Type a logic expression to get its truth table, its simplest forms, and a Karnaugh map.

Expression

Examples

Truth Table

Simplest Forms

Karnaugh Map

Operators

Any of these spellings work. Click one to add it to the expression.

Operators, Tightest First

: NOT¬p !p ~p not p p′
: ANDp ∧ q p & q p && q p and q p · q (p)(q)
: NAND, not bothp ↑ q p nand q
: XOR, one or the other but not bothp ⊕ q p ^ q p xor q
: ORp ∨ q p | q p || q p or q p + q
: NOR, neitherp ↓ q p nor q
: Implies: false only when p is true and q is false. Groups to the right, so p → q → r is p → (q → r).p → q p -> q p => q p implies q
: If and only if, XNOR: true when both sides matchp ↔ q p <-> q p iff q p == q p xnor q

Values and Names

: True. Also true, ⊤0, false, and ⊥ are false
: Variables are letters, optionally followed by letters, digits, or underscores, like x1 or ready. With Letters Multiply on, each letter is its own variable and AB means A AND B.
: Parentheses group. Two groups side by side multiply: (A + B)(A + C).

About the Truth Table Generator

Builds the truth table for a logic expression, with a column for each step, and works out its minterms and maxterms, its simplest sum-of-products and product-of-sums forms, and its Karnaugh map.

Every Setting

Expression

Type it with symbols (¬ ∧ ∨ ⊕ → ↔), words (not, and, or, xor, implies, iff), or code (! && || ^). The row of buttons and the Operators drawer add symbols that are hard to type. Up to 12 variables. The line under the box shows how it was read, with every group in parentheses, so you can check the order the operators apply in.

Values

Show the table in 1 and 0 or in T and F.

Row Order

False First counts up in binary from all 0s, which matches minterm numbers and digital logic courses. True First starts from all true, as most discrete math books do.

Formulas As

How the simplest forms and the step columns are written: logic symbols, Boolean algebra with primes and + (A′B + C), or code (!a && b).

Show Each Step

A column for every part of the expression, innermost first, so the table shows the working. Turn it off for just the variables and the result.

Letters Multiply

Reads AB as A AND B and A′ as NOT A, the way digital logic writes it. Every variable is then one letter, optionally followed by digits.

Simplest Forms

The minimal sum of products (DNF) and product of sums (CNF), found exactly with the Quine–McCluskey method for up to 10 variables, plus the full canonical forms built from every minterm and maxterm.

Karnaugh Map

For 2 to 4 variables, laid out in Gray code order so neighbors differ in one variable. Each colored ring is one group from the minimal sum of products; a group of 2, 4, or 8 cells drops 1, 2, or 3 variables. Point at a term to light up its cells.

Copy / Download CSV

The table as tab-separated text that pastes into a spreadsheet or document, or as a CSV file.

Common Questions

Why is p → q true when p is false?

An implication only promises something when p is true. When p is false the promise is not broken, so the statement counts as true. It is false on one row only: p true and q false.

What makes an expression a tautology?

It is true on every row, whatever the variables are. The summary says when that happens; a contradiction is false on every row.