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Karnaugh maps

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Karnaugh maps

  1. 1. KARNAUGHKARNAUGH MAPSMAPS (K MAPS)(K MAPS) DLD FINAL PROJECT PRESENTATION Course supervision by: SIR HAQ NAWAZ LASHARI
  2. 2. GROUP MEMBERS 1. MOIN ALI SHAH (14CS27) 2. MUDASIR NAZAR (14CS28) 3. UMERFAROOQ (14CS73)
  3. 3. KARNAUGH MAPS • Karnaugh maps, or K-maps, are a lot used to simplify logic problems with 2, 3 or 4 variables. BA For the case of 2 variables, we form a map consisting of 22 =4 cells as shown in Figure A B 0 1 0 1 Cell = 2n ,where n is a number of variables 00 10 01 11 A B 0 1 0 1 A B 0 1 0 1 BA BA AB BA+ BA + BA+ BA + Maxterm Minterm 0 2 1 3
  4. 4. KARNAUGH MAPS • 3 variables Karnaugh map CBA ABAB CC 00 01 11 10 0 1 CBA CAB CBA CBA BCA ABC CBA 0 2 6 4 531 7 Cell = 23 =8
  5. 5. KARNAUGH MAPS • 4 variables Karnaugh map ABAB CDCD 00 01 11 10 00 01 11 10 5 3 1 7 62 0 4 9 15 13 11 1014 12 8 Cell = 24 =16
  6. 6. KARNAUGH MAPS • The Karnaugh map is completed by entering a ‘1‘(or ‘0’) in each of the suitable cells. • Within the map, adjacent cells containing 1's (or 0’s) are grouped together in twos, fours, or eights.
  7. 7. EXAMPLE A B Y A B Y 0 0 0 0 1 1 1 0 1 1 1 1 2-variable Karnaugh maps are small but can be used to present the methods you need to learn. The map for a 2-input OR gate looks like this: A B 0 1 0 1 1 11 BB AA A+BA+B
  8. 8. EXAMPLE AA BB CC YY 00 00 00 11 00 00 11 11 00 11 00 00 00 11 11 00 11 00 00 11 11 00 11 11 11 11 00 11 11 11 11 00 CA CAB + B ABAB CC 00 01 11 10 0 1 1 1 1 1 1
  9. 9. DOYOU MEAN 00,01,11,10 IN ITS PLACE OF 00,01,10,11? • If so, it's because in the first sequence, each entry differs in only one bit whereas in the second sequence the transition from 01 to 10 changes two bits which produces a race condition. In asynchronous logic, nothing ever happens at the same time, so 01 to 10 is either 01 00 10 or 01 11 10 and that causes problems. • References: http://stackoverflow.com/questions/9047009/why-k-map-has-states-in-sequence • Just for remember: 3d example
  10. 10. THANKS!THANKS!

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