🎓 Computer Science • Logic
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Truth Table Generator
Generates exhaustive truth tables for multi-variable boolean logic propositions with 2 or 3 inputs.
Presets:
Truth Table (4 Minterm Rows)
| m | A | B | Output (Y) |
|---|---|---|---|
| m0 | 0 | 0 | 0 |
| m1 | 0 | 1 | 1 |
| m2 | 1 | 0 | 1 |
| m3 | 1 | 1 | 0 |
Canonical Sum of Products (SOP / Minterms)
Σ m(1, 2)
Canonical Product of Sums (POS / Maxterms)
Π M(0, 3)
What is a Truth Table?
A truth table is a mathematical table used in logic and computer science to determine all possible functional truth values of boolean statements.
Formula & Step-by-Step Calculation
Rows = 2^n (where n is the number of boolean variables)
Exhaustive combination of binary inputs.
Worked Step-by-Step Examples
Example 1
Generate truth table for XOR (A ⊕ B)
Solution: 0⊕0=0, 0⊕1=1, 1⊕0=1, 1⊕1=0
• Outputs 1 only when inputs differ
Common Real-World & Academic Use Cases
- ✓ Verifying digital adder logic circuits
- ✓ Propositional calculus logic homework
- ✓ Safety-critical software condition testing
How to Use the Truth Table Generator
1
Select Operator
Choose AND, OR, XOR, NAND, NOR, or XNOR.
2
Choose Variable Count
Toggle 2 inputs (A, B) or 3 inputs (A, B, C).
3
Inspect Truth Matrix
Review all input combinations and calculated outputs.
Frequently Asked Questions
Q: Why is NAND called a universal gate?
Because any boolean function or logic gate (AND, OR, NOT, XOR) can be constructed using only NAND gates.