1. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Chapter 6
Karnaugh Maps

2. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
What are Karnaugh Maps?
These are grids that all you to easily find the
simplest algebraic expression for a truth
table.
K-Maps consists of one square for each possible
minterm in a function.

3. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Karnaugh Mapping Steps
1. Sketch a Karnaugh map grid for the problem.
2. Fill in the 1’s and 0’s from the truth table.
3. Circle groups of 1’s.
 Circle the largest groups of 2, 4, 8, etc. first.
 Minimize the number of circles but make sure that every 1
is in a circle.
4. Write an equation using these circles.
Example: f(x,y,z) = m(2,3,4,5,7)

4. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Copyright © 2005 The McGraw-Hill
Companies, Inc. Permission required for
reproduction or display.
Map 2.12 x yz + x yz +
xy z + xy z + xyz.
Map 2.13 A better solution.
Map 2.14 The minimum solutions.

5. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Karnaugh Mapping Steps
1. Sketch a Karnaugh map grid for the problem.
2. Fill in the 1’s and 0’s from the truth table.
3. Circle groups of 1’s.
 Circle the largest groups of 2, 4, 8, etc. first.
 Minimize the number of circles but make sure that every 1
is in a circle.
4. Write an equation using these circles.
Example: f(w,x,y,z) = m(1,3,5,6,7,12,13,14,15)

6. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Copyright © 2005 The McGraw-Hill
Companies, Inc. Permission required for
reproduction or display.
= wx + w z + w xyz
= wx + w (z + xyz )
= wx + w (z + xy) [P10a]
= wx + w z + w xy
= w z + x(w + w y)
= w z + x(w + y) [P10a]
= w z + wx + xy

7. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Karnaugh Mapping Steps
1. Sketch a Karnaugh map grid for the problem.
2. Fill in the 1’s and 0’s from the truth table.
3. Circle groups of 1’s.
 Circle the largest groups of 2, 4, 8, etc. first.
 Minimize the number of circles but make sure that every 1
is in a circle.
4. Write an equation using these circles.
Example: Problem 1 (a-e)

8. Subject Name Code Credit Hours
Digital Electronics and Logic Design DEL-244 3
Copyright © 2005 The McGraw-Hill
Companies, Inc. Permission required for
reproduction or display.
wx + wxy + w yz + w y z + w xyz
= (wx + wxy) + (w yz + w y z) + w xyz
= wx + w z + w xyz [P12a, P9a]