Logic Operations Calculator
Choose two binary inputs, optionally negate either input, then evaluate a Boolean operation.
Formula Used
General Setup
Let X represent A or ¬A. Let Y represent B or ¬B.
The calculator first applies any selected negation.
It then evaluates the chosen Boolean operator on X and Y.
Common Rules
AND: X ∧ Y
OR: X ∨ Y
XOR: X ⊕ Y
NAND: ¬(X ∧ Y)
NOR: ¬(X ∨ Y)
XNOR: (X ∧ Y) ∨ (¬X ∧ ¬Y)
Implication: ¬X ∨ Y
Reverse Implication: X ∨ ¬Y
How to Use This Calculator
- Select the value of input A.
- Select the value of input B.
- Choose a Boolean operation from the list.
- Tick NOT for A or B when needed.
- Press the calculate button.
- Read the final output and truth table.
- Use the chart to compare row outcomes quickly.
- Export the result section as CSV or PDF.
Example Data Table
These examples show common logic outcomes for quick checking.
| A | B | Operation | Output | Explanation |
|---|---|---|---|---|
| 1 | 1 | AND | 1 | Both inputs are true. |
| 1 | 0 | OR | 1 | At least one input is true. |
| 1 | 0 | XOR | 1 | The inputs differ. |
| 0 | 0 | NOR | 1 | Neither input is true. |
| 1 | 0 | Implication | 0 | True implies false gives false. |
| 0 | 1 | Reverse Implication | 0 | Here B implies A is false. |
Frequently Asked Questions
1. What does this calculator compute?
It evaluates Boolean operations using two binary inputs. You can apply NOT to either input, test several operators, generate a truth table, view a chart, and export the results.
2. What values can I enter?
Use 0 for false and 1 for true. The calculator is designed for binary logic, so it normalizes the inputs to standard Boolean values.
3. What is the difference between XOR and OR?
OR returns true when at least one input is true. XOR returns true only when the two inputs are different.
4. Why would I use NOT on an input?
NOT flips a binary value. It turns 1 into 0 and 0 into 1. This helps test complements, inverse conditions, and more complex logic setups.
5. What is implication in logic?
Implication means “if X, then Y.” It is false only when X is true and Y is false. In every other case, it evaluates to true.
6. What is XNOR used for?
XNOR checks equivalence. It returns true when both inputs match. This makes it useful in equality tests, matching conditions, and digital comparison circuits.
7. What does the chart show?
The chart plots the result for every truth table row. It helps you compare which raw input combinations produce true or false outputs for the chosen operation.
8. Can I use this for digital logic study?
Yes. It is useful for Boolean algebra practice, truth table checking, gate behavior review, and quick verification during homework, exam preparation, or circuit design exercises.