Truth Tables

1. What Is a Truth Table?

A truth table describes a logic operation by listing the output for each combination of input signals:

Inputs → logic operation → output

For FBD, it helps predict when the output should be TRUE or FALSE before running the diagram.

2. Why Truth Tables Help

Reading the diagram visually is useful; a table adds a systematic check. It helps you understand a block's rule, test all input states, find output conditions, catch mistakes before execution, and explain the diagram to another person.

3. One Input

A Boolean input has two possible states:

This table describes a direct connection:

[Input_1] ───────────────> [Output_1]

4. NOT Truth Table

NOT produces the opposite value:

Output_1 = NOT Input_1

5. Two Inputs

Two Boolean inputs have four combinations:

These rows form the basis for testing AND, OR, XOR, and other two-input operations.

6. AND Truth Table

AND produces TRUE only when every input is TRUE:

Output_1 = Input_1 AND Input_2

This suits permissives: a motor may run only when Start is pressed and Safety_OK is active.

7. OR Truth Table

OR produces TRUE when at least one input is TRUE:

Output_1 = Input_1 OR Input_2

This suits an action requested by several different conditions.

8. Building a Truth Table

• 1. List all diagram inputs.
• 2. List every TRUE/FALSE combination.
• 3. Calculate the block results for each row.
• 4. Record the final output.
• 5. Compare the table with the simulator.

The number of rows grows quickly: two inputs require 4 rows, three require 8, and four require 16.

9. FBD Example: Motor Start

The motor should run only when Start is pressed and Safety_OK is active:

[Start_Button] ───┐
                  ├── [AND] ──> [Motor_Run]
[Safety_OK] ──────┘

The table shows that pressing Start alone is insufficient.

10. Simulator Practice

Open the lesson example and start the simulation. Test both inputs FALSE, only Start_Button TRUE, only Safety_OK TRUE, and both TRUE. Compare Motor_Run with the table above.

The goal is to check the diagram against a prepared table rather than trying inputs at random.

11. Key Points

A truth table shows a diagram's output for every input combination. It is a reliable way to understand and check AND, OR, NOT, and other logic blocks.