DIGITAL LOGIC 201
The Intermediate Guide to Universal Gates
The Universal Gates
You've mastered the basics. Now, let's get to the really powerful stuff. In the world of digital logic, some gates are more special than others. The NAND and NOR gates are known as "universal gates." This means you can build ANY other logic gate (AND, OR, NOT, etc.) using only NAND gates or only NOR gates. This is huge for circuit design, making them incredibly efficient and important.
NAND Gate (The "Not AND")
The NAND gate is the inverse of an AND gate. It outputs a 0 only when ALL of its inputs are 1. In all other cases, it outputs a 1. Think of it as an AND gate with a NOT gate attached to its output.
Truth Table
| Input A | Input B | Output |
|---|---|---|
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 0 | 0 |
Interactive Simulation
NOR Gate (The "Not OR")
Similarly, the NOR gate is the inverse of an OR gate. It will output a 1 only if ALL of its inputs are 0. If any input is a 1, the output is 0. It's an OR gate with an inverter on the end.
Truth Table
| Input A | Input B | Output |
|---|---|---|
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 0 |
Interactive Simulation
XNOR Gate (The Equality Checker)
The XNOR (Exclusive NOR) gate is the inverse of XOR. It outputs a 1 only if its inputs are the SAME (both 0 or both 1). This makes it a great "equality gate" to check if two values are identical.
Truth Table
| Input A | Input B | Output |
|---|---|---|
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |