karnaugh maps

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karnaugh maps

  1. 1. Subject Name Code Credit Hours Digital Electronics and Logic Design DEL-244 3 Chapter 6 Karnaugh Maps
  2. 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. 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. 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. 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. 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. 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. 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]

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