Lecture 6

Karnaugh Map

Logic Reduction Using Karnaugh Map

• Create a Karnaugh Map• Circle (2, 4, 8..) 1’s. • OR the minterm generated by each

loop

Setting Up Karnaugh Map

Karnaugh Map for 2-Variables

3-Variables Karnaugh Map

3-Variable Karnaugh Map

Notice the order:00011110(outputs)

Karnaugh Map for 4-Variables

Example 1

𝑂𝑢𝑡𝑝𝑢𝑡=𝐵𝐶+𝐵𝐶+ 𝐴𝐶

Example 2

𝑂𝑢𝑡𝑝𝑢𝑡=𝐵𝐶+𝐵𝐶+ 𝐴𝐶

Home Alarm Example

Notation

𝐹 (𝑥 , 𝑦 ,𝑧 )=Σ(2,3,4,5)

Looping

• Groups of Two• Groups of Four• Group of Eight

Looping Groups of Two

Looping Groups of Four

Looping Groups of Eight

Problem 1

Solution to Problem 1

Problem 2

Solution to Problem 2

Problem 3

Solution for Problem 3

Two Equally Valid Solutions