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What is a Logic Gate, and what does it do?

A logic gate is a device that is used as a building block for digital circuits. They perform basic logical functions that are a basic part of digital circuits. Most electronic devices we use have some form of logic gates in them.
For example, logic gates can be used in smartphones, tablets, control circuits, and obviously computers.
In a circuit, logic gates work based on a combination of digital signals coming from its inputs. Most logic gates have two inputs and one output, and their operation is based on Boolean algebra. At any given moment, any terminal is in one of the two binary conditions: true or false. False represents 0, and true represents 1.
Depending on the type of logic gate being used and the combination of inputs, the binary output will differ. A logic gate can be thought of like a light switch, where in one position the output is off (0), and in another, it is on (1).

Typical Logic gate chips

Logic Voltage Levels in Synthedit.

The logic gate emulations in SynthEdit are similar in operation to hardware logic chips with a few additions for reliability.
1) Input pins incorporate ‘hysteresis’ to give noise-immunity.
2) An input registers ‘ON’ when the voltage exceeds 3.33, but isn’t ‘OFF’ until the voltage drops below 1.66, this helps the device to handle imperfect input signals. i.e. small errors, fluctuations or noise in a input signal.
This means they generally can’t jump the ‘grey area’ and create a false “on” or “off” signal.

The "grey area" of logic voltages.

Important note regarding logic gates:
A logic gate cannot be used for audio purposes for example- to pass audio through an OR gate when one input is high. You will just get a very distorted audio signal from the output. Although they have dark blue Audio Voltage pins we are dealing with a simple on/off (True/False) signal.

Truth table for logic gates
One method of showing how the various gates operate is a “Truth Table”.

The way I have chosen to try and make things a little easier is to show the state of the inputs and outputs with LED indicators showing the logic states:
LED Lit = 1 (true)
LED Unlit = 0 (false)

AND Gate.

The And gate gives an output of 0 unless ALL inputs are 1, when it the outputs 1.

Both inputs 0 = Output 0
One input 1, one input 0
= Output 0
Both inputs 1 = Output 1

NAND Gate

A Nand Gate is the inverse of an And Gate

Both inputs 1 = Output 1
One Input 1, one Input 0
= Output 1
Both Inputs 1 = Output 0

Or Gate.

An Or Gate gives an output of 1 if either or both inputs are 1, and a 0 if either or both inputs are 0

Both Inputs 0 = Output 0
One Input 1, One Input 0
= Output 1
Both Inputs 1 = Output 1

Nor Gate.

A Nor Gate is the inverse of an Or Gate

Both Inputs 0 = Output 1
One Input 1, One Input 0
= Output 0
Both Inputs 1 = Output 0

Logic Inverter (Not Gate)

A Not Gate gives an output of 1 if the input is 0, and an output of 0 if the input is 1.
It only has one input.

Input 1 = Output 0
Input 0 = Output 1

XOR Gate (Exclusive OR gate)

An XOR gate gives an output of 1 if either input is 1, if both inputs are 1 or 0 it outputs a 0.

Both inputs 1 = Output 0
One Input 0 = Output 1
Other input 1 = Output 0
Both Inputs 0 = Output 0