1 Truth Table Generator

Online Truth Table Generator

Feeling puzzled? How about (A ∧ B)¬C? Explore more to master it!

Struggling to figure out how your logic expression works? Manually checking all input combinations can be slow and confusing, especially when you have multiple variables and operators.

Our Truth Table Generator does it for you in seconds. It is an online tool that quickly builds a full truth table based on the logic expression you enter. It shows every possible input and the correct output in a clear, easy-to-read format. You can choose between your output in Binary or Boolean format, copy the table with one click, and even share it using a simple link. Whether you're learning logic or testing complex expressions, this tool makes the process fast and simple.

What is a Truth Table?

A truth table is a simple chart that shows how a logic statement works. It lists all the possible outcomes of a logical expression or circuit based on its inputs. Truth tables use binary values, where each input can be either 1 (true) or 0 (false).

Each row in the table represents one possible combination of these input values. The last column shows the result of the logic expression for each combination. The number of rows in a truth table depends on the number of inputs. If there are n inputs, the table will have 2n rows. For example, a logic expression with 3 inputs will have 8 rows (23), showing every possible input case.

Some of the common logic operators used in truth tables include AND, OR, NOT, NAND, NOR, XOR, and XNOR. Truth tables are widely used in math, computer science, electronics, and even philosophy to understand logic rules and design digital circuits.

Features of Our Advanced Truth Table Generator

Wide Range of Logic Operators

Our truth table generator supports a wide range of logic operators, including AND, OR, NOT, NAND, NOR, XOR, XNOR, Implication, Biconditional, and Negation. You can combine these operators however you like and build your expressions.

Various Input Formats

The tool supports any letter from A to Z as input variables. By default, it shows three variables: A, B, and C. But you can type and add as many variables as you need. The input is case-insensitive, so whether you enter uppercase or lowercase letters, like A or a, they'll be treated the same.

You can also use 1 or 0 directly as your input in place of variables if you want to test specific values quickly. In your input expression, you can use multiple symbols for the same logical operator. For example, both '⋀' and '&&' work for the AND operator. This makes it easier to use the symbols you're most comfortable with. You can find all the supported operator symbols and their alternatives in our Logic Operator Cheat Sheet.

Clear and Interactive Table Layout

A clear layout helps you easily spot errors, patterns, or logical behavior, especially in expressions with many variables. That's why this tool generates clean and easy-to-read tables. You can quickly see which input combinations give which outputs. It's useful for both learning how logic works and debugging your expressions.

Different Output Format

Different users prefer different formats. For example, programmers often work with binary, where logic students may be more comfortable with Boolean values. That's why our tool lets you pick the format you like most.

You can choose between Boolean (True/False) format and Binary (1/0) format. This way, you can view the output in a style that matches your needs or feels most familiar.

One-Click Copy

Once your table is generated, you can copy it using the 'Copy to Clipboard' button. The copied output is ready to paste into your notes, documents, or chat.

Device Compatibility

This truth table generator works on any device, whether you're using a desktop, tablet, or phone. As long as you're connected to the internet, you can use it anytime, anywhere.

Built-in Logic Symbols Guide

Logical notation can be confusing, especially if you're just starting out. That's why this tool includes a built-in cheat sheet that shows all supported operators, their symbols, how to write them in your input, and any alternative symbols you can use. So even if you're new to logic, you'll know exactly how to build your expressions with ease.

Supported Logic Operators of Our Truth Table Generator

AND Gate

The AND gate is a basic logic gate that checks if all the inputs are true. It only gives a true (or 1) result when every input is true (1). If even one input is false (or 0), the result will be false. It's commonly used in logic, programming, and digital circuits.

The symbol for AND is a dot (·). The Boolean expression for a basic AND gate with two inputs is: Y = A · B, where A and B are the inputs, and Y is the output.

A B Y

Truth Table:

Input Output
ABY = A · B
000
010
100
111

OR Gate

The OR gate is a basic logic gate that checks if at least one input is true. It gives a true (or 1) result if any one or more inputs are true (1). The result is false only when all inputs are false (0). It's often used in logic, programming, and digital systems.

The Boolean expression for a basic OR gate with two inputs is: Y = A + B, where A and B are the inputs, and Y is the output.

A B Y

Truth Table:

Input Output
ABY = A + B
000
011
101
111

NOT Gate

The NOT gate is a basic logic gate that gives the opposite of the input. If the input is true (1), the output will be false (0), and if the input is false (0), the output will be true (1). It's also called an inverter.

The Boolean expression for a NOT gate is: Y = A′, where A is the input, and Y is the output.

A Y

Truth Table:

Input Output
AY = A′
01
10

NAND Gate

The NAND gate is a combination of AND and NOT. It gives the opposite result of an AND gate. That means it only gives a false (0) output when all inputs are true (1). In all other cases, the output is true (1). It's used a lot in digital circuits because it's easy to build and very useful.

The Boolean expression for a basic NAND gate with two inputs is: Y = (A ↑ B) or Y = (A · B)′, where A and B are the inputs, and Y is the output.

A B Y

Truth Table:

Input Output
ABY = (A ↑ B) = (A · B)′
001
011
101
110

NOR Gate

The NOR gate is a combination of OR and NOT. It gives the opposite result of an OR gate. It only gives a true (1) output when all inputs are false (0). If any input is true, the result will be false (0). This gate is also widely used in digital logic systems.

The Boolean expression for a basic NOR gate with two inputs is: Y = (A ↓ B) or Y = (A + B)′, where A and B are the inputs, and Y is the output.

A B Y

Truth Table:

Input Output
ABY = (A ↓ B) = (A + B)′
001
010
100
110

XNOR Gate

The XNOR (Exclusive NOR) gate is the opposite of XOR. It gives a true (1) result only when the inputs are the same, both 0 or both 1. If the inputs are different, the output is false (0). This gate is used when you want to check if two values are equal.

The Boolean expression for a basic XNOR gate is: Y = (A ⊕ B)′ or Y = A ⊙ B, where A and B are the inputs, and Y is the output.

A B Y

Truth Table:

Input Output
ABY = (A ⊕ B)′ = A ⊙ B
001
010
100
111

Implication

Implication is a logical operator that connects two statements A and B, like 'If A happens, then B happens'. It is false only when A is true but B is false. In all other cases, it is true.

The Boolean expression for implication is: Y = A ⇒ B, where A and B are the inputs, and Y is the output.

Truth Table:

Input Output
ABY = A ⇒ B
001
011
100
111

Biconditional

Biconditional is a logical operator that connects two statements A and B as 'A if and only if B'. It is true when both A and B are the same (both 0 or both 1). If they are different, it is false.

The Boolean expression for biconditional is: Y = A ↔ B, where A and B are the inputs, and Y is the output.

Truth Table:

Input Output
ABY = A ↔ B
001
010
100
111

Negation

Negation is a logical operator that reverses the input value. It changes true to false, and false to true. The Boolean expression for negation is: Y = A′ or Y = ¬A, where A is the input, and Y is the output.

Truth Table:

Input Output
AY = A′ = ¬A
01
10

Why Use Our Truth Table Generator?

Using our online truth table generator is quite easy. Just follow the steps:

Enter Your Logical Expression

Input the logical expression you want to evaluate. Use the symbols and operators our tool supports, like AND, OR, NOT, and parentheses, to build your formula. The on-screen keypad makes it easy to insert operators without memorizing them.

Student entering a logical expression on a laptop

Generate the Table

Once you've entered your expression, click the Generate button. The tool will quickly process your input and create a complete truth table. This table will show every possible combination of input values and the resulting output for your expression.

You can view the results in two formats: Binary or Boolean, depending on your choice. If you select Binary, the results will be shown using 1s and 0s like the following preview:

Binary output
ABA ∧ B
000
010
100
111

If you choose Boolean, the results will be shown using True and False values as below:

Boolean output
ABA ∧ B
FalseFalseFalse
FalseTrueFalse
TrueFalseFalse
TrueTrueTrue

Analyze Results

Once the truth table is generated, take a moment to look at it carefully. The table shows all the different ways the inputs can be true or false, and the result of your logic expression for each case.

By studying the table, you can see patterns in how the logic works, check if your expression is giving the right results, and understand how different logical operators like AND, OR, and NOT work together. This makes it easier to learn and confirm that your logic is correct.

Generate Truth Tables for Multiple Expressions at Once

Want to compare multiple logic expressions side by side? With our truth table generator, you can do it easily. Just enter each expression using a comma (,) in the input field. The tool will evaluate them all at once and display the results as separate output columns in a single truth table.

A∧B, A∨B, A⊕B
A B A∧B A∨B A⊕B
00000
01011
10011
11110

An Overview of the Logic Symbols Cheat Sheet

To start, convert your argument into symbolic logic. The cheat sheet below shows every supported operator, its symbol, the input format you should use, and any alternative symbols that also work. Click the info icon next to the input box at the top of the page to open the full Essential Logic Symbols Guide at any time.

Operator Symbol Input Format Alternative
AND∧A ∧ B&, &&, ·
OR∨A ∨ B|, ||, +
NOT~~A!, ¬, ′
NAND (AND + NOT)↑A ↑ B—
NOR (OR + NOT)↓A ↓ B—
XOR⊕A ⊕ B—
XNOR⊙A ⊙ B—
IMPLIES⇒A ⇒ B→, ⊃
BICONDITIONAL↔A ↔ B⇔
NEGATION¬¬A!, ~, ′

Share Your Truth Table with Others

Learning and collaboration are easier when you can quickly share your work. Whether you're asking for help in a forum or showing your solution to a teacher or friend, sharing a link is much simpler than explaining everything step by step.

After generating a truth table, the tool creates a unique URL using the hash of your expression. Just copy and share it. Anyone with the link will see the exact same inputs and outputs you did. It's perfect for study groups, classrooms, or online discussions.

For example, if you generate the truth table for B⊕C, you'll get a URL like: https://truthtablegenerator.org/#B⊕C

Importance of Truth Table in Philosophy

Truth tables are really useful in philosophy, especially when you're trying to figure out if an argument makes sense. In logic, we often deal with statements like "If this happens, then that should happen." A truth table helps you see all the possible situations and whether the argument still works in each one.

It's like laying everything out on a table to check your thinking. You don't have to guess. You can actually see which parts are true and which aren't.

Here's a simple example: Let's say the argument is, "If it rains, the ground gets wet. It is raining. So, the ground is wet." We can break that into parts. Let P be "It rains" and Q be "The ground gets wet." So the logic becomes: If P, then Q.

P (It rains) Q (Ground gets wet) P → Q
FalseFalseTrue
FalseTrueTrue
TrueFalseFalse
TrueTrueTrue

This shows that the only time the argument does not work is when it is raining but the ground is not wet. In all the other cases, the argument is true. So, why is this important in philosophy? Because instead of just saying "I think this is right," you can prove whether something is logically correct. It helps you build stronger arguments and spot weak ones. That's why truth tables are important in philosophy and in learning how to think clearly.

Frequently Asked Questions (FAQs)

Yes, you can. The tool is case-insensitive, so it doesn't matter whether you type a variable in uppercase or lowercase. For example, A and a will be treated the same.

There's no limit. You can add as many variables as you want. You can even use the same variable more than once in your expression if needed.

Yes, you can. If you enter a constant expression like 1 (true) or 0 (false), the tool will still create a truth table that shows the result in a single row.

Yes, when you share the generated link, it keeps your entire setup, including the logic expression, selected variables, and the output format. Anyone who opens the link will see the exact same inputs and outputs in the same order, just as you did.

Yes, you can. The tool fully supports parentheses, so you can group and nest parts of your logic expression as needed. Just make sure the syntax is correct to get accurate results.

If you enter an invalid expression, the tool will show an 'Invalid Syntax' message and won't generate a truth table. This usually happens when there are missing operators, unmatched parentheses, or unsupported symbols. To fix it, you can delete the incorrect input using the Delete option, then check the built-in cheat sheet or reference guide to see how to write the expression correctly. Once you've reviewed the format, you can retype your expression properly and generate the table again.