📊 Truth Table – Complete Notes (Ready to Use for ComputerGS)
🔷 What is a Truth Table?
A Truth Table is a table used in Boolean Algebra and digital electronics to show all possible values of logical expressions based on different combinations of inputs.
👉 It represents how a logic gate or expression behaves for every possible input.
🔷 Basic Logic Values
| Symbol | Meaning |
|---|---|
| 0 | False |
| 1 | True |
🔷 Basic Logic Gates Truth Tables
1. AND Gate ( ∧ )
👉 Output is 1 only when both inputs are 1
| A | B | A ∧ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
2. OR Gate ( ∨ )
👉 Output is 1 when at least one input is 1
| A | B | A ∨ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
3. NOT Gate ( ¬ )
👉 Output is the opposite of input
| A | ¬A |
|---|---|
| 0 | 1 |
| 1 | 0 |
4. NAND Gate
👉 Opposite of AND
| A | B | NAND |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
5. NOR Gate
👉 Opposite of OR
| A | B | NOR |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
6. XOR Gate ( ⊕ )
👉 Output is 1 when inputs are different
| A | B | A ⊕ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
7. XNOR Gate
👉 Output is 1 when inputs are same
| A | B | XNOR |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
🔷 Truth Table Formula Rule
👉 For n inputs, number of rows = 2^n
Example:
2 inputs → 4 rows
3 inputs → 8 rows
🔷 Example: Combined Expression
Expression:
👉 Y = (A ∧ B) ∨ ¬A
| A | B | A ∧ B | ¬A | Y |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 1 |
🔷 Applications of Truth Table
✔ Digital Circuits Design
✔ Computer Logic & Programming
✔ Error Detection Systems
✔ Decision Making Systems
✔ Competitive Exams (UPTET, SSC, RRB)
🔷 Important Exam Points
⭐ Truth table shows all possible combinations
⭐ Based on binary logic (0 & 1)
⭐ Used in Boolean Algebra & Logic Gates
⭐ NAND and NOR are Universal Gates
⭐ Number of rows = 2ⁿ
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