Boolean logic, also known as Boolean algebra, is a branch of mathematics and a system of symbolic logic that deals with the manipulation and analysis of binary values, which can be represented as true or false, 1 or 0, or on or off.
It was introduced by the English mathematician George Boole in the mid-19th century and is the basis for digital logic and computer circuits used in modern digital technology.
Boolean logic operates with a set of logical operators that take one or more binary inputs and produce binary outputs. The most common Boolean operators are:
- AND: The output is true (1) if and only if both inputs are true. Otherwise, the output is false (0).
- OR: The output is true (1) if at least one of the inputs is true. Otherwise, the output is false (0).
- NOT: This is a unary operator that takes a single input. The output is true (1) if the input is false (0), and vice versa.
- XOR (Exclusive OR): The output is true (1) if exactly one of the inputs is true, and false (0) otherwise.
- NAND (NOT-AND): The output is the inverse of the AND operator, i.e., true (1) if at least one input is false (0), and false (0) if both inputs are true.
- NOR (NOT-OR): The output is the inverse of the OR operator, i.e., true (1) if both inputs are false (0), and false (0) if at least one input is true.
Boolean logic is used in various applications, such as computer programming, digital circuit design, and even in the context of modular synthesizers, where it can be employed to control signal routing, create complex modulation patterns, or process gate and trigger signals.
