How to Find the Truth Table of a Logic Function

In logic, a truth table is a table that lists all possible values for the variables. The table provides a graphic display of the combinations of potential values for each variable, the values of each operator involved, and the value of the complete function when there is more than one operator. Typical logical operators are “AND,” “OR” and “NOT,” but there are other less common ones as well. Setting up a truth table can help to clarify how the values of each variable relate to the value of the total function.

Instructions

    • 1

      Set up the truth table for each of the variables involved in the function. If there are "n" variables in the function, there will be "n" columns for this part of the truth table, and 2ⁿ rows. For two variables there will be two columns and four rows, for three variables there will be three columns and eight rows, and so on. For each true value of the first variable, the second variable might be true or false, and likewise for each false value, and for each combination of values if there are more than two variables. Each variable will have an equal number of true potential values and false potential values.

    • 2

      Determine what logical operators are involved in the function. Set up a separate column for each of the operations to the right of the variables. There is an order of operations for logical operators, just as there is for mathematical operators. The “NOTs” are applied first, then the “ANDs,” and then the “ORs.” The other operators, if any, are applied last. As in math, equivalent operators are applied from left to right.

    • 3

      Determine the values of each operation and write them in the table in their respective rows and columns. All the variables have to be true for the operator “AND” to be true, so there would be only one true value for the “AND” operator. Any of the variables have to be true for the “OR” operator to be true, so it would have only one false value.

    • 4

      Combine the operations into the complete function if there are multiple operations. Set up a column for the complete function to the right of the variables and single operations. Compute separately the values for each combination of true and false variables and operations, and place the function values in the respective spots in the function column.

Learnify Hub © www.0685.com All Rights Reserved