Digital Logic

Truth Tables

In true digital logic a component can be in one of two states: on or off. If it is on a voltage of (usually) 5V is present across the component, if off the voltage is nominally zero, though it never quite attains that. The way to achieve this is through a logic device, and this is commonly a gate or chain of gates. Logic gates can be ready purchased in the form of integrated circuits. We can analyse the behaviour of any logic gate by constructing a truth table, which is a grid listing all possible input combinations and then the resulting output. Let us begin then with the following circuit for which we shall construct a truth table:

Step 1: The conditions that produce (in red) a zero output and therefore a zero input to the Xor gate, input x. In black, those that produce a logic condition 1.

Step 2: Adding in all the possible combinations of A, B, and C. Now remember, the output condition of A and B is the input condition x of the Xor gate. The truth table we worked out for the Xor gate tells us that when conditions to both inputs are equal, we get logic condition 0 as the output. We have made the red print here equal to 0, and the black to 1. It is now a simple matter to compare and insert our final output conditions: where the inputs are the same put logic zero and where not put logic 1, and you get the table shown below:

Step 3: The finished table.

By breaking down like this any size of logic circuit can be quickly analysed, and any branch that flows into any other can be broken down into the constituent parts. Truth tables can be used to quickly "see" the path of a decision making circuit under any circumstance.