As u can see the most basic gate of these is Not gate because it only 1 path for its input and 1 for its output. We should know that 1 is called as "high" in electronic language i.e. approx +5V while 0 is called as "low" which is 0V or neutral.
NOT gate depends on single input that if we give low input, a high output results whereas if we give a high input, a low output results.
AND gate has 2 inputs and a single output. Actually AND gate works on the principle of multiplication(binary). You can easily understand it using truth table.
OR gate has also 2 inputs and a single output. But OR gate works on the principle of addition(binary). You can understand it easily using truth table.
NAND and NOR gates are just opposite to the AND and OR gates respectively. Actually NAND and NOR gates are the combination of (AND and NOT) gate and (OR and NOT) gate respectively. That's why their working is just opposite to their respective logic gates. You can understand it easily using truth table.
Exclusive OR (XOR) gate is some what a different type of gate in which a high output results if one and only one of the inputs to the gate is high other wise a low output results. You can also understand it easily using truth table.
Exclusive NOR (XNOR) can be easily defined as it is a gate which is opposite to XOR gate. You can also understand its working easily using truth table.
Note: NAND gate is also known as "universal gate" because we can make any logic gate using NAND gate.
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