FREE LESSON · Digital logic · 1 OF 4
Logic Gates and Truth Tables Explained
From truth table to circuit — Composition turns switches into decisions
Combinational logic maps present inputs to present outputs.
AND, OR, and NOT are sufficient to express any Boolean function; NAND or NOR alone are also functionally complete. A truth table specifies behaviour for every input combination. Algebra and circuit structure then provide implementations with different area, delay, power, and fan-out.
Logical equivalence does not imply physical equivalence: two correct circuits can have very different cost.
A multiplexer is controlled choice
A 2-to-1 multiplexer outputs A when selector S is 0 and B when S is 1: (NOT S AND A) OR (S AND B). That one pattern routes register values, chooses ALU operands, and selects the next program counter. Control is often data selection expressed in gates.
Complex datapaths are built from a small vocabulary repeated with disciplined interfaces.