1. Instructor: Alexander Stoytchev
CprE 281: Digital Logic
Instructor: Alexander Stoytchev

2. Incompletely Specified Functions & Multiple-Output Circuits
CprE 281: Digital Logic
Iowa State University, Ames, IA
Copyright © Alexander Stoytchev

3. Administrative Stuff
HW4 is due today.

4. Administrative Stuff HW5 is out It is due on Monday Oct 7 @ 4pm.
Please write clearly on the first page (in block capital letters) the following three things:
Your First and Last Name
Your Student ID Number
Your Lab Section Letter

5. Administrative Stuff Homework Office Hours TA name: Pratik Mishra
Where: TLA
When
Mondays 5:30-7:30pm
Fridays 2:00-4:00pm

6. Administrative Stuff Midterm Exam #1 When: Monday Sep 30.
Where: This classroom
What: Chapter 1 and Chapter 2
The exam will be open book and open notes (you can bring up to 3 pages of handwritten notes).
More details to follow.

7. Quick Review

8. The Combining Theorems of Boolean Algebra

9. Two-Variable K-map (a) Truth table (b) Karnaugh map x x x x m 1 1 m m2 x 1 x 2 m 1 1 m m m 1 2 1 m 2 1 m m 1 3 1 1 m 3
(a) Truth table
(b) Karnaugh map
[ Figure 2.49 from the textbook ]

10. Two-Variable K-map 1
[ Figure 2.50 from the textbook ]

11. Three-Variable K-map
[ Figure 2.51 from the textbook ]

12. Three-Variable K-map
[ Figure 2.52 from the textbook ]

13. Four-Variable K-map
[ Figure 2.53 from the textbook ]

14. Four-Variable K-map
[ Figure 2.54 from the textbook ]

15. Which of these are valid combinations?

16. Why are these two not valid?

17. Adjacency Rules
adjacent
rows
adjacent
columns
adjacent
columns

18. What is the expression?

19. Example: Incompletely Specified Function

20. Three Ways to Specify the Function
f(x1, x2, x3, x4) = Σ m(2, 4, 5, 6, 10) + D(12, 13, 14, 15)

21. Three Ways to Specify the Function
f(x1, x2, x3, x4) = Σ m(2, 4, 5, 6, 10) + D(12, 13, 14, 15) x 1 2 3 4 00 01 11 10 d

22. SOP implementation x 00 01 11 10 d (a) SOP implementation 1 2 3 400 01 11 10 d
(a) SOP implementation
[ Figure 2.62 from the textbook ]

23. POS implementation x ( ) 00 01 11 10 d + (b) POS implementation 1 2 34 00 01 11 10 d + ( )
(b) POS implementation
[ Figure 2.62 from the textbook ]

24. Example: A circuit with multiple outputs

25. Seven-Segment Indicator

26. Seven-Segment Indicator

27. Seven-Segment Indicator

28. Another Example

29. (c) Combined circuit for and [ Figure 2.64 from the textbook ]1 2 3 4 00 01 11 10
(a) Function f x 1 2 3 4 00 01 11 10
(b) Function f f 1 2 x 3 4
(c) Combined circuit for
and
[ Figure 2.64 from the textbook ]

30. Yet Another Example

31. Individual vs Joint Optimizationx x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 00 01 1 1 1 01 1 1 1 11 1 1 1 11 1 1 1 10 1 10 1
(a) Optimal realization of f
(b) Optimal realization of f 3 4 x x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 00 01 1 1 1 01 1 1 1 11 1 1 1 11 1 1 1 10 1 10 1
(c) Optimal realization of f
and f
together 3 4
[ Figure 2.65 from the textbook ]

32. Individual vs Joint Optimizationx x x x 1 2 1 2 x x x x 3 4 00 01 11 10 3 4 00 01 11 10 00 00 01 1 1 1 01 1 1 1 11 1 1 1 11 1 1 1 10 1 10 1
(c) Optimal realization of f
and f
together 3 4 f 3 4 x 1 2
(d) Combined circuit for
and
[ Figure 2.65 from the textbook ]

33. Questions?

34. THE END