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Given a logic diagram for a combinational circuit, such as Figure 4-9, there are a number of ways to obtain a formal descripiton of the circuit's function. The most basic functional description is the truth table.
Using only the basic axioms of switching algebra, we can obtain the truth table of an n-input circuit by working our way through all 2^n input combinations. For each input combination, we determine all of the gate outputs produced by that input, propagating information from the circuit inputs to the circuit outputs.