Introduction to boolean gates in digital circuits

There are three basic boolean gates:

• AND
• OR
• NOT

They perform multiple, addition and inverse of the input, respectively.

We can represent Boolean Gates with simple switches:

AND Gate

OR Gate

NOT Gate

Logic Gates Symbols

The bubble in the NOT gate represents the inversion of signals. If the signal is 1 then the output will be inverted and it will be 0. Keeping this in mind we can make more gates like NAND and NOR gate:

NAND and NOR Gate

Let&s take NAND gate, this is the combination of AND and NOT gate:

nand_gate_circuit.svg

NAND Gate representation with basic boolean gates

There is one more gate to mention, it is the Excusive-OR gate or XOR gate, it has 1 as output if only one of inputs is 1. And XOR gate with inverter is the the XNOR Gate:

XOR and XNOR Gate

We can combine these gates to implement any boolean function. For example, let’s implement A.B + (~C):

In real life, we get integrated circuits that are implemented with these gates. For example, there is a 7400 series integrated circuits. One of the IC have 4 two-input NAND Gates. The pin diagram is as follows:

Source: https://en.wikipedia.org/wiki/7400-series_integrated_circuits#/media/File:TexasInstruments_7400_chip,_view_and_element_placement.jpg

There are other special integrated circuits also that are available that has special functions. We can use these ICs to connect and create more complex functions like Decoders, Encoders, Multiplexers, Adders, etc.