E6: Logic Gates
AND, OR, NOT, NAND, NOR, XOR gates and truth tables
Logic Gates
AND, OR, NOT, NAND, NOR, XOR gates and truth tables
Key Fact: An AND gate outputs 1 only when ALL inputs are 1; its truth table has one high output for two inputs.
Key Fact: An OR gate outputs 1 when ANY input is 1; it produces a low output only when all inputs are 0.
Key Fact: A NOT gate (inverter) outputs the complement of its single input: 0 becomes 1 and 1 becomes 0.
Key Fact: A NAND gate is the complement of AND: output is 0 only when all inputs are 1; it is a universal gate.
Key Fact: A NOR gate is the complement of OR: output is 1 only when all inputs are 0; also a universal gate.
Key Fact: An XOR (exclusive OR) gate outputs 1 when inputs are different; XNOR outputs 1 when inputs are the same.
Key Fact: NAND and NOR are universal gates: any Boolean function can be implemented using only NAND or only NOR gates.
Key Fact: Logic 1 typically corresponds to a high voltage (e.g. 5 V); logic 0 to a low voltage (e.g. 0 V).
Key Fact: Truth tables list all possible input combinations and the corresponding output for each.
Key Fact: For n inputs, a truth table has 2ⁿ rows covering every input combination.
Key Fact: Logic gates are built from transistors; CMOS technology uses complementary pairs of MOSFETs.
Key Fact: Propagation delay is the time between a change at the input and the corresponding change at the output.
📋 Key Vocabulary and Concepts
For Logic Gates, you must know:
- Logic gate: A digital circuit that performs a Boolean logic operation on one or more inputs to produce a single output.
- Truth table: A table listing all possible input combinations and the resulting output of a logic circuit.
- Universal gate: A gate (NAND or NOR) that can implement any Boolean function without any other gate type.
- Propagation delay: The time taken for a signal change at the input to produce a change at the output.
- XOR gate: Exclusive OR gate; outputs 1 when the two inputs are different.
- CMOS: Complementary Metal-Oxide-Semiconductor; a technology for building low-power logic gates.
❓ Practice Questions
Q: Draw the truth table for a 2-input AND gate.
Q: What is the output of a NAND gate when both inputs are 1?
Q: Why are NAND and NOR called universal gates?
Q: How many rows does a truth table for a 3-input logic gate have?
Q: What is the difference between XOR and XNOR gates?
✅ Answers
- A=0,B=0→0; A=0,B=1→0; A=1,B=0→0; A=1,B=1→1.
- 0. A NAND gate produces the complement of the AND output.
- Because any Boolean function can be implemented using only NAND gates or only NOR gates, without needing any other gate type.
- 2³ = 8 rows.
- XOR outputs 1 when inputs are different; XNOR outputs 1 when inputs are the same (XOR followed by NOT).
🎯 Exam Tips
- Always write truth tables with inputs in binary counting order (00, 01, 10, 11).
- Remember: NAND = NOT(AND); NOR = NOT(OR); the bubble on the symbol indicates inversion.
- When asked to identify a gate from a truth table, look at which rows give output 1.
- For universal gate questions, show how NOT, AND and OR can each be made from NAND gates.
- Label gate symbols clearly with the gate type and input/output labels.
📝 Exam Technique
GCSE Electronics Exam Tips — Logic Gates:
1. For Logic Gates questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Logic Gates, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
1. For Logic Gates questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Logic Gates, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
⚠️ Common Errors
✗ Confusing OR and XOR truth tables. ✓ OR outputs 1 when any input is 1; XOR outputs 1 only when inputs differ (0,1 or 1,0).
✗ Forgetting the bubble (inversion) on NAND and NOR gate symbols. ✓ NAND has a bubble on the output of an AND symbol; NOR has a bubble on the output of an OR symbol.
✗ Omitting rows from a truth table. ✓ A complete truth table for n inputs must have 2ⁿ rows covering all combinations.
✗ Stating that AND and OR are universal gates. ✓ Only NAND and NOR are universal gates; AND and OR cannot implement inversion alone.
✍️ Model Answer
Full-Mark Response
Describe the function of each fundamental logic gate (AND, OR, NOT, NAND, NOR, XOR) and explain why NAND is a universal gate.
An AND gate outputs 1 only when all inputs are 1. An OR gate outputs 1 when any input is 1. A NOT gate inverts its single input. A NAND gate outputs 0 only when all inputs are 1 (complement of AND). A NOR gate outputs 1 only when all inputs are 0 (complement of OR). An XOR gate outputs 1 when its inputs are different. NAND is a universal gate because any Boolean function can be built using only NAND gates: a NOT gate is a NAND with both inputs tied together; an AND gate is a NAND followed by a NOT (two NANDs); an OR gate is implemented by inverting both inputs first then feeding them to a NAND (De Morgan's equivalence). Since NOT, AND and OR together can implement any Boolean expression, and all three can be built from NAND alone, NAND is universal. The same reasoning applies to NOR.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of logic gates, including electronic components, circuit theory and systems concepts relevant to WJEC Eduqas C690QS.
AO2 (Application): Apply knowledge and understanding of logic gates to analyse, design and construct electronic circuits and systems.
AO3 (Evaluation): Evaluate electronic circuits and systems, making reasoned judgements about design choices, performance and practical considerations, constructing supported arguments.
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