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Digital Logic & Design Vishal Jethava Lecture 11

Digital Logic & Design Vishal Jethava Lecture 11. Recap. Karnaugh Maps Mapping Standard SOP expressions Mapping Non-Standard SOP expressions Simplification of K-maps Don’t care states. Mapping a Standard POS expression. Selecting n-variable K-map 0 marked in cell for each maxterm

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Digital Logic & Design Vishal Jethava Lecture 11

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  1. Digital Logic & Design Vishal Jethava Lecture 11 svbitec.wordpress.com

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

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

  4. Mapping of Standard POS expression • POS expression svbitec.wordpress.com

  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 svbitec.wordpress.com

  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 svbitec.wordpress.com

  7. Simplification of POS expressions using K-map svbitec.wordpress.com

  8. Simplification of POS expressions using K-map svbitec.wordpress.com

  9. Simplification of POS expressions using K-map svbitec.wordpress.com

  10. Simplification of POS expressions using K-map svbitec.wordpress.com

  11. Simplification of POS expressions using K-map svbitec.wordpress.com

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

  13. Conversion between SOP & POS using K-map svbitec.wordpress.com

  14. 5-Variable K-map • Represented as two, 4 variable K-map svbitec.wordpress.com

  15. 5-Varaible K-map svbitec.wordpress.com

  16. 5-Varaible K-map svbitec.wordpress.com

  17. Simplification of a 5-Variable K-map • 5 variable K-map mapping • 5 variable K-map grouping • 5 variable K-map simplification svbitec.wordpress.com

  18. 5-Varaible K-map simplification svbitec.wordpress.com

  19. 5-Varaible K-map simplification svbitec.wordpress.com

  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 < svbitec.wordpress.com

  21. 7-Segment Display svbitec.wordpress.com

  22. Function Table for Segment ‘a’ svbitec.wordpress.com

  23. Function Table for Segment ‘b’ svbitec.wordpress.com

  24. Function Table for Segment ‘c’ svbitec.wordpress.com

  25. Function Table for Segment ‘d’ svbitec.wordpress.com

  26. Function Table for Segment ‘e’ svbitec.wordpress.com

  27. Function Table for Segment ‘f’ svbitec.wordpress.com

  28. Function Table for Segment ‘g’ svbitec.wordpress.com

  29. Karnaugh Map for Segment ‘a’ svbitec.wordpress.com

  30. Karnaugh Map for Segment ‘b’ svbitec.wordpress.com

  31. Karnaugh Map for Segment ‘c’ svbitec.wordpress.com

  32. Karnaugh Map for Segment ‘d’ svbitec.wordpress.com

  33. Karnaugh Map for Segment ‘e’ svbitec.wordpress.com

  34. Karnaugh Map for Segment ‘f’ svbitec.wordpress.com

  35. Karnaugh Map for Segment ‘g’ svbitec.wordpress.com

  36. 7-Segment Circuit svbitec.wordpress.com

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