Logic Gates: The Building Blocks of Digital Systems
Explore the fundamental logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) that form the basis of digital electronics. This guide provides a clear explanation of each gate's functionality, using truth tables and symbols, essential for understanding digital circuit design.
Logic Gates in Digital Systems
What are Logic Gates?
Logic gates are fundamental electronic circuits in digital systems. They perform basic logical operations (AND, OR, NOT, etc.) on their binary inputs (0 or 1, representing false or true), producing a binary output.
Basic Logic Gates
Seven basic logic gates are commonly used. Each gate has a unique symbol and truth table:
1. AND Gate (∧)
Outputs 1 only if all inputs are 1. The AND operation is often represented by a dot (.) or an asterisk (*) symbol.
| A | B | A ∧ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
2. OR Gate (∨)
Outputs 1 if at least one input is 1. The OR operation is often represented by a plus (+) symbol.
| A | B | A ∨ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
3. NOT Gate (¬)
Outputs the inverse of the input. Also called an inverter. The NOT operation is often represented by a prime symbol (') or a bar over the variable (¬A).
| A | ¬A |
|---|---|
| 0 | 1 |
| 1 | 0 |
4. NAND Gate (↑)
NAND (Not AND) is equivalent to an AND gate followed by a NOT gate. Outputs 0 only if all inputs are 1.
5. NOR Gate (↓)
NOR (Not OR) is equivalent to an OR gate followed by a NOT gate. Outputs 1 only if all inputs are 0.
6. XOR Gate (⊕)
Exclusive-OR. Outputs 1 if exactly one input is 1.
| A | B | A ⊕ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
7. XNOR Gate (≡)
Exclusive-NOR (or Equivalence). Outputs 1 if the inputs are the same (both 0 or both 1).
| A | B | A ≡ B |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Conclusion
Logic gates are the fundamental building blocks of digital circuits. Understanding their functionality is crucial for designing and analyzing digital systems.