The AND Gate

Definition. An AND gate is a logic circuit with two (or more) inputs and a single output, whose output is HIGH ($1$) only when ALL of its inputs are simultaneously HIGH -- the electronic realisation of the everyday requirement 'both … and …' -- and its output is LOW ($0$) if EVEN ONE of its inputs is LOW.

Symbol. The standard AND-gate symbol (shown in the accompanying figure) has a flat, straight back edge where the input lines enter and a rounded, semicircular (D-shaped) front where the output line emerges -- distinguishing it visually from the curved-back OR-gate symbol of Section 9.26.

Truth table and Boolean equation. For two inputs $A$ and $B$, the AND gate's truth table (shown alongside) gives output $Y=1$ only in the single row where $A=1$ AND $B=1$ simultaneously, and $Y=0$ in every other combination. Its Boolean equation is written

where the '$\cdot$' (or plain juxtaposition, as in ordinary algebra) denotes the logical AND operation -- and, usefully, AND behaves exactly like ordinary multiplication of $0$s and $1$s (unlike OR's '+', which does NOT behave like ordinary addition), which is one reason the dot notation was chosen for it in the first place. …