1. Digital Technology

2. Outline Week 1: Logic Gates, Boolean Algebra and Intro to HDL
Week 2: Multi-level Gate Networks and Combinational Circuits
Week 3: Propagation Delays and Hazards
Week 4: Flips-Flops and Sequential Circuits
Week 5: FSM and Revision
Week 6 Test

3. Some Details First test: First assignment submission:
First week after mid-semester
First assignment submission:
Friday 30 April
Lecture notes are available on Moodle

4. Lecture Outline Logic and Logic Gates Boolean identities
Truth tables
Algebraic expressions
Boolean identities
Boolean algebra

5. Positive and Negative Logic
If the signal that activates the circuit (the “1” state) has a voltage level that is more positive than the 0 state, then the logic polarity is considered to be POSITIVE
If the signal that activates the circuit (the “1” state) has a voltage level that is more negative than the 0 state, then the logic polarity is considered to be NEGATIVE

6. Examples of Logic Polarity
Positive logic
Active signal
Compliment
TRUE
FALSE 1
HIGH: +5 volts
LOW: 0 volts
Negative logic
HIGH: 0 volts
LOW: -5 volts

7. A Simple Circuit A X 1
(input)
(output)

8. NOT Gate (Inverter) A X 1

9. AND Gate A B X 1

10. OR Gate A B X 1

11. NAND Gate A B X 1

12. NOR Gate A B X 1

13. XOR Gate (eXclusive OR)B X 1

14. XNOR Gate A B X 1

15. Boolean Algebra
1854 George Boole introduced a systematic approach to logic
Hence Boolean Algebra
1938 C.E. Shannon introduced a two-valued Boolean algebra called switching algebra
Bistable electrical circuits can expressed using this algebra

16. Null Law (AND) A B X 1

17. Null Law (OR) A B X 1

18. Identity Law (AND) A B X 1

19. Identity Law (OR) A B X 1

20. Idempotent Law (AND) A B X 1

21. Idempotent Law (OR) A B X 1

22. Inverse Law (AND) A B X 1

23. Inverse Law (OR) A B X 1

24. Commutative Law

25. Associative Law (AND)
Note: same for the
OR form

26. Distributive Law

27. Absorption Law

28. DeMorgan’s Law Change the sign (AND to OR, OR to AND)
Invert the individual terms
Invert the whole expression
(tidy up any multiple inversions)

29. DeMorgans Law (hints) Use it:
when you need to change the logical operation (product-of-sums for example)
to get rid of any nasty inversions