A combinational circuit produces an output from the present inputs without intentional stored state. An AND output is one only when both inputs are one. OR is one when either or both are one. XOR is one when the two inputs differ. Start with a truth table when the verbal condition is ambiguous; it forces you to consider every combination.

Consider an indicator that should light when a system is enabled and a door is open. Name the signals E and D, then write Y = E AND D. If an input is active-low, first define what its raw logic value means. A low electrical signal may represent a true physical condition, so signal naming and inversion must be explicit.

De Morgan's laws help rewrite inverted expressions: NOT(A AND B) equals (NOT A) OR (NOT B). You invert each input and swap the combining operator. This is useful when using NAND gates or interpreting active-low signals. Check the rewritten result against the original truth table rather than relying on how the symbols look.

Real logic gates have propagation delay. If multiple input paths change at different times, a brief glitch can appear even when the intended steady-state output is unchanged. A correct Boolean equation is not a timing guarantee. For actions that must occur on a defined clock edge, use a suitable sequential design and meet its timing requirements.