🔹 What is Karnaugh Map (K-Map)?
A Karnaugh Map (K-Map) is a graphical method used for simplifying Boolean algebra expressions without using algebraic theorems. It helps reduce logical expressions to their simplest form using visual grouping of 1’s in a truth table.
👉 In Hindi: Karnaugh Map ek tarika hai jisse hum Boolean expressions ko asaani se simplify kar sakte hain. Isme hum truth table ke 1s ko group karke minimal logic function nikalte hain.
🧩 Why Use K-Map?
- To simplify complex Boolean expressions.
- To reduce number of logic gates in circuits.
- To design efficient combinational logic (like adders, multiplexers, etc.).
📘 Types of K-Maps
- 2-variable K-map: For expressions with A and B.
- 3-variable K-map: For expressions with A, B, C.
- 4-variable K-map: For expressions with A, B, C, D.
- 5-variable or 6-variable: Used in digital design using software tools.
🔸 Example 1: 2-Variable K-Map Simplification
Given Boolean function: F(A,B) = Σ(1,3)
| A\B | 0 | 1 |
|---|---|---|
| 0 | 0 | 1 |
| 1 | 0 | 1 |
Here, cells (A=0,B=1) and (A=1,B=1) contain 1s. They can be grouped together vertically.
Hence Simplified Expression: F = B
Hindi: Dono 1s column “B=1” mein hain, to simplified result B hai.
🔸 Example 2: 3-Variable K-Map Simplification
Given: F(A,B,C) = Σ(1,3,5,7)
| AB\C | 0 | 1 |
|---|---|---|
| 00 | 0 | 1 |
| 01 | 0 | 1 |
| 11 | 0 | 1 |
| 10 | 0 | 1 |
All 1s appear in the column C=1, so expression simplifies to F = C.
Hindi: Yahan sabhi 1s “C=1” column mein hain, isliye output C hai.
🔸 Example 3: 4-Variable K-Map
F(A,B,C,D) = Σ(0,2,8,10)
Group cells (0,2) and (8,10): they differ in C,D only → Combine horizontally.
Final Simplified Expression: F = A'B'
Hindi: Yahan grouping ke baad sirf A'B' bachta hai, jo final output hai.
🧮 Interactive K-Map Simulator
Click cells below to toggle 1/0 values and see simplification result:
📙 Applications of Karnaugh Map
- Used in designing Digital Circuits such as adders, multiplexers, decoders.
- Helps in reducing logical expressions for microcontrollers and FPGA circuits.
- Used in computer architecture and embedded systems optimization.
💡 Quick Summary
- K-Map reduces Boolean expressions graphically.
- Groups of 1s (1,2,4,8 cells) form simplified terms.
- Useful for designing minimal and efficient logic gates.
