Topics / Boolean Logic / Logic Circuits into Truth Tables
Logic Circuits into Truth Tables
What is a logic circuit?
When logic gates are connected they form a circuit.
Logic circuits are designed to perform a particular function. Understanding the nature of that function requires a logic circuit truth table.
A truth table shows all the expected outputs for every possible combination of inputs.
How to create a truth table for a logic circuit diagram
Creating a truth table for a logic circuit is trickier than doing so for a single gate.
It is advisable to follow the method below which will eventually lead you to the final output for the circuit. It is not advisable to try and work it all out in your head!
Method:
- On the circuit diagram, add temporary letters after each gate (C, D, E in the above example)
- Create a blank truth table, allowing space for all the temporary letters (stages)
- Write into the truth table all the possible unique input combinations (A and B combinations in this example)
- In the truth table, calculate the output at each temporary letter, treating them as separate mini logic problems (e.g. D is the result of A OR B)
- Eventually you will reach a stage where you are able to find the final output for the logic circuit (Z in this example)
| Input A | Input B | C | D | E | Output Z |
|---|---|---|---|---|---|
| A | B | NOT A | A OR B | C AND D | E OR D |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 | 1 |
