In any digital electronics textbook you will find description on various logic operations and different logic gates; e.g. AND, OR, NOT, NAND, NOR, XOR and XNOR. But AND, OR and NOT these three gates are known as basic gates. Because you can design any other logic gates or digital electronics circuits using only these three gates.
Suppose you are about to design a logic circuit where you need two XOR gates and three NAND gates. You don’t have those gate ICs in hand. But you have enough AND, OR and NOT gate ICs, then you can easily use those three gates to design your circuit.
In simple words you will design XOR gate and NAND gate using AND, OR and NOT gates. Then you can use those gates in your main circuit.
Actually it’s like elements, there are numerous compounds in our world but all consists of only 118 elements like oxygen, carbon, hydrogen, nitrogen, sulfur etc.
Not to be confused with NAND and NOR gate. Those two are known as universal logic gates.
Let’s see how we can design other logic gates using only basic gates, i.e. AND, OR and NOT gate.
NAND gate from basic gates
By definition when a NOT gate is placed on AND gate output that is NAND gate. So it very simple:
Which is expressed as below:
NOR gate from basic gates:
It’s same as above.
So now we can say NAND gate and NOR gate can be designed from basic gates. So any gate or other circuits designed using NAND or NOR gate can be designed using only three basic gates.
Exclusive OR or XOR gate from basic gates:
The digital circuit above is actually a XOR gate circuit, which is expressed as below:
Let’s analyze the circuit (i). We consider all possible input logic combinations of the circuit.
From the truth table above we can see that the output is same as XOR gate truth table. To know more about XOR gate please go to XOR gate section.
XNOR gate from basic gates:
I am not discussing in detail about XNOR gate because it’s simply adding a NOT gate to XOR gate output and NOT gate is one of the three basic gates.