1. ECE 331 – Digital System Design Basic Logic Functions, Truth Tables, and Standard Logic Gates

2. ECE 331 - Digital System Design2 Basic Logic Functions

3. ECE 331 - Digital System Design3 Basic Logic Functions AND  Logical multiplication (product)  A. B = AB = “A and B” OR  Logical addition (sum)  A + B = “A or B” NOT  Logical complement  A‘ = “not A” Order of Precedence: 1. NOT 2. AND 3. OR - can be modified by parenthesis

4. ECE 331 - Digital System Design4 Truth Table

5. ECE 331 - Digital System Design5 Logic Gates

6. ECE 331 - Digital System Design6 Additional Logic Functions NAND  F = (A. B)‘ = (AB)’  F = not (A and B)  Compound logic function NOR  F = (A + B)’  F = not (A or B)  Compound logic function Not the same as F = A’. B’ Not the same as F = A’ + B’

7. ECE 331 - Digital System Design7 Truth Tables Exercise: Derive the Truth Table for the NAND and NOR gates.

8. ECE 331 - Digital System Design8 Logic Gates shorthand for a NOT gate

9. ECE 331 - Digital System Design9 Additional Logic Functions Exclusive-OR  F = (A.B') + (A'.B)  Output = 1 iff one of the inputs is 1 (but not both).  Inclusive-OR: F = A + B Exclusive-NOR  F = (A.B) + (A'.B')  Output = 1 iff both input are 0 or both inputs are 1.  Also known as the Equivalence function.

10. ECE 331 - Digital System Design10 Truth Tables Exercise: Derive the Truth Table for the XOR and XNOR gates.

11. ECE 331 - Digital System Design11 Additional Logic Operations XOR gate XNOR gate AB F = A xor B F = A xnor B

12. ECE 331 - Digital System Design12 Truth Tables

13. ECE 331 - Digital System Design13 Truth Tables Used to describe the functional behavior of a Boolean expression and/or Logic circuit. Each row in the truth table represents a unique combination of the input variables.  For n input variables, there are 2 n rows. The output of the logic function is defined for each row. Each row is assigned a numerical value, with the rows listed in ascending order. The order of the input variables defined in the logic function is important.

14. ECE 331 - Digital System Design14 3-input Truth Table

15. ECE 331 - Digital System Design15 4-input Truth Table

16. ECE 331 - Digital System Design16 Standard Logic Gates

17. ECE 331 - Digital System Design17 Standard Logic Gates Discrete components used to build logic circuits.  74xx08AND gate  74xx32OR gate  74xx04NOT gate  74xx00NAND gate  74xx02NOR gate  74xx86XOR gate Logic Families (TTL, LS-TTL, F, HC)

18. ECE 331 - Digital System Design18 Standard Logic Gates: Data sheets Data sheets provide essential information:  Logic Function  Truth Table  Pin-out  Electrical Characteristics  Timing Characteristics  Package Description(s) This information is necessary when building logic circuits from discrete components. Each Logic Family has a unique set of characteristics.

19. ECE 331 - Digital System Design19 Logic Families TTL  Low-Power TTL (“L”)  High-Speed TTL (“H”)  Schottky (“S”)  Low-Power Schottky (“LS”)  Advanced Schottky (“AS”)  Advanced Low-Power Schottky (“ALS”)  Fast (“F”) CMOS  High-Speed CMOS (“HC”)  Advanced CMOS (“AC”)

20. ECE 331 - Digital System Design20 Table E.4 (p. 916 of textbook)

21. ECE 331 - Digital System Design21 Combinational Logic Circuits

22. ECE 331 - Digital System Design22 Combinational Logic Circuits Composed of an interconnected set of logic gates. Also known as Switching Circuits Logic circuits can be designed from  Truth tables  Boolean expressions Logic circuits realized through  Interconnection of discrete components  Synthesis from a Hardware Description Language

23. ECE 331 - Digital System Design23 Example: Derive the Boolean expression and draw the circuit diagram for the following truth table:

24. ECE 331 - Digital System Design24 f x 1 x 2 Example F = x’ 1.x’ 2 + x’ 1.x 2 + x 1.x 2

25. ECE 331 - Digital System Design25 Example: Derive the Boolean expression and draw the circuit diagram for the following truth table:

26. ECE 331 - Digital System Design26 Wiring Diagrams

27. ECE 331 - Digital System Design27 (a) Dual-inline package (b) Structure of 7404 chip V DD Gnd Standard Logic Gate: Pin-out

28. ECE 331 - Digital System Design28 Standard Logic Gate: Pin-out

29. ECE 331 - Digital System Design29 Standard Logic Gate: Pin-out

30. ECE 331 - Digital System Design30 Example: Draw the circuit diagram and the wiring diagram for the following Boolean expression: F = x’ 2.x 3 + x 1.x 2

31. ECE 331 - Digital System Design31 Example