The NAND Gate

Definition, as a combination. A NAND gate (short for 'NOT-AND') is functionally an AND gate (Section 9.27) whose single output is immediately passed through a NOT gate (Section 9.28) -- its output is, at every instant, the exact complement of what a plain AND gate, fed the same two inputs, would produce.

Symbol. The NAND-gate symbol (shown in the accompanying figure) is drawn EXACTLY like the AND-gate symbol of Section 9.27 -- flat input edge, rounded output edge -- but with a small inversion bubble added at the single output point, the identical bubble convention used for the NOT gate in Section 9.28: the bubble alone converts the AND symbol into the NAND symbol.

Truth table and Boolean equation. For two inputs $A$ and $B$, the NAND gate's truth table (shown alongside) is the row-for-row COMPLEMENT of the AND gate's own truth table (Section 9.27): output $Y=0$ only in the single row where $A=1$ AND $B=1$, and $Y=1$ in every other combination. Its Boolean equation is written

the bar drawn over the WHOLE product $A\cdot B$, showing the inversion is applied to the combined AND result, not to $A$ or $B$ individually (which would instead describe two separately inverted inputs feeding an ordinary AND gate -- a different, and much less useful, circuit). …