NAND Gate: The Universal Logic Gate
A NAND gate is “universal” because any fundamental logic gate can be constructed using only combinations of NAND gates.
1. NOT Gate
Created by connecting both inputs of a single NAND gate together.
Output = A ⋅ A = A
2. AND Gate
A NAND gate followed by a NAND-based NOT gate (Inverter).
Output = A ⋅ B = A ⋅ B
3. OR Gate
Invert inputs A and B using NAND gates, then feed them into a third NAND gate.
Output = A ⋅ B = A + B
4. NOR Gate
Constructed by adding a NAND-based NOT gate to the output of an OR gate.
Output = A + B
5. XOR Gate (4 NAND Gates)
Uses four NAND gates to produce a HIGH output only when inputs differ.
Output = A ⊕ B = AB + AB
6. XNOR Gate (5 NAND Gates)
The inverse of XOR; constructed by adding a NOT gate to the XOR output.
Output = A ⊕ B = AB + AB
* Note: In Boolean algebra, the bar above a variable represents the NOT operation.
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