1. ENEE244-02xx Digital Logic Design Lecture 12

2. Announcements HW4 due today HW5 is up on course webpage. Due on 10/16. Recitation quiz on Monday, 10/13 – Will cover the material from lectures 10,11,12.

3. Agenda Examples of finding minimal sums for 3- variable and 4-variable Boolean functions.

4. Using Karnaugh Maps to Find Minimal Sums 0132 4576 00011110 0 1

5. Using Karnaugh Maps to Find Minimal Sums 0001 1111 00011110 0 1

6. Using Karnaugh Maps to Find Minimal Sums Step 1: Find all prime implicants Verify these are the only prime implicants. 0001 1111 00011110 0 1

7. Using Karnaugh Maps to Find Minimal Sums 0001 1111 00011110 0 1

8. Using Karnaugh Maps to Find Minimal Sums 0132 4576 00011110 0 1

9. Using Karnaugh Maps to Find Minimal Sums 1111 1011 00011110 0 1

10. Using Karnaugh Maps to Find Minimal Sums Step 1: Find all prime implicants Verify these are the only prime implicants. 1111 1011 00011110 0 1

11. Using Karnaugh Maps to Find Minimal Sums 1111 1011 00011110 0 1

12. Using Karnaugh Maps to Find Minimal Sums 0132 4576 00011110 0 1

13. Using Karnaugh Maps to Find Minimal Sums 1011 0010 00011110 0 1

14. Using Karnaugh Maps to Find Minimal Sums Step 1: Find all prime implicants Verify these are the only prime implicants. 1011 0010 00011110 0 1

15. Using Karnaugh Maps to Find Minimal Sums 1011 0010 00011110 0 1

16. Using Karnaugh Maps to Find Minimal Sums 1011 0010 00011110 0 1

17. Using Karnaugh Maps to Find Minimal Sums 0132 4576 12131514 891110 00011110 00 01 11 10

18. Using Karnaugh Maps to Find Minimal Sums 1100 0011 0011 1000 00011110 00 01 11 10

19. Using Karnaugh Maps to Find Minimal Sums Step 1: Find all prime implicants Verify these are the only prime implicants. 1100 0011 0011 1000 00011110 00 01 11 10

20. Using Karnaugh Maps to Find Minimal Sums 1100 0011 0011 1000 00011110 00 01 11 10

21. Using Karnaugh Maps to Find Minimal Sums 0132 4576 12131514 891110 00011110 00 01 11 10

22. Using Karnaugh Maps to Find Minimal Sums 1100 0111 0000 1000 00011110 00 01 11 10

23. Using Karnaugh Maps to Find Minimal Sums Step 1: Find all prime implicants Verify these are the only prime implicants. 1100 0111 0000 1000 00011110 00 01 11 10

24. Using Karnaugh Maps to Find Minimal Sums 1100 0111 0000 1000 00011110 00 01 11 10

25. Using Karnaugh Maps to Find Minimal Sums 1100 0111 0000 1000 00011110 00 01 11 10