BOOL Logic Expression Utility

Boolean Expression Evaluator

Evaluate Boolean logic expressions with assigned true or false variable values. Use AND, OR, NOT, XOR, XNOR, NAND, NOR, parentheses and Boolean constants, then inspect the parsed expression and step-by-step evaluation.

✓ AND / OR / NOT ✓ XOR / XNOR ✓ NAND / NOR ✓ Parentheses ✓ TRUE / FALSE ✓ Evaluation Steps

A→?

Boolean Expression Evaluation

● Ready

Boolean Expression Use single-letter variables A–Z, constants TRUE/FALSE or 1/0, and operators AND, OR, NOT, XOR, XNOR, NAND and NOR.

Variable Values

Variables are detected automatically from the expression.

Result Display

Precedence: NOT is evaluated first, followed by AND/NAND, XOR/XNOR, and finally OR/NOR. Parentheses override normal precedence. This evaluator uses a dedicated Boolean parser rather than JavaScript eval().

Boolean Evaluation Result Valid Expression

Final Boolean Result — —

Variables —

Operators —

TRUE Variables —

FALSE Variables —

Tokens —

Evaluation Steps —

Root Result —

Status —

Variable Assignments —

Step-by-Step Evaluation —

Parser Details —

Boolean Expression Evaluator

The Boolean Expression Evaluator calculates the true or false result of a logical expression after you assign Boolean values to its variables. It supports common operators including AND, OR, NOT, XOR, XNOR, NAND and NOR together with nested parentheses.

Unlike a truth table generator, which evaluates every possible variable combination, this tool evaluates one specific set of variable values at a time. For example, you can set A to true, B to false and C to true and immediately determine the result of a larger expression.

The evaluator also shows the detected variables, parser output and individual logic operations so you can verify how the final answer was obtained.

How to Evaluate a Boolean Expression

Enter an expression such as (A OR B) AND NOT C. The evaluator detects the variables automatically and displays True and False selectors for each one.

Choose the value of every variable and press Evaluate Boolean Expression. The final result and evaluation steps appear below.

Expression:
(A OR B) AND NOT C

Assignments:
A = TRUE
B = FALSE
C = FALSE

Evaluation:
A OR B
= TRUE OR FALSE
= TRUE

NOT C
= NOT FALSE
= TRUE

TRUE AND TRUE
= TRUE

Final result:
TRUE

What Is a Boolean Expression?

A Boolean expression is a logical statement whose final value is either true or false. Expressions can contain Boolean variables, constants, operators and parentheses.

A AND B

NOT A

A XOR B

(A OR B) AND C

A AND (B OR NOT C)

(A NAND B) XOR C

Boolean expressions are widely used in programming conditions, digital logic, search filters, permissions, electronic circuits and formal logic.

Boolean AND Evaluation

AND returns true only when both operands are true.

A	B	A AND B
FALSE	FALSE	FALSE
FALSE	TRUE	FALSE
TRUE	FALSE	FALSE
TRUE	TRUE	TRUE

Boolean OR Evaluation

OR returns true when at least one operand is true.

TRUE OR TRUE   = TRUE
TRUE OR FALSE  = TRUE
FALSE OR TRUE  = TRUE
FALSE OR FALSE = FALSE

Boolean NOT Evaluation

NOT is a unary operator. It reverses the Boolean state of the expression immediately following it.

NOT TRUE
= FALSE

NOT FALSE
= TRUE

NOT (A AND B)
= complement of the entire parenthesized result

Boolean XOR Evaluation

XOR, or exclusive OR, returns true when two operands have different Boolean values.

FALSE XOR FALSE = FALSE
FALSE XOR TRUE  = TRUE
TRUE XOR FALSE  = TRUE
TRUE XOR TRUE   = FALSE

Boolean XNOR Evaluation

XNOR is the complement of XOR. It returns true when both operands have the same Boolean value.

FALSE XNOR FALSE = TRUE
FALSE XNOR TRUE  = FALSE
TRUE XNOR FALSE  = FALSE
TRUE XNOR TRUE   = TRUE

For this reason, XNOR is often described as a Boolean equivalence operation.

Boolean NAND Evaluation

NAND means NOT AND. It produces false only when both operands are true.

A NAND B
=
NOT (A AND B)

TRUE NAND TRUE
= FALSE

TRUE NAND FALSE
= TRUE

Boolean NOR Evaluation

NOR means NOT OR. It evaluates to true only when both operands are false.

A NOR B
=
NOT (A OR B)

FALSE NOR FALSE
= TRUE

TRUE NOR FALSE
= FALSE

Using TRUE, FALSE, 1 and 0

The evaluator supports Boolean constants in addition to variables. TRUE and 1 are treated as true values, while FALSE and 0 represent false.

A AND TRUE

FALSE OR B

NOT 0

1 XOR A

A NAND TRUE

Constants do not create variable controls because their values are already defined by the expression itself.

Boolean Expression Operator Precedence

When parentheses do not explicitly define the order of evaluation, the calculator uses a consistent Boolean precedence system.

Priority	Operators	Meaning
1 – Highest	NOT	Unary complement
2	AND, NAND	AND-family operations
3	XOR, XNOR	Exclusive comparison
4 – Lowest	OR, NOR	OR-family operations

Why Parentheses Matter

Parentheses explicitly define which expression should be evaluated first and are recommended whenever a Boolean expression contains several operators.

A OR B AND C

is evaluated as:

A OR (B AND C)

But:

(A OR B) AND C

evaluates the OR expression first.

These two expressions can produce different results for the same variable assignments.

Nested Boolean Expressions

Parentheses can be nested to represent multiple levels of logical decision making.

Expression:

(A AND (B OR C)) XOR (NOT D)

Example assignments:

A = TRUE
B = FALSE
C = TRUE
D = FALSE

B OR C
= TRUE

A AND TRUE
= TRUE

NOT D
= TRUE

TRUE XOR TRUE
= FALSE

Boolean Expression Evaluation Example

Consider the expression A AND (B OR NOT C).

A = TRUE
B = FALSE
C = FALSE

Step 1:
NOT C
= TRUE

Step 2:
B OR TRUE
= TRUE

Step 3:
A AND TRUE
= TRUE

Result:
TRUE

Boolean Expression Evaluator vs Truth Table Generator

Both tools work with Boolean expressions, but they answer different questions.

Tool	Purpose	Variable Values	Output
Boolean Expression Evaluator	Evaluate one specific case	User assigns each value	One final Boolean result
Truth Table Generator	Test every possible case	Automatically generates all combinations	Complete truth table

Use this evaluator when you already know the values of the variables and need to determine whether the expression is true or false.

Boolean Expressions in Programming

Programming languages use Boolean expressions to control decisions, loops, validation, permissions and application state.

Conceptual condition:

LoggedIn AND (Admin OR Editor)

Example:

LoggedIn = TRUE
Admin = FALSE
Editor = TRUE

Result:
TRUE

The syntax used by actual programming languages varies, but the underlying Boolean logic follows the same truth rules.

Boolean Expressions in Digital Logic

Digital circuits can also be described with Boolean expressions. Variables represent logic-level inputs while operators correspond to logic gates.

Expression:
(A AND B) OR C

Possible gate structure:

A ──┐
    AND ──┐
B ──┘     OR ── Output
C ────────┘

Evaluating the expression for a chosen set of input states predicts the output of the corresponding combinational circuit.

Boolean Expressions for Permissions and Rules

Logical expressions are frequently used to represent access-control rules and feature conditions.

Expression:

Premium AND NOT Suspended

Premium = TRUE
Suspended = FALSE

Result:
TRUE

More complex policies can combine multiple conditions with nested AND, OR and NOT expressions.

Common Boolean Expression Errors

A common error is writing two variables next to one another without an operator, such as A B. The evaluator requires an explicit operator such as A AND B.

Another error is leaving an operator without a right-hand operand, such as A OR. Parentheses must also be balanced, so expressions such as (A AND B without a closing parenthesis are rejected.

NOT is unary and must appear before a variable, constant or parenthesized expression. For example, NOT A and NOT (A OR B) are valid.

Why This Evaluator Does Not Use eval()

The tool uses a dedicated tokenizer, operator-precedence parser and stack-based Boolean evaluator. Only the supported variables, constants, parentheses and Boolean operators are accepted.

This keeps expression interpretation limited to Boolean logic instead of executing arbitrary JavaScript code supplied in the input field.

Boolean Expression Evaluator Limitations and Notes

Variables are represented by individual letters A through Z. Operator names are case-insensitive, so A and B and A AND B are interpreted equivalently.

The evaluator is intended for Boolean logic rather than arithmetic comparison. Expressions such as A > 5, X == Y or numeric addition are outside the scope of this tool.

Each detected variable must be assigned either true or false. Constants TRUE, FALSE, 1 and 0 require no assignment.

Boolean Expression Evaluator FAQs

What does a Boolean Expression Evaluator do?

It calculates whether a Boolean expression is true or false for a specific set of assigned variable values.

Which Boolean operators are supported?

The evaluator supports AND, OR, NOT, XOR, XNOR, NAND and NOR.

Can I use parentheses?

Yes. Parentheses can be nested and override the default operator precedence.

Can I use TRUE and FALSE directly?

Yes. TRUE and FALSE are supported Boolean constants.

Can I use 1 and 0 as Boolean constants?

Yes. 1 represents true and 0 represents false.

What is TRUE AND FALSE?

TRUE AND FALSE evaluates to FALSE.

What is TRUE OR FALSE?

TRUE OR FALSE evaluates to TRUE.

What is NOT TRUE?

NOT TRUE evaluates to FALSE.

What is TRUE XOR FALSE?

TRUE XOR FALSE evaluates to TRUE because the two values differ.

What is TRUE XNOR TRUE?

TRUE XNOR TRUE evaluates to TRUE because both operands are equal.

What is TRUE NAND TRUE?

TRUE NAND TRUE evaluates to FALSE.

What is FALSE NOR FALSE?

FALSE NOR FALSE evaluates to TRUE.

Which Boolean operator is evaluated first?

NOT has the highest priority, followed by AND/NAND, XOR/XNOR, and then OR/NOR. Parentheses override this order.

How is this different from a truth table generator?

An evaluator calculates one chosen set of variable assignments. A truth table generator calculates every possible assignment combination.

Does this tool execute JavaScript code?

No. The expression is interpreted with a dedicated Boolean parser and not with JavaScript eval().