Boolean Logic is the brain of the computer. It helps machines make decisions using binary values (0 and 1). In this post, we will explore logic gates, truth tables, and De Morgan’s laws — the backbone of computer circuits.
🔹 What is Boolean Logic?
Boolean logic is a form of algebra in which all values are reduced to either TRUE (1) or FALSE (0). It's widely used in computer science, programming, and circuit design.
🔌 Basic Logic Gates
1. NOT Gate (Inverter)
- It inverts the input.
- Input: A → Output: ¬A
| A | NOT A |
|---|---|
| 0 | 1 |
| 1 | 0 |
2. AND Gate
- Output is 1 only if both inputs are 1.
- Output: A ∧ B
3. OR Gate
- Output is 1 if at least one input is 1.
- Output: A ∨ B
🔐 Derived Gates
4. NAND Gate (NOT + AND)
- Output is 0 only when both inputs are 1.
- Output: ¬(A ∧ B)
5. NOR Gate (NOT + OR)
- Output is 1 only when both inputs are 0.
- Output: ¬(A ∨ B)
6. XOR Gate (Exclusive OR)
- Output is 1 if inputs are different.
- Output: A ⊕ B
📊 Truth Table for All Logic Gates
| A | B | NOT A | AND | OR | NAND | NOR | XOR |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |
🧠 De Morgan’s Laws
These laws are useful for simplifying Boolean expressions and designing circuits:
- Law 1: ¬(A ∧ B) = ¬A ∨ ¬B
- Law 2: ¬(A ∨ B) = ¬A ∧ ¬B
These laws convert NAND/NOR expressions into simpler AND/OR/NOT combinations.
⚙️ Logic Circuits (Introduction)
Logic circuits are visual representations of Boolean expressions using logic gates. Each gate performs a function based on the inputs, helping in processing data at the hardware level.
- Simple Circuit: A AND B
- Complex Circuit: (A AND B) OR (¬C)
Practice drawing circuits with combinations of gates using truth tables.
📝 Summary
- Boolean logic uses binary inputs and logical operations.
- Basic gates: AND, OR, NOT; Derived gates: NAND, NOR, XOR
- Truth tables help visualize gate behavior.
- De Morgan’s laws are used to simplify Boolean expressions.
💡 Pro Tip: Use digital logic simulators (like Logisim) to experiment with gates and circuits!
Keep learning — logic today, innovation tomorrow! 🔍💻