Quick questions on Truth tables and combinational logic explained: O-Level Electronics Digital Electronics

For $n$ inputs there are $2^n$ combinations: two inputs give $4$ rows, three inputs give $8$ rows. Always list them in standard binary counting order ($00, 01, 10, 11$ for two inputs) so that no combination is forgotten and the table is easy to check.

The reliable method is to add a column for the output of each gate inside the circuit:

The Boolean expression is built the same way, from the inputs outward. Replace each gate with its operator: AND becomes a dot, OR becomes a plus, NOT becomes a bar, and use brackets to show which signals feed which gate. For example, an AND fed by $\bar{A}$ and $B$ gives $Q = \bar{A} \cdot B$. The expression and the truth table describe the same circuit in two languages.