Boolean Algebra

Within these castle walls be forged Mavens of Computer Science ...

— Merlin, The Coder

Logic Gates

An idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output.

Research

Formal Name	Abbreviated Name	Symbol	Gate	Truth Table
Buffer				Inputs Outputs $A$ $Q=A$ 0 0 1 1
Conjunction	AND	$A\land B$		Inputs Outputs $A$ $B$ $Q=A\land B$ 0 0 0 0 1 0 1 0 0 1 1 1
Disjunction	OR	$A\lor B$		Inputs Outputs $A$ $B$ $Q=A\lor B$ 0 0 0 0 1 1 1 0 1 1 1 1
Exclusive OR	XOR	$A\oplus B$		Inputs Outputs $A$ $B$ $Q=A\oplus B$ 0 0 0 0 1 1 1 0 1 1 1 0
Inverter	NOT	$\neg A$		Inputs Outputs $A$ $Q={\overline {A}}$ 0 1 1 0
Negated Conjunction	NAND	${\overline {A\land B}}$		Inputs Outputs $A$ $B$ $Q={\overline {A\land B}}$ 0 0 1 0 1 1 1 0 1 1 1 0
Negated Disjunction	NOR	${\overline {A\lor B}}$		Inputs Outputs $A$ $B$ $Q={\overline {A\lor B}}$ 0 0 1 0 1 0 1 0 0 1 1 0
Negated Exclusive OR	NOT XOR	${\overline {A\oplus B}}$		Inputs Outputs $A$ $B$ $Q={\overline {A\oplus B}}$ 0 0 1 0 1 0 1 0 0 1 1 1