1. 1 Karnaugh Map Method

2. 2 0 1 2 3 Truth Table -TO- K-Map Y0101Y0101 Z1011Z1011 X0011X0011 minterm 0  minterm 1  minterm 2  minterm 3 

3. 3 Y Y XX 0 0 1 0 Y Y XX 0 0 0 1 Y Y XX 1 0 0 0 Y Y XX 0 1 0 0 2 Variable K-Map : Groups of One

4. 4 Adjacent Cells Y Y XX 1 0 1 0 Y Y XX 1 0 1 0 Z =

5. 5 Y Y XX 1 1 0 0 Y Y XX 1 0 1 0 2 Variable K-Map : Groups of Two Y Y XX 0 1 0 1 Y Y XX 0 0 1 1

6. 6 Y Y XX 1 1 1 1 2 Variable K-Map : Group of Four

7. 7 T = = Two Variable Design Example S S RR 0 1 2 3 S0101S0101 T1010T1010 R0011R0011

8. 8 3 Variable K-Map : Vertical minterm 0  minterm 1  minterm 2  minterm 3  minterm 4  minterm 5  minterm 6  minterm 7  C01010101C01010101 Y10110010Y10110010 B00110011B00110011 A00001111A00001111 AA B C 0 1 4 5 3 2 7 6

9. 9 3 Variable K-Map : Horizontal C C A B minterm 0  minterm 1  minterm 2  minterm 3  minterm 4  minterm 5  minterm 6  minterm 7  C01010101C01010101 Y10110010Y10110010 B00110011B00110011 A00001111A00001111 0 1 2 3 6 7 4 5

10. 10 3 Variable K-Map : Groups of Two C C A B 1 0 1 0 0 0 0 0 A C 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 B C 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 A B 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1

11. 11 3 Variable K-Map : Groups of Four C C A B 1 1 1 1 0 0 0 0 A 0 0 0 0 1 1 1 1 A 0 0 1 1 1 1 0 0 B 1 1 0 0 0 0 1 1 B 1 0 1 0 1 0 1 0 C 0 1 0 1 0 1 0 1 C

12. 12 3 Variable K-Map : Group of Eight C C A B 1 1 1 1 1 1 1 1 1

13. 13 Simplification Process 1. Construct the K-Map and place 1’s in cells corresponding to the 1’s in the truth table. Place 0’s in the other cells. 2. Examine the map for adjacent 1’s and group those 1’s which are NOT adjacent to any others. These are called isolated 1’s. 3. Group any hex. 4. Group any octet, even if it contains some 1’s already grouped, but are not enclosed in a hex. 5. Group any quad, even if it contains some 1’s already grouped, but are not enclosed in a hex or octet. 6. Group any pair, even if it contains some 1’s already grouped, but are not enclosed in a hex, octet or quad. 7. Group any single cells remaining. 8. Form the OR sum of all the terms grouped.

14. 14 Three Variable Design Example #1 L01010101L01010101 M10110100M10110100 K00110011K00110011 J00001111J00001111 M = F (J,K,L) =

15. 15 Three Variable Design Example #2 C01010101C01010101 Z10001101Z10001101 B00110011B00110011 A00001111A00001111 Z = F (A,B,C) =

16. 16 Three Variable Design Example #3 C01010101C01010101 F2 1 0 1 0 1 B00110011B00110011 A00001111A00001111 F 2 = F (A,B,C) =