# What is a Truth Table?

The **Truth Table** is used to simplify boolean equations obtained from digital circuits. It can have many columns, but all tables operate in the same way. There is always an ouput column (last column on the right side) that represents the result of all possible combinations of the inputs.

The total number of columns in a truth table is the sum of the inputs + 1 (the exit column). The number of rows of the truth table is the number of combinations that can be achieved with the inputs and it is equal to 2^{n}, where n is the number of columns in the truth table (with no output column)

For Example: In the following truth table there are 3 input columns, then we will have 2^{3}= 8 combinations (8 rows). A three input switches circuit (with 2 posible binary states: binary “0” or “1”), has 8 possible combinations. The output (exit column) is determined by the state of the input switches.

Logic circuits are basically an array of switches known as “logic gates” (AND gate, NAND, OR, NOR, NOT, etc.). Each of this logic gates has its truth table.

If we could see in more detail the construction of these “logic gates”, we would realize that they are built with transistors, resistors, diodes, etc.. and they are connected in a way that we obtain especific outputs for specific inputs. The widespread use of logic gates simplifies the design and the analysis of complex circuits. Modern technology allows the construction of integrated circuits (IC’s) that are composed of thousands (or millions) of logic gates.

## Example of a 2 & 3 Input NOR gate Truth Tables

Analyzing the truth table of the 2 input NOR gate and the truth table of the 3 input NOR gate, we see that the outputs of the gates are “high” or “1”, when their inputs are all “low” or “0”.