Basic Gates

There are 5 basic gates used in performing logic operations in Digital Electronic namely BUFFER gate, NOT gate, AND gate, OR gate, XOR gate . Each Logic Gate has A Symbol for easy to identify , a Mathematical Expression to identify mathematic logic operation and a Truth Table to completely describe operation of the Logic Gate

Five Basic Logic Gates

Digital gates	Symbol	Logic Operation	Mathematic Expression
BUFFER		Y = BUFFER A	Y = A
NOT		Y = NOT A	Y = ${\displaystyle {\bar {A}}}$
AND		Y = A AND B	Y = A . B
OR		Y = A OR B	Y = A + B
XOR		Y = A XOR B	Y = ${\displaystyle {A\oplus B}}$

The Truth Table of the five basic logic gates above

A	B	Q = A	Q = NOT A	Q = A AND B	Q = A OR B	Q = A XOR B
0	0	0	1	0	0	0
0	1	0	1	0	1	1
1	0	1	0	0	1	1
1	1	1	0	1	1	0

Complement of Basic Logic gates

Basic Gates	Combination Gates	Symbol	Mathematical Expression
BUFFER			Q = is NOT NOT A Y = A
NOT			Y = is NOT A
NAND			Q = NOT A AND B
NOR			Y = NOT A OR B
XNOR			Q = NOT A XOR B

The Truth table of the combination gates above

A	B	Q = A	Q = NOT A	Q = A NAND B	Q = A NOR B	Q = A XNOR B
0	0	0	1	1	1	1
0	1	0	1	1	0	0
1	0	1	0	1	0	0
1	1	1	0	0	0	1

Summary

Gates	Function	Symbol
		ANSI	IEC
Buffer	${\displaystyle Q=A}$
NOT gate (Inverter)	${\displaystyle Q={\overline {A}}}$
AND gate	${\displaystyle Q=A\cdot B}$
NAND gate (NOT−AND)	${\displaystyle Q={\overline {A\cdot B}}}$
OR gate	${\displaystyle Q=A+B}$
NOR gate (NOT−OR)	${\displaystyle Q={\overline {A+B}}}$
XOR gate (Exclusive-OR)	${\displaystyle Q=A\oplus B}$
XNOR gate (NOT−exclusive−OR)	${\displaystyle Q={\overline {A\oplus B}}}$

A	B	Q = A	Q = NOT A	Q = A AND B	Q = A OR B	Q = A XOR B	Q = A NAND B	Q = A NOR B	Q = A XNOR B
0	0	0	1	0	0	0	1	1	1
0	1	0	1	0	1	1	1	0	0
1	0	1	0	0	1	1	1	0	0
1	1	1	0	1	1	0	0	0	1