Boolean Algebra Calculator
Boolean algebra is the algebra of true and false, the foundation of digital logic, computer circuits and the conditions in every program. Its values are just 1 and 0, and its operations are AND, which is 1 only when both inputs are 1, OR, which is 1 when at least one input is 1, and NOT, which flips a value. This calculator evaluates a fixed three-variable Boolean expression for a set of input values you choose. The expression is (A AND B) OR (NOT C), a small formula that combines all three basic operations. You set each of A, B and C to 1 or 0, and the calculator computes the intermediate results, A AND B and NOT C, and then the final value of the whole expression. Working through the parts makes the order of operations explicit, which is the same reasoning a logic gate or an if-statement follows. Every value is computed deterministically from the inputs you choose, never guessed, so the same inputs always give the same result. A full truth-table view of every input combination is available in the companion truth table calculator. The expression, the operations and a worked example that reconciles to the default inputs are shown below.
This tool evaluates (A AND B) OR (NOT C). With the default inputs A = 1, B = 1, C = 0, A AND B is 1 and NOT C is 1, so the expression evaluates to 1 (true).
Formula
Expression: (A AND B) OR (NOT C)
AND: 1 only when both inputs are 1
OR: 1 when at least one input is 1
NOT: flips 1 to 0 and 0 to 1
Each variable is read as 1 (true) or 0 (false). The calculator computes A AND B and NOT C first, then combines them with OR to get the final value of the expression.
Worked example
Evaluate (A AND B) OR (NOT C) with A = 1, B = 1 and C = 0.
- A AND B = 1 AND 1 = 1
- NOT C = NOT 0 = 1
- (A AND B) OR (NOT C) = 1 OR 1 = 1
These are the calculator's default inputs, so the result 1 (true) matches the widget exactly.
Boolean Algebra Calculator: frequently asked questions
What are the basic Boolean operations?
AND returns 1 only when both inputs are 1, OR returns 1 when at least one input is 1, and NOT flips a value. Every Boolean expression is built from these three operations.
What expression does this evaluate?
It evaluates (A AND B) OR (NOT C), a three-variable expression that uses all three basic operations so you can see how they combine.
What do 1 and 0 mean?
In Boolean algebra 1 means true and 0 means false. The same values drive logic gates in hardware and conditions in software.
How is the order of operations decided?
NOT is applied first, then AND, then OR, exactly as the parentheses in the expression indicate. The calculator computes the inner parts before combining them.
How can I see all input combinations?
Use the truth table calculator, which lists the output for every combination of A, B and C rather than a single chosen set of inputs.
Official sources
- Digital logic and Boolean algebra reference: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.