This document discusses Karnaugh maps, which are grids that allow finding the simplest algebraic expression for a truth table. It outlines the steps for Karnaugh mapping as sketching the grid, filling in the truth table values, circling groups of 1s starting with the largest, and writing an equation using the circles. Examples of mapping different functions are provided.

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]