Boolean Truth Table Calculator
Generate the complete truth table for two boolean variables under any common logical operator.
Operator
out of 4 input combinations
1
TRUETRUE
25%
FALSE
75%
How does this calculator work?
A truth table for two boolean variables has four rows (00, 01, 10, 11). Pick a logical operator — AND, OR, XOR, NAND, NOR, XNOR, IMPLIES or IFF — and the calculator evaluates it on every row, lists the full table, and counts how many results are TRUE versus FALSE.
Formula
How this is calculated
A truth table enumerates every possible combination of input values for a logical expression. With two boolean variables A and B there are exactly 2² = 4 rows: (A=0,B=0), (A=0,B=1), (A=1,B=0) and (A=1,B=1), where 0 means FALSE and 1 means TRUE.
The operator you select determines the output column. AND is true only when both inputs are true; OR is true when at least one is true; XOR is true when the inputs differ; NAND and NOR are the negations of AND and OR; XNOR (equivalence) is true when the inputs match; IMPLIES (A → B) is false only when A is true and B is false; and IFF (biconditional) is true when both inputs are equal — making it identical to XNOR.
The calculator evaluates op(A,B) for all four rows, lists the full table, and counts how many rows yield TRUE versus FALSE. The donut chart visualizes that TRUE/FALSE split. Because the domain is finite and discrete, there are no rounding or unit concerns; every operator produces an exact, deterministic 4-row table.
Frequently asked questions
With two boolean variables, each can be TRUE or FALSE, giving 2 × 2 = 4 distinct combinations. More generally n variables produce 2ⁿ rows.
The biconditional (IFF) is true exactly when both operands have the same truth value, which is precisely the definition of XNOR (negated exclusive-or). They are logically equivalent.
A → B is false only in the single case where A is TRUE and B is FALSE. In all other rows it is TRUE, including when A is FALSE (vacuously true).
Also known as
TG we-Calculate Editorial Team. (2026). Boolean Truth Table Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/truth-table-calculator
TG we-Calculate Editorial Team. "Boolean Truth Table Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/truth-table-calculator.
TG we-Calculate Editorial Team, "Boolean Truth Table Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/truth-table-calculator
@misc{wecalculate_truth_table_calculator, title = {Boolean Truth Table Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/truth-table-calculator}}, year = {2026}, note = {TG we-Calculate} }
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