Construct logic diagrams

• A logic diagram is a visual representation of a logical expression using gate symbols.
• Shows: inputs, gates used, order of operations, final output.

Basic method

1. Identify the input variables.
2. Identify the operations in the expression.
3. Build the circuit in the correct order of operations.
4. Connect the final output.

Example 1

Q = A AND B

A visual trace of the relationships described in this objective.

Example 2

Q = (A AND B) OR C

A visual trace of the relationships described in this objective.

Example 3

Q = NOT (A OR B) — equivalent to a NOR gate.

A visual trace of the relationships described in this objective.

How to analyse a logic diagram

1. Start from the inputs.
2. Follow the signal through each gate in order.
3. Work out the intermediate outputs.
4. Determine the final output.

Converting between expressions, truth tables, and diagrams

• Expression → diagram: turn each operation into the correct gate.
• Diagram → truth table: test every input combination.
• Truth table → expression: identify when output is 1 and build the corresponding rule.

Common mistakes

• Mixing up OR and XOR.
• Forgetting NOT changes the input before the next operation.
• Evaluating gates in the wrong order.
• Forgetting NAND = NOT(AND) and NOR = NOT(OR).

Quick summary