The NOT gate performs the basic logical function called inversion or complementation. NOT gate is also called as invertor. The purpose of this gate is to convert one logic level into the opposite logic level. It has one input and one output. When a HIGH level is applied to an inverter, A LOW level appears its output and vice versa.

If X is the input, then output F can be represented mathematically as F = X', Here dot ('). denotes the NOT (inversion) operation. There are couple other ways to represent the the inversion, F= !X, here ! represents inversion. Truth table and symbol of the NOT gate is shown in the figure below.

Symbol

Truth Table

NOT gate using "transistor-resistor" logic is shown in figure below. Where X is input and F is the output.

Circuit

When X = 1, The transistor input pin 1 is HIGH, this produces the forward bias across the emitter base junction and so the transistor conducts. As the collector current flows, the voltage drop across RL increases and hence F is LOW.

When X = 0, The transistor input pin 2 is LOW, this produces no bias voltage across the transistor's base emitter junction. Thus Voltage at F is HIGH.

Buffer or BUF is also a gate, with exception that, it does not perform any logical operation on its input. Buffers just pass input to output. Buffers are used to increase the drive strength or sometime just to introduce delay. We will look at this in detail later.

If X is the input, then output F can be represented mathematically as F = X. Truth table and symbol of the Buffer gate is shown in the figure below.

Symbol

Truth Table

NAND gate is cascade of AND gate and NOT gate, as shown in figure below. It has two or more inputs and only one output. The output of NAND gate is HIGH when any one of its input is LOW (i.e. even if one input is LOW, Output will be HIGH).

NAND From AND and NOT

If X and Y are two inputs, then output F can be represented mathematically as F = ( X.Y)', Here dot (.) denotes the AND operation and (') denotes inversion. Truth table and symbol of the N AND gate is shown in the figure below.

Symbol

Truth Table

NOR gate is cascade of OR gate and NOT gate, as shown in figure below. It has two or more inputs and only one output. The output of NOR gate is HIGH when any all its inputs are LOW (i.e. even if one input is HIGH, Output will be LOW).

Symbol

If X and Y are two inputs, then output F can be represented mathematically as F = (X+Y)', Here plus (+) denotes the OR operation and (') denotes inversion. Truth table and symbol of the NOR gate is shown in the figure below.

Truth Table

An Exclusive-OR (XOR) gate is gate with two or three more inputs and one output. The output of a two-input XOR gate assumes a HIGH state if one and only one input assumes a HIGH state. This is equivalent to saying that the output is HIGH if either input X or input Y is HIGH exclusively, and LOW when both are 1 or 0 simultaneously.

If X and Y are two inputs, then output F can be represented mathematically as F = XY, Here denotes the XOR operation. XY and is equivalent to X.Y' + X'.Y. Truth table and symbol of the XOR gate is shown in the figure below.

XOR From Simple gates

Symbol

Truth Table

An Exclusive-OR (XOR) gate is gate with two or three more inputs and one output. The output of a two-input XOR gate assumes a HIGH state if one and only one input assumes a HIGH state. This is equivalent to saying that the output is HIGH if either input X or input Y is HIGH exclusively, and LOW when both are 1 or 0 simultaneously.

If X and Y are two inputs, then output F can be represented mathematically as F = XY, Here denotes the XOR operation. XY and is equivalent to X.Y' + X'.Y. Truth table and symbol of the XOR gate is shown in the figure below.

Symbol

Truth Table

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