Combinational Logic Design Using Truth Tables

The following steps are a useful formal approach to combinational problems:

1. Devise a truth table of the independent input variables and the resulting output quantities.
2. Write Boolean algebra statements that describe the truth table.
3. Reduce the Boolean algebra.
4. Mechanize the Boolean statements using the appropriate logic gates.

Consider the truth table that defines the OR gate. Using the lines in this table that yield a true result gives.

Since Q is a two-state variable all other input state combinations must yield a false. If the truth table had more than a single output result, each such result would require a separate equation. An alternative is to write an expression for the false condition.