Learning Objectives
- Identify the standard symbols for NOT, AND, OR, NAND, NOR and XOR gates.
- Recognise the inversion bubble used on NOT, NAND and NOR outputs.
- Draw circuits with signals flowing clearly from inputs to output.
- Apply the syllabus rule that only NOT has one input and all other gates have two inputs.
Key Terms
- Gate symbol
- The standard diagram shape used to represent a logic gate.
- Inversion bubble
- The small circle that shows that a value is reversed or NOT applied.
- Input line
- A wire carrying a binary value into a gate.
- Output line
- A wire carrying the result away from a gate.
- Branch
- A point where one signal is copied to more than one destination.
- Junction
- A deliberate connection between wires, normally shown clearly where required.
- Signal flow
- The direction in which inputs are processed towards the final output.
The Six Required Gates
The syllabus requires six gate types: NOT, AND, OR, NAND, NOR and XOR, which may also be written EOR. Every candidate should be able to identify each symbol and use it when drawing a circuit.
NOT is drawn as a triangle with a small circle at the output. AND has a flat left side and a curved right side. OR has a curved input side and a pointed curved output side. NAND is the AND shape with an output bubble. NOR is the OR shape with an output bubble. XOR resembles OR but has one extra curved line on the input side.
The small output circle is an inversion bubble. It means that the normal result is reversed. This is why NAND is NOT AND and NOR is NOT OR.
Input Counts
NOT is a single-input gate. It accepts one input and produces the opposite output.
Every other required gate is limited to two inputs in Cambridge questions. Even when a condition mentions three variables, a three-input operation must be represented by connecting two-input gates in stages.
For example, A AND B AND C can be drawn using one AND gate for A and B, followed by a second AND gate that combines the first result with C. Do not draw a single three-input AND symbol for this syllabus.
Signal Direction And Layout
Inputs are normally placed on the left and the output on the right. The lines connecting gates should be horizontal or neatly routed so that the sequence of operations is unambiguous.
Label every external input with the variable shown in the question. Label the final output. Intermediate outputs may also be labelled, especially when they help explain a truth table or expression.
The drawing should show exactly the statement or expression given. The syllabus specifically states that circuits must be drawn without simplification. If an expression contains a NOT gate followed by another operation, show that structure even if an alternative circuit might produce the same truth table.
The Meaning Of The Bubble
A bubble on the output of a gate reverses the result produced by the main gate shape. An AND gate followed by a bubble is NAND. An OR gate followed by a bubble is NOR.
A bubble is not decoration. Missing the bubble changes the gate and therefore changes the output for every input combination. Similarly, adding a bubble to an ordinary AND or OR symbol creates the wrong circuit.
In Cambridge symbols, NOT also uses a triangle and an output bubble. The bubble is the visual indication that the input is inverted.
Branches And Reused Inputs
One input signal may be required by more than one gate. The line can branch so that the same value is copied to both destinations. A branch does not change the value.
For example, expression X = (A AND B) OR (NOT A) uses A twice. One branch of A enters the AND gate and another branch enters the NOT gate. Both branches carry the same current Boolean value of A.
When drawing branches, keep the connection clear. Avoid crossing lines where it is uncertain whether the wires are connected.
Symbol Recognition Table
| Gate | Shape Clue | Inputs | Output Bubble |
|---|---|---|---|
| NOT | Triangle | 1 | Yes |
| AND | Flat left, rounded right | 2 | No |
| OR | Curved input side, pointed curved output | 2 | No |
| NAND | AND shape | 2 | Yes |
| NOR | OR shape | 2 | Yes |
| XOR (EOR) | OR shape with extra input curve | 2 | No |
Drawing From An Expression
Read an expression from the inside out. Draw the gate for the deepest bracket first, then connect its output to the gate that combines it with the next term.
For X = (A OR B) AND (NOT C), draw an OR gate for A and B, a NOT gate for C, and then an AND gate receiving the two intermediate results.
Do not place all three inputs into one gate. The structure of the expression determines the stages.
Worked Examples
Recognising A Gate
Question: A symbol has the AND shape and a small circle at its output. Name the gate.
- Identify the main shape as AND.
- Interpret the output circle as inversion.
- Combine the two ideas.
Answer: NAND.
Checking A Three-Input Circuit
Question: How should A AND B AND C be drawn under the syllabus input rules?
- Use a two-input AND gate for A and B.
- Use a second two-input AND gate.
- Connect the first output and C to the second gate.
Answer: Two AND gates in sequence, not one three-input gate.
Examination Guidance
- Practise drawing the six symbols exactly as shown in the syllabus.
- Count gate inputs before finishing a circuit.
- Check every inversion bubble carefully.
- Draw the structure given without simplifying it.
- Label inputs and the single final output clearly.
Common Mistakes
- Drawing XOR as an OR gate without the extra input curve.
- Drawing NAND or NOR without the output bubble.
- Giving NOT two inputs.
- Using a three-input AND, OR, NAND, NOR or XOR gate.
- Crossing wires in a way that makes connections unclear.
Knowledge Check
1. Which gate is an AND shape with a bubble?
2. Which gate has an extra curved input line?
3. How many inputs does NOT have?
4. How many inputs do the other gates have in this syllabus?
5. Should a circuit be simplified before drawing?
