1. Karnaugh Maps

2. Karnaugh Map
D
C
B
A

3. Karnaugh Map
D
C
B
A

4. Karnaugh Map
D
C
B
A

5. Karnaugh Map
1010 1011 0011 0010
11111110 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
D
C
B
A

6. Karnaugh Map
1010 1011 0011 0010
11111110 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
D
C
B
A

7. A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
1010 1011 0011 0010
11111110 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
D
C
B
A

8. A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
1010 1011 0011 0010
11111110 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
D
C
B
A
1

9. A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
1010 1011 0011 0010
11101101 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
D
C
B
A
1 1
1 1

10. A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
1010 1011 0011 0010
11111110 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
D
C
B
A
0 0 0 0
00 0
1 1
0
0
0 1 0 1
0

11. 1 1
1
0100
1
1010 1011 0011 0010
11111110 0111
0101
0110
1100
1000 1001 0001 0000
1101
0 0 0 0
00 0 0
0
0 0
0
A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
D
C
B
A

12. 1
1
0100
1
1
1010 1011 0011 0010
11111110 0111
0101
0110
1100
1000 1001 0001 0000
1101
0 0 0 0
00 0 0
0
0 0
0
A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
D
C
B
A

13. 1
1
0100
1
1
1010 1011 0011 0010
11111110 0111
0101
0110
1100
1000 1001 0001 0000
1101
0 0 0 0
00 0 0
0
0 0
0
A B C D X
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 1
0 1 0 1 1
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 0
1 1 0 0 0
1 1 0 1 0
1 1 1 0 0
1 1 1 1 0
Example
D
C
B
A

14. 1
1
0100
1
1
1010 1011 0011 0010
11111110 0111
0101
0110
1100
1000 1001 0001 0000
1101
0 0 0 0
00 0 0
0
0 0
0
Example
D
C
B
A
ABC + ACD + ABCD

15. 1010 1011 0011 0010
11111110 0111
0101 0100
0110
1100
1000 1001 0001 0000
1101
Example II
D
C
B
A
1 1
1 1
1
1
1
1 1 1
A B C D Y
0 0 0 0 1
0 0 0 1 1
0 0 1 0 1
0 0 1 1 0
0 1 0 0 1
0 1 0 1 0
0 1 1 0 1
0 1 1 1 1
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 0
1 1 1 0 0
1 1 1 1 1
Y = AD + ACD + BCD
+ BCD + BCD

16. Conclusion