Invitation
How would you test every switch combination?
Imagine a security system with two switches.
Testing only one combination would not be enough. You would need to check what happens when both are off, when one is on, when the other is on, and when both are on.
A truth table is simply a checklist that makes sure every possible combination is tested.
Two switches
A = 0Off
B = 0Off
↓
A = 0Off
B = 1On
Big Idea
List every input combination
Each input can hold one of two binary values:
0Off or false
1On or true
With two inputs, there are four possible combinations.
0, 0Both off
0, 1Only B on
1, 0Only A on
1, 1Both on
The reliable order is 00, 01, 10, 11.
Bridge
The table is built in two stages
Stage 1: Inputs
| A | B |
|---|---|
| 0 | 0 |
| 0 | 1 |
| 1 | 0 |
| 1 | 1 |
→
Stage 2: Add output
| A | B | X |
|---|---|---|
| 0 | 0 | ? |
| 0 | 1 | ? |
| 1 | 0 | ? |
| 1 | 1 | ? |
First list every input combination. Then calculate the output for each row.
Visual Guide
Complete one row at a time
Do not try to complete the whole truth table in your head.
Read one row, apply the gate rule, and write the output. Then move to the next row.
One row means one decision.
AND gate example
A = 1
B = 0
AND ↓
X = 0
Worked Example
Represent an AND gate
An AND gate outputs 1 only when both inputs are 1.
| A | B | X |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
The four input combinations stay the same. Only the output column changes for different gates.
Hinge Question
Why are there four rows?
Question
A truth table has two binary inputs, A and B. Why must it contain four rows of input combinations?
“Because each input can be 0 or 1, producing the four combinations 00, 01, 10 and 11.”
The rows are not random. They represent every possible input state.
Pattern
The input sequence never changes
00First row
01Second row
10Third row
11Fourth row
Exam shortcut: Write 00, 01, 10, 11 before calculating any outputs. This prevents missing or repeating a combination.
Exam Explainer
Use a reliable method
Step 1Write the input headings.
Step 2List 00, 01, 10, 11.
Step 3Calculate one output per row.
Exam answer: “A truth table shows every possible input combination and the corresponding output.”
Common Mistake
Do not miss or repeat a combination
✗ Incorrect
00, 01, 11, 11
✓ Correct
00, 01, 10, 11
Remember: Check the sequence before you work out the outputs.
Summary
A truth table checks every possibility
InputsEach input can be 0 or 1.
RowsTwo inputs create four combinations.
OutputApply the gate rule to each row.
Final rule: List every input combination first, then complete one output at a time.
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