# Boolean Logic and Electronic Logic Gates

In digital electronics, *Boolean logic *refers to the manipulation of binary values in which a 1 represents the concept of *true *and a 0 represents the concept of *false*.

In electronic circuits that implement logic, binary values are represented by voltage levels. In the most common convention, a binary value of one is represented by +5 V (also called *HIGH*), and a binary zero is represented by 0 V (also called *LOW).*

This type of logic is called *Boolean *because it was invented in the 19th century by George Boole, an English mathematician and philosopher. In 1854, he published a book titled *An Investigation of the Laws of Thought, *which laid out the initial concepts that eventually came to be known as Boolean algebra, also called Boolean logic.

Boolean logic is among the most important principles of modern computers. Thus, most people consider Boole to be the father of computer science.

In Boolean logic, *true *is represented by the binary digit 1 and *false *by the binary digit 0. *Logical operations* (also called *logical functions)* are functions that can be applied to one or more logic inputs and produce a single logic output.

One of the most common types of logic operations is NOT, which simply inverts the state of its input. In other words, with the NOT operation, if the input is true, the output is false; if the input is false, the output is true.

A *gate* is a circuit or device that implements a logical function. Thus, a NOT gate is a circuit or device that implements the logical NOT operation. NOT gates are very common in digital circuits.

You can create gate switches in a variety of ways. The most common method uses transistors as switches, arranged in such a way that the correct output is generated based on the logical inputs and the type of gate being implemented.

Regardless of the method used to create gate circuits, all logic circuits depend on different voltage ranges to represent 1 and 0. As I’ve already mentioned, the most common voltage convention is to represent 1 by approximately +5 V and 0 by approximately 0 V. The +5 V signal is usually referred to as *HIGH,* and the 0 V signal is usually called simply *LOW.*

Seven of the most common types of logic gates are: NOT, AND, OR, NAND, NOR, XOR, and NXOR. All these gates except NOT use at least two inputs; the NOT gate has just one input.

Gate | Description |
---|---|

NOT | Inverts the input (HIGH becomes LOW, LOW becomes HIGH) |

AND | Outputs HIGH if all the inputs are HIGH; otherwise, outputs LOW |

OR | Outputs HIGH if at least one of the inputs is HIGH; otherwise, outputs LOW |

NAND | Outputs HIGH if all the inputs are LOW; otherwise, outputs LOW |

NOR | Outputs HIGH if at least one of the inputs is LOW; otherwise, outputs LOW |

XOR | Outputs HIGH if one, and only one, of the inputs is HIGH; otherwise, outputs LOW |

NXOR | Outputs HIGH if one, and only one, of the inputs is LOW; otherwise, outputs LOW |