Lecture 3

1. Lecture 3 Hardware Description Methods, Review of Switching Algebra

2. A binary switch x = 0 x = 1 (a) Two states of a switch S x (b) Symbol for a switch

3. A light controlled by a switch S Battery Light L x (a) Simple connection to a battery S Power L x supply (b) Using a ground connection as the return path

4. Two basic functions S S Power Light x x L supply 1 2 (a) The logical AND function (series connection) S x 1 Power Light L supply S x 2 (b) The logical OR function (parallel connection)

5. A series parallel connection S x S 1 Power Light x L supply S 3 x 2

6. An inverting circuit R Power supply x S L

7. Truth table for AND and OR

8. Three input AND and OR

9. x x 1 1 . x x x + x 1 2 1 2 x x 2 2 x 1 x x 2 1 x + x 1 2 x 2 … x + x + + x 1 2 n x n x x (b) OR gates Basic gates x 1 . x x 1 2 x 2 (c) NOT gate x 1 x 2 (d) NAND gate . … x x x 1 2 n x n (a) AND gates (e) NOR gate

10. Logic network 0 0 1 1 1 1 0 0 x 1 A 1 1 0 1 f 0 0 0 1 B 0 1 0 1 x 2 ( , ) x x f x x 1 2 1 2 (a) Network that implements 0 0 1 0 1 1 f = x1 + x1 x2 1 0 0 1 1 1 (b) Truth table for f

11. 1 x 1 0 1 x 2 0 1 A 0 1 B 0 1 f 0 Time Logic network (c) Timing diagram 0 0 1 1 1 1 0 0 x 1 1 1 0 1 0 1 0 1 g x 2 (d) Network that implements g = x + x 1 2

12. Boolean algebra - axioms x*0 = 0 0*0 = 0 DeMorgan laws x + 1 = 1 1 + 1 = 1 x*y = x + y x*1 = x 1*1 = 1 x + y = x*y x +0 = x 0 +0 = 0 x* x = x 0* 1 = 1* 0 = 0 x + x*y = x + y x + x = x 1 + 0 = 0 + 1 = 1 x* x = 0 x*(x + y) = x*y x = x x+ x = 1

13. DeMorgan’s theorem

14. Please see “portrait orientation” PowerPoint file for Chapter 2 Figure 2.12 The Venn diagram representation

15. Please see “portrait orientation” PowerPoint file for Chapter 2 Figure 2.13 Verification of the distributive property

16. Please see “portrait orientation” PowerPoint file for Chapter 2 Figure 2.14 Verification example

17. A function to be synthesised

18. Two implementations x 1 x 2 f x 1 f x 2 (b) Minimal-cost realization (a) Canonical sum-of-products

19. Minterms and maxterms

20. A three variable function

21. x 2 f x 3 x 1 x 1 x 3 f x 2 Two implementations (b) A minimal product-of-sums (a) A minimal sum-of-products

22. Three way light controller Specification (for logic only): • A room with three doors. • Light switch at each door. • Light turned on/off at each door. • 1 - turned on. • 0 – turned off.

23. f x 1 x 2 x 3 Sum of Products – SOP

24. x 3 x 2 x 1 f Products of Sums – POS

25. s x1 x2 f (s, x1, x2) 0 0 0 0 0 0 1 0 x 1 0 1 0 1 0 1 1 1 f 1 0 0 0 s 1 0 1 1 x 2 1 1 0 0 1 1 1 1 s f (s, x1, x2) s x1 x 0 0 1 f x2 x 1 1 2 Multiplexer (b) Circuit (c) Graphical symbol (a) Truth table (d) More compact truth table

26. x 1 x2 XOR XNOR x1 f 0 0 0 1 0 1 1 0 x 2 1 0 1 0 1 1 0 1 XOR, XNOR gates (a) Truth table (b) One of XOR Circuits (c) XOR Graphical symbol (d) XNOR Graphical symbol

27. Waveform Editor

28. Graphic Editor

29. Please see “portrait orientation” PowerPoint file for Chapter 2

30. x 1 x 2 f x 3 first touch of VHDL

31. A bit more of VHDL

32. x 1 x 3 f x 2 g x 4 Four-input function