Calculator Form
Example Data Table
| A | B | C | A ∧ B | A ∨ B ∨ C | A ⊕ B ⊕ C | A → B |
|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Formula Used
Logical operators use Boolean algebra, where TRUE is represented by 1 and FALSE is represented by 0.
- NOT: ¬A flips the value of A.
- AND: A ∧ B is true only when both inputs are true.
- OR: A ∨ B is true when at least one input is true.
- XOR: A ⊕ B is true when the inputs differ.
- NAND: ¬(A ∧ B) is the negation of AND.
- NOR: ¬(A ∨ B) is the negation of OR.
- XNOR / Equivalence: A ≡ B is true when inputs match.
- Implication: A → B is logically equivalent to ¬A ∨ B.
- Biconditional: A ↔ B is true when both values are equal.
- Three-variable XOR: A ⊕ B ⊕ C is true when an odd count of inputs is true.
- Three-variable equality: A ↔ B ↔ C is true when all three values match.
- Implication chain: (A → B) ∧ (B → C) requires both linked implications to hold.
How to Use This Calculator
- Select whether you want to work with 2 variables or 3 variables.
- Choose the current truth values for A, B, and optionally C.
- Tick the logical operators you want to evaluate.
- Click Calculate Logical Results.
- Review the result block shown above the form.
- Study the generated truth table for every possible input combination.
- Use the chart to compare TRUE counts for selected operators.
- Download the truth table as CSV or PDF when needed.
FAQs
1) What does the calculator actually compute?
It evaluates common logical operators using the truth values you choose. It also builds a full truth table, counts TRUE outcomes, and visualizes results with a comparison chart.
2) What is the difference between AND and OR?
AND needs every required input to be true. OR needs only one qualifying input to be true. That makes AND stricter and OR more inclusive.
3) When is XOR true?
XOR is true when inputs differ. For three variables, chained XOR is true when an odd number of inputs are true, which makes it useful for parity checks.
4) What does implication mean in logic?
Implication, written as A → B, is false only when A is true and B is false. In all other cases, the statement is considered true.
5) Why is a truth table useful?
A truth table lists every possible combination of inputs and shows each resulting output. It helps verify logic rules, compare operators, and catch design mistakes quickly.
6) Can I use this for digital logic study?
Yes. The outputs, truth table, and operator comparisons are helpful for Boolean algebra, discrete mathematics, circuit design basics, and exam practice.
7) What is XNOR or equivalence?
XNOR is true when the compared inputs are the same. With two variables, it matches the biconditional idea because both evaluate equality of truth values.
8) Why download CSV or PDF?
CSV is useful for spreadsheet work and further analysis. PDF is useful for printing, sharing, or keeping a fixed report of your current truth table.