Lesson 0111: What is a truth table?

In evaluating and simplifying boolean expressions, it becomes difficult to see the final possible outcomes of the expression just by examining it. Truth tables are an efficient way to move step by step through an expression to see the eventual outcomes. You will see in later lessons that truth tables are also helpful for organizing data to look for patterns and creating expressions.

For instance, in Lesson 8, you will see each boolean operator in a truth table. Let's use the AND operator as an example. To create a truth table, first you must show each of the possible inputs. The possible inputs for the AND operator are A and B, because it is a binary operator.

Notice how the inputs were numbered downward. The possible combinations, because there are two inputs, is 4 (2 squared). Also notice that if there were no space between the A and B, the numbers would be the equivalent of the binary numbers 0-3. When you move into larger numbers of inputs, the inputs should be represented in this same manner. All the inputs should make binary numbers starting at 0 and going through the number of cominations minus 1.

Now, we must evaluate each of these combinations to get our results.

In this example, the truth table wasn't very helpful. It does, however, illustrate the AND operator and its results. It also shows how to construct a truth table. As you procede through the next few lessons, you will notice that truth tables will get more complicated, but there will be more instruction when we get to that point.

Construct a truth table for A+B. A basic skeleton is constructed for you, just fill in the letters and numbers in the appropriate boxes.

 | |
---+---+-----
 | | 
 | | 
 | | 
 | |