Boolean Expression Truth Table Calculator

Calculator

Boolean expression

Examples: A && B, A OR !B, A -> B, A NAND B

Maximum variable count

Row order

Output style

Supported operators

!, AND, OR, XOR, NAND, NOR, ->, <->

Constants

1, 0, true, false

Formula Used

For n variables, the truth table has 2ⁿ rows. Each row is one assignment of true or false values.

The calculator evaluates the expression on every row. It uses operator priority, parentheses, and these rules:

NOT A is true when A is false.
A AND B is true when both values are true.
A OR B is true when at least one value is true.
A XOR B is true when the values are different.
A -> B is false only when A is true and B is false.
A <-> B is true when both values match.

How to Use This Calculator

Enter a Boolean expression using variables such as A, B, or input_1.
Choose the maximum variable count for safe table generation.
Select whether rows should start with false or true values.
Select the output style that matches your worksheet.
Press the submit button to show the result above the form.
Use CSV for spreadsheet work, or PDF for printing.

Example Data Table

Expression	Variables	Rows	Expected type
A && B	A, B	4	Contingency
A \|\| !A	A	2	Tautology
A && !A	A	2	Contradiction
(A -> B) <-> (!B -> !A)	A, B	4	Tautology

Understanding Boolean Tables

A Boolean expression truth table shows every possible input set. It then shows the final output for each set. This calculator helps students, teachers, and digital logic learners test expressions quickly. It supports common symbols, word operators, constants, and grouped terms.

Operator Logic

The tool reads the expression from left to right, but it still follows operator priority. NOT is handled first. AND and NAND are next. XOR follows them. OR and NOR come after that. Implication and equivalence use lower priority. Parentheses can change that order. This makes the result closer to classroom logic rules.

Where It Helps

Use it for homework, circuit checks, gate design, and algebra practice. You can compare tautologies, contradictions, and contingent statements. A tautology is always true. A contradiction is always false. A contingent expression changes with the inputs. The summary area reports these labels after calculation.

Useful Options

The form includes useful options. You can choose the maximum variable count. You can decide whether rows start with false or true. You can select the output style as one and zero, true and false, or T and F. These choices make the table easier to match with your notes.

Table Growth

A truth table grows quickly. Two variables produce four rows. Three variables produce eight rows. Four variables produce sixteen rows. Each added variable doubles the table. For this reason, the calculator limits variables by your selected setting. This keeps the page usable.

Export and Study

The export tools help with records. CSV works well for spreadsheets. PDF works well for printing and sharing. After a table is generated, use the export buttons above the form. The calculator keeps the same expression and options.

Writing Good Expressions

For best results, write expressions clearly. Use parentheses around mixed operations. Avoid spaces inside variable names. Try A, B, C, input_1, or gate2. Use 1 or true for a true constant. Use 0 or false for a false constant.

Why It Matters

Boolean logic is the base of many systems. Search filters, conditions, switches, and digital circuits all use it. A clear table makes hidden behavior visible. It also helps you find errors before using the rule in a larger design with better confidence.

FAQs

What is a Boolean expression truth table?

It is a table that lists every possible true or false input combination. It also shows the final result for each row.

Which operators can I use?

You can use NOT, AND, OR, XOR, NAND, NOR, implication, and equivalence. Symbol versions are also supported.

Can I use words instead of symbols?

Yes. You can type A AND B, NOT A, A XOR B, A NAND B, and similar word based expressions.

Why is my table very large?

Each added variable doubles the number of rows. Four variables make sixteen rows, while ten variables make 1024 rows.

What does tautology mean?

A tautology is always true. Its result column is true for every possible input row in the truth table.

What does contradiction mean?

A contradiction is always false. Its result column is false for every possible input row in the truth table.

Can I export my result?

Yes. Use the CSV button for spreadsheet work. Use the PDF button when you need a printable copy.

Should I use parentheses?

Parentheses are recommended for mixed operations. They make the intended order clear and reduce mistakes in complex expressions.