Online Truth Table Generator
Feeling puzzled? How about (A ∧ B)¬C? Explore more to master it!
Binary
Boolean
Copy to Clipboard
Feeling puzzled? How about (A ∧ B)¬C? Explore more to master it!
Binary
Boolean
Copy to Clipboard
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.
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.
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.
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.
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 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.
Once your table is generated, you can copy it using the ‘Copy to Clipboard’ button.
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.
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.
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.
Truth Table:
| Input | Output | |
|---|---|---|
| A | B | Y = A.B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
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.
Truth Table:
| Input | Output | |
|---|---|---|
| A | B | Y = A.B |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
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.
Truth Table:
| Input | Output |
|---|---|
| A | Y = A′ |
| 0 | 1 |
| 1 | 1 |
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.
Truth Table:
| Input | Output | |
|---|---|---|
| A | B | Y = (A↑B) = (A.B)′ |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
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.
Truth Table:
| Input | Output | |
|---|---|---|
| A | B | Y = (A↓B) = (A + B)′ |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
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.
Truth Table:
| Input | Output | |
|---|---|---|
| A | B | Y = (A ⊕ B)′ = A ⊙ B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
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 | |
|---|---|---|
| A | B | Y = A⇒B |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
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 | |
|---|---|---|
| A | B | Y = A↔B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Negation is a logical operator that reverses the input value. It changes true to false, and false to true.
Y = A′ or Y = ¬A
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 |
|---|---|
| A | Y = A′ = ¬A |
| 0 | 0 |
| 1 | 1 |
Using our online truth table generator is quite easy. Just follow the steps:
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
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 image:
If you choose Boolean, the results will be shown using True and False values as below:
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.
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.
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. 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 the following URL.
https://truthtablegenerator.org/#B⊕C
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 |
|---|---|---|
| False | False | True |
| False | True | True |
| True | False | False |
| True | True | True |
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.
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.