Truth Table Generator (Boolean)

A truth table is the honest way to check a piece of logic: every combination of inputs, one row each, nothing assumed. Writing one out by hand stops being fun at three variables and becomes error-prone at four. Type the expression here and every row appears at once.

It reads the notation you already use, whether that is a textbook'sA AND NOT B, a programmer's !a && b or a digital-electronics A'B + AB'. Alongside the table you get the minterms and maxterms, the canonical sum-of-products and product-of-sums forms, and a verdict on whether the expression is always true, never true or somewhere in between.

Worked Example: a Two-Way Multiplexer

The page opens on (A AND B) OR (NOT A AND C), the logic of a 2-to-1 multiplexer: when A is 1 the output follows B, and when A is 0 it follows C. The tool reads it back as A ∧ B ∨ ¬A ∧ C and finds it true on 4 of the 8 rows, which gives mintermsΣm(1, 3, 6, 7), maxterms ΠM(0, 2, 4, 5) and the canonical form A'B'C + A'BC + ABC' + ABC.

Tick Show step columns to add a column for each piece of the expression (A ∧ B, ¬A, ¬A ∧ C), which is the part teachers ask students to show. T / F switches the table from 1 and 0, and Copy Table (CSV) pastes straight into a spreadsheet.

Input Format: Words, Symbols and Shorthand

• NOT: NOT, !, ~, ¬ or a trailing apostrophe, so (AB)' is NOT (A AND B).
• AND: AND, &&, &, *, ·, ∧, or simply writing two terms side by side: AB and (A + B)(A + C) both work.
• OR: OR, ||, +, ∨. XOR: ^ or ⊕. Also NAND, NOR, implication -> and biconditional <->.
• Precedence, tightest first: NOT, AND, XOR, OR, implication, biconditional. Implication groups to the right, so A -> B -> C means A → (B → C).
• Variables are single letters, case-insensitive, and the constants are 0, 1, TRUE and FALSE. An unknown symbol stops with a message naming its position, such as “Unexpected character “#” at position 3.”

What Happens When Two Expressions Differ

Fill in Compare with and both expressions are evaluated over the combined set of variables. If every row agrees, they are logically equivalent, which is how De Morgan's law or the distributive law in the samples are confirmed. If not, the first row where they disagree is highlighted in red and spelled out: forA -> B against its converse B -> A, row 1 (A=0, B=1) gives 1 and 0.

Tables go up to 8 variables, which is 256 rows. The written-out SOP and POS forms appear up to 5 variables, where they are still short enough to read; the minterm and maxterm lists cover every size. At most 12 step columns are shown, the outermost ones. Simplifying an expression to its smallest form is a separate job for a Karnaugh map.