1. Digital Logic & Design Dr. Waseem Ikram Lecture 11

2. Recap Karnaugh Maps Mapping Standard SOP expressions Mapping Non-Standard SOP expressions Simplification of K-maps Don’t care states

3. Mapping a Standard POS expression Selecting n-variable K-map 0 marked in cell for each maxterm Remaining cells marked with 1

4. Mapping of Standard POS expression POS expression AB\C01 0010 0101 1110 1010 A\BC00011110 01010 11001

5. Simplification of POS expressions using K-map Mapping of expression Forming of Groups of 0s Each group represents sum term 3-variable K-map 1 cell group yields a 3 variable sum term 2 cell group yields a 2 variable sum term 4 cell group yields a 1 variable sum term 8 cell group yields a value of 0 for function

6. Simplification of POS expressions using K-map3 4-variable K-map 1 cell group yields a 4 variable sum term 2 cell group yields a 3 variable sum term 4 cell group yields a 2 variable sum term 8 cell group yields a 1 variable sum term 16 cell group yields a value of 0 for function

7. Simplification of POS expressions using K-map AB\C 01 0001 0110 1111 1001 A\BC 00011110 00111 11000

8. Simplification of POS expressions using K-map AB\C 01 0000 0111 1111 1001 A\BC 00011110 00011 11110

9. Simplification of POS expressions using K-map AB\CD00011110 000110 010011 111111 101110

10. Simplification of POS expressions using K-map AB\CD00011110 000010 010011 111011 101010

11. Simplification of POS expressions using K-map AB\CD00011110 001011 010001 111110 101011

12. Conversion between SOP & POS using K-map Groups of 1s represents SOP expression Groups of 0s represents POS expression

13. Conversion between SOP & POS using K-map AB\CD00011110 001011 010001 111110 101011

14. 5-Variable K-map Represented as two, 4 variable K-map

15. 5-Varaible K-map BC\DE00011110 000132 014576 1112131514 10891110

16. 5-Varaible K-map BC\DE00011110 0016171918 0120212322 1128293130 1024252726

17. Simplification of a 5-Variable K-map 5 variable K-map mapping 5 variable K-map grouping 5 variable K-map simplification

18. 5-Varaible K-map simplification BC\DE00011110 000101 010100 110001 100011

19. 5-Varaible K-map simplification BC\DE00011110 001100 011100 110001 100111

20. Functions having multiple outputs Ckt receives a BCD number input Displays decimal number 0 to 9 on a single digit 7-segment display Ckt receives two 2-bit numbers A and B Sets one of three outputs to >, =, or <

21. 7-Segment Display

22. InputsOutput ABCDa 00001 00010 00101 00111 01000 01011 01101 01111 InputsOutput ABCDa 10001 10011 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘a’

23. InputsOutput ABCDb 00001 00011 00101 00111 01001 01010 01100 01111 InputsOutput ABCDb 10001 10011 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘b’

24. InputsOutput ABCDc 00001 00011 00100 00111 01001 01011 01101 01111 InputsOutput ABCDc 10001 10011 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘c’

25. InputsOutput ABCDd 00001 00010 00101 00111 01000 01011 01101 01110 InputsOutput ABCDd 10001 10011 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘d’

26. InputsOutput ABCDe 00001 00010 00101 00110 01000 01010 01101 01110 InputsOutput ABCDe 10001 10010 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘e’

27. InputsOutput ABCDf 00001 00010 00100 00110 01001 01011 01101 01110 InputsOutput ABCDf 10001 10011 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘f’

28. InputsOutput ABCDg 00000 00010 00101 00111 01001 01011 01101 01110 InputsOutput ABCDg 10001 10011 1010X 1011X 1100X 1101X 1110X 1111X Function Table for Segment ‘g’

29. Karnaugh Map for Segment ‘a’ AB\CD00011110 001011 010111 11xxxx 1011xx

30. Karnaugh Map for Segment ‘b’ AB\CD00011110 001111 011010 11xxxx 1011xx

31. Karnaugh Map for Segment ‘c’ AB\CD00011110 001110 011111 11xxxx 1011xx

32. Karnaugh Map for Segment ‘d’ AB\CD00011110 001011 010101 11xxxx 1011xx

33. Karnaugh Map for Segment ‘e’ AB\CD00011110 001001 010001 11xxxx 1010xx

34. Karnaugh Map for Segment ‘f’ AB\CD00011110 001000 011101 11xxxx 1011xx

35. Karnaugh Map for Segment ‘g’ AB\CD00011110 000011 011101 11xxxx 1011xx

36. 7-Segment Circuit