HesapHanem

Truth Table Generator

Enter a boolean expression and its variables to build the truth table.

Result

A B C | R --------- 0 0 0 | 0 0 0 1 | 0 0 1 0 | 1 0 1 1 | 0 1 0 0 | 1 1 0 1 | 0 1 1 0 | 1 1 1 1 | 0
3 variables
8 rows

How it is calculated

The tool accepts the variables A, B and C only (up to three), so a table has 2n rows: 2, 4 or 8. Write the expression with the words AND, OR, NOT, XOR or the symbols &, |, !, ^, plus parentheses; case does not matter. Precedence from strongest to weakest is NOT, then AND, then XOR, then OR, so A XOR B AND C means A XOR (B AND C) while A XOR B OR C means (A XOR B) OR C. If the variables box is empty, the tool uses whichever of A, B, C appear in the expression. Rows count up in binary with A as the leftmost, most significant bit, and the column R shows the result, 1 for true and 0 for false. The tool also reports the number of variables and rows. Any other letter, operator or symbol, or a syntax error such as an unmatched bracket, makes the tool return nothing.

Worked example

Expression (A OR B) AND NOT C with variables A, B, C gives 3 variables and 8 rows. The result is true only when at least one of A or B is true and C is false. Row 0 0 0: (false OR false) AND true = 0. Row 0 1 0: (false OR true) AND true = 1. Row 1 1 1: true AND false = 0. Reading R from top to bottom the table is 0, 0, 1, 0, 1, 0, 1, 0: the table shows 3 variables and 8 rows.

Try this example →

Common mistakes

  • Using a fourth variable or letters beyond A to C, such as X and Y. Only A, B and C are recognised, and an expression using other letters returns nothing.
  • Assuming XOR binds as tightly as AND or as loosely as OR. It sits between them: A XOR B AND C is A XOR (B AND C), but A XOR B OR C is (A XOR B) OR C. When in doubt, write the brackets you mean.
  • Using operators that are not supported, such as NAND, NOR, -> or =. Build them from AND, OR and NOT, for example NOT (A AND B) for NAND.
  • Reading the rows in the wrong order. A is the first column and changes slowest, so 0 0 1 means A false, B false, C true.
  • Leaving a bracket unclosed or putting two operators in a row, such as A AND OR B. A syntax error produces no table at all.

About this calculator

A truth table lists every possible combination of true/false values for a boolean expression's variables alongside the resulting output, giving a complete and unambiguous definition of the expression's logic — for n variables there are exactly 2^n rows, so a 3-variable expression (A, B, C) produces 8 rows covering every possible input state.

This generator evaluates expressions built from AND, OR, NOT and XOR (accepting either the words or the symbols &, |, !, ^) and fills in every combination automatically. Truth tables are the basic verification tool in digital logic design and computer engineering — used to check that a circuit or boolean condition behaves as intended, to simplify expressions with Karnaugh maps, and to prove logical equivalence between two different-looking expressions.

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Comments (1)

  • Editorial team

    The tool is handy for proving two expressions are the same: run each one and compare the R columns row by row. NOT (A AND B) and NOT A OR NOT B both give 1, 1, 1, 0 for the rows 00, 01, 10 and 11, which is De Morgan's law in action. Matching columns over every row is a full proof for up to three variables. Which simplification or equivalence are you trying to confirm?

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