We usually start the design of a digital circuit with a purpose for the circuit. From the stated purpose, we define symbols and build a truth table.  Then, from the truth table, we figure out how to put the various logic gates together to build the desired circuit.  We will study this normal design of a circuit in the next lecture.

Once a circuit has been designed, it is important to be able to check it by examining the circuit diagram and determining the truth table that it generates; the truth table can then  be compared with the desired truth table in our design.  This is a means of catching a possible mistake in the circuit design or construction.  This approach to examining a circuit by forming the truth table from the circuit diagram and answering the question “What does this circuit really do?” is called reverse design.  To help keep us from making an easy mistake in building the truth table for the circuit, we label intermediate stages of the circuit diagram between the input(s) and the output and build these labels into our truth table. The next example shows the ideas of reverse design by working with a specific circuit.