karnaugh maps
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Subject Name Code Credit Hours Digital Electronics and Logic Design DEL-244 3 Chapter 6 Karnaugh Maps
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Transcript of karnaugh maps
Subject Name Code Credit HoursDigital Electronics and Logic Design DEL-244 3
Chapter 6Karnaugh Maps
Subject Name Code Credit HoursDigital 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.
Subject Name Code Credit HoursDigital Electronics and Logic Design DEL-244 3
Karnaugh Mapping Steps1. 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) = Sm(2,3,4,5,7)
Subject Name Code Credit HoursDigital 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.
Subject Name Code Credit HoursDigital Electronics and Logic Design DEL-244 3
Karnaugh Mapping Steps1. 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) = Sm(1,3,5,6,7,12,13,14,15)
Subject Name Code Credit HoursDigital Electronics and Logic Design DEL-244 3
Copyright © 2005 The McGraw-Hill Companies, Inc. Permission required for
reproduction or display.
= wx + wz + wxyz= wx + w(z + xyz)= wx + w(z + xy) [P10a]
= wx + wz + wxy
= wz + x(w + wy)
= wz + x(w + y) [P10a]
= wz + wx + xy
Subject Name Code Credit HoursDigital Electronics and Logic Design DEL-244 3
Karnaugh Mapping Steps1. 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)
Subject Name Code Credit HoursDigital Electronics and Logic Design DEL-244 3
Copyright © 2005 The McGraw-Hill Companies, Inc. Permission required for
reproduction or display.
wx + wxy + wyz + wyz + wxyz
= (wx + wxy) + (wyz + wyz) + wxyz
= wx + wz + wxyz [P12a, P9a]
