Truth table generator

A truth table lists a logic function's output for every possible combination of its inputs. Type a boolean expression and get its complete truth table, one row for every combination of inputs. It understands the words AND, OR, NOT, and XOR, plus NAND and NOR, and the usual symbols (&, |, +, !, ~, ^, a middle dot, and a trailing prime for NOT). It runs entirely in your browser, with no sign-up.

How to use it

Type an expression into the box (or click one of the example chips) and the table updates as you type. Use single letters A to H for the inputs. The tool finds which variables you used, sorts them, and enumerates every combination: two variables give four rows, three give eight, four give sixteen, and so on, up to eight variables.

You can write operators as words or as symbols, and mix them freely. These all mean the same AND: A AND B, A & B, A * B, and A · B. NOT can be a word (NOT A), a prefix symbol (!A or ~A), or a trailing prime (A', and (A + B)' for the whole group). When you are unsure how an expression will be grouped, add parentheses: they always win.

Worked example: A XOR B

Exclusive OR (XOR) is 1 when its two inputs differ and 0 when they are the same. With two inputs A and B there are four rows. The first variable, A, is the most significant bit, so the rows count up in binary from 00 to 11:

The middle two rows (A and B different) are 1, and the outer two rows (A and B equal) are 0. That is exactly what an XOR gate does, and it is the heart of a half adder: the sum bit of A plus B is A XOR B, while the carry is A AND B.

Accepted syntax and operator precedence

Operators, with every spelling the tool accepts:

• NOT: NOT A, !A, ~A, or a trailing prime A'
• AND: AND, &, *, or a middle dot ·
• OR: OR, |, or +
• XOR: XOR or ^; XNOR as the word XNOR
• NAND and NOR as words, read as NOT(A AND B) and NOT(A OR B)
• Grouping: parentheses ( )
• Variables: single letters A to H (lowercase is treated the same)

Precedence runs from highest (binds tightest) to lowest like this. Binary operators are left-associative. When in doubt, parenthesize.

NOT  >  AND  >  XOR / XNOR  >  OR  >  NOR  >  NAND

So A OR B AND C reads as A OR (B AND C), because AND binds tighter than OR. Writing two operands side by side, like AB or A B, is read as an implicit AND (A AND B). It is convenient, but for anything non-trivial an explicit operator is clearer, so prefer A AND B and reach for parentheses whenever the grouping is not obvious.

Frequently asked

What syntax does the truth table generator accept?

Use the words AND, OR, NOT, XOR, NAND, NOR, or the symbols and (&), or (| or +), not (! or ~ or a trailing prime), xor (^), and a middle dot or star for and. Group with parentheses. Variables are single letters A to H.

How many rows does a truth table have?

Two to the power of the number of input variables. Two variables give four rows, three give eight, four give sixteen, and so on, one row for every combination of inputs.

What is the truth table for A XOR B?

Exclusive OR is 1 when the inputs differ. A=0 B=0 gives 0, A=0 B=1 gives 1, A=1 B=0 gives 1, and A=1 B=1 gives 0.