A truth table is a mathematical table used in logic, specifically in connection with Boolean algebra, Boolean functions, and propositional calculus, which sets out the functional values of logical expressions on each of their functional arguments. It is a tabular representation of all the combinations of values for inputs and their corresponding outputs. A truth table has one column for each input variable and one final column showing all of the possible results of the logical operation that the table represents. Each row of the truth table contains one possible configuration of the input variables and the result of the operation for those values. Truth tables are used to reduce basic Boolean operations to simple correlations of inputs to outputs, without the use of logic gates or code.
In a truth table, each variable in the expression has a column, and each possible combination of truth values has a row. The table includes a column that shows the outcome of each set of values. Truth tables can also be used for expressions that include Boolean functions other than OR, AND, or NOT, such as the conditional (→), biconditional (↔), or XOR exclusive disjunction (⊻ or ⊕) . Truth tables are often used to map out possible combinations of logic gate input and their expected output.
Truth tables provide a method for mapping out the possible truth values in an expression and to determine their outcomes. They are especially useful when working with more complex expressions that include multiple variables and Boolean functions. Truth tables also provide a quickly recognizable characteristic "shape" of the distribution of the values in the table, which can assist the reader in grasping the rules more quickly.
