logic expressions
A logic expression writes a circuit in words, using the gate names and brackets to show the order. For example: X = (A AND B) OR (NOT C). Work out the brackets first, just like in maths.
4. From a problem statement to a circuit
Example: an alarm (X) sounds if the door is open (A) and the alarm is switched on (B), or if the window is open (C) and the alarm is switched on (B).
- Find the inputs and the output: A, B, C and X.
- Pick out each condition: “A and B” → A AND B; “C and B” → C AND B.
- Join them with the linking word: “or” → X = (A AND B) OR (C AND B).
- Draw one gate per operation: two AND gates feeding one OR gate. Draw it exactly as stated; don’t simplify.
5. Completing a three-input truth table
- Write 8 rows (2³ = 8). Fill A, B and C by counting in binary from 000 to 111.
- Add a column for each part of the expression (the working), e.g. A AND B, then NOT C.
- Fill the output column from those working columns.
Try it: three-input circuits
Click A, B or C to change the inputs; the matching row is highlighted. The middle columns are the working: fill them in first in the exam.
6. Examiner tips
- Use the standard symbols and make sure the bubble is drawn on NAND, NOR and NOT.
- Draw the circuit for the statement as given, without simplifying it.
- Limit gates to two inputs (NOT has one). Three inputs need two gates.
- Fill the input columns in binary order (000, 001, 010 … 111) so no row is missed.
- Add working columns for each bracket; they help you and can earn marks.
- XOR vs OR: XOR is 0 when both inputs are 1; OR is 1.
- Use brackets in expressions to make the order clear.
7. Practice questions
Practice: answer and check instantly
Type a short answer, then press Check or Enter.
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0: AND needs both inputs to be 1.
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NOR.
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XOR (also called EOR).
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0: NAND is NOT AND, and 1 AND 1 = 1.
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8 rows (2³).
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A OR B = 1 and NOT C = 1, so X = 1.
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NOT.
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01011101: X is 1 when C = 1, or when A = 1 and B = 0.
Exam-style questions
9. A greenhouse fan (X) switches on when the temperature is high (A) and the window is closed (B), or when the humidity is high (C). Write the logic expression and draw the circuit. [4]
Show mark guide
X = (A AND B) OR C [2: 1 for A AND B, 1 for OR C]. Circuit: A and B into an AND gate; its output and C into an OR gate; output X [2].
10. Complete the truth table for X = NOT (A OR B) AND C. [4]
Show mark guide
Rows 000 → 111: outputs 0, 1, 0, 0, 0, 0, 0, 0. Working: A OR B = 0,0,1,1,1,1,1,1; NOT (A OR B) = 1,1,0,0,0,0,0,0; then AND C. [4: 1 mark per 2 correct rows]
8. Topic test: predict your grade
Topic test: predict your grade
15 questions, about 10 minutes. Answer them all, then press Mark my test.
Frequently asked questions
What are the main logic gates for IGCSE?
The six gates are NOT, AND, OR, NAND, NOR and XOR. You need to know their symbols, truth tables and how to combine them into logic circuits.
How many rows does a truth table have?
A truth table has 2 to the power of n rows, where n is the number of inputs. So 2 inputs give 4 rows and 3 inputs give 8 rows.
What does an XOR gate do?
An XOR gate outputs 1 when exactly one of its two inputs is 1, and outputs 0 when both inputs are the same.