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B01: Introduction to Digital Logic Design

B01: Introduction to Digital Logic Design. Instructor: Katherine Compton Tech L470 (moving to L458 around 7/1) <kati@ece.nwu.edu>, (847)491-2083 Office Hours: by appointment TA: Probably not. Book: Randy H. Katz’s Contemporary Logic Design. Grading. 20% - Homeworks 25% - Tutorials & Labs

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B01: Introduction to Digital Logic Design

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  1. B01: Introduction to Digital Logic Design • Instructor: Katherine ComptonTech L470 (moving to L458 around 7/1)<kati@ece.nwu.edu>, (847)491-2083Office Hours: by appointment • TA: Probably not. • Book: Randy H. Katz’s Contemporary Logic Design

  2. Grading • 20% - Homeworks • 25% - Tutorials & Labs • 25% - Midterm Exam • 30% - Final Exam • Homework is due at the beginning of class on the specified date. • Late penalties: • <24 hours: -15% • <48 hours: -30% • <72 hours: -60% • >72 hours: not accepted

  3. Joint Work Policy • All work done for the class must be a student’s own, original work. • Everyone must do their own work separately. • You cannot work together on the specifics of homeworks or labs. • You also cannot use answers from previous years or answer keys. • Any students caught using someone else’s work will receive a 0 for that assignment/lab/exam.

  4. Class & Lab Meetings • Lectures: TTh 6:30-9:30PM • Labs : Must sign up for a weekly time slot • Sign-up sheet will go up on door of L470 on Wednesday • Sign up by next class time! • Will have open labs (help sessions), time to be announced later.

  5. Motivation • Electronics an increasing part of our lives • Computers & the Internet • Car electronics • Robots • Electrical Appliances • Telephones • Class covers digital logic design & implementation

  6. Example: Car Electronics • Brake Light (foot brake, parking brake): • High-beam indicator (lights, high beam selected):

  7. Example: Car Electronics (cont.) • Seat Belt Light (driver belt in): • Seat Belt Light (driver belt in, passenger belt in, passenger present):

  8. Basic Logic Gates • AND: If A and B are True, then Out is True • OR: If A or B is True, or both, then Out is True • Inverter (NOT): If A is False, then Out is True A Out B A Out B Out A

  9. TTL Logic (Transistor-transistor Logic) Vdd (TRUE) GND (False)

  10. Digital vs. Analog Digital: only assumes discrete values Analog: values vary over a broad range continuously

  11. Advantages of Digital Circuits • Analog systems: slight error in input yields large error in output • Digital systems more accurate and reliable • Readily available as self-contained, easy to cascade building blocks • Computers use digital circuits internally • Interface circuits (i.e., sensors & actuators) often analog This course is about logic design, not system design (processor architecture), not circuit design (transistor level)

  12. Binary/Boolean Logic • Two discrete values (TTL): yes, on, 5 volts, TRUE, "1" no, off, 0 volts, FALSE, "0" • Advantage of binary systems: rigorous mathematical foundation based on logic both the door must be open and the car running before I can back out IF the garage door is open AND the car is running THEN the car can be backed out of the garage IF passenger is in the car AND passenger belt is in AND driver belt is in THEN we can turn off the fasten seat belt light the three preconditions must be true to imply the conclusion

  13. X X Z Z 1 1 1 1 X X Z Z Logic 2 2 2 2 - - - - Network - - - - - - - - X X Z Z n n m m Combinational vs. Sequential Logic Sequential logic Network implemented from logic gates. The presence of feedback distinguishes between sequential and combinational networks. Combinationallogic No feedback among inputs and outputs. Outputs are a function of the inputs only. Logic Network

  14. Black Box (Majority) • Given a design problem, first determine the function • Consider the unknown combination circuit a “black box” Truth Table Out A C B

  15. “Black Box” Design & Truth Tables • Given an idea of a desired circuit, implement it • Example: Odd parity - inputs: A, B, C, output: Out

  16. Truth Tables Algebra: variables, values, operations In Boolean algebra, the values are the symbols 0 and 1 If a logic statement is false, it has value 0 If a logic statement is true, it has value 1 Operations: AND, OR, NOT

  17. Boolean Algebra values: 0, 1 variables: A, B, C, . . ., X, Y, Z operations: NOT, AND, OR, . . . NOT X is written as X X AND Y is written as X & Y, or sometimes X Y X OR Y is written as X + Y Boolean Equations Deriving Boolean equations from truth tables: Sum = A B + A B Carry 0 0 0 1 A 0 0 1 1 B 0 1 0 1 Sum 0 1 1 0 OR'd together product terms for each truth table row where the function is 1 if input variable is 0, it appears in complemented form; if 1, it appears uncomplemented Carry = A B

  18. Boolean Algebra Another example: Sum = A B Cin + A B Cin + A B Cin + A B Cin Sum 0 1 1 0 1 0 0 1 Cout 0 0 0 1 0 1 1 1 A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 Cin 0 1 0 1 0 1 0 1 Cout = A B Cin + A B Cin + A B Cin + A B Cin

  19. A B C in C out 0 0 0 0 B C in 0 0 1 0 0 1 0 0 0 1 1 1 A C in 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Boolean Algebra Reducing the complexity of Boolean equations Laws of Boolean algebra can be applied to full adder's carry out function to derive the following simplified expression: Cout = A Cin + B Cin + A B A B Verify equivalence with the original Carry Out truth table: place a 1 in each truth table row where the product term is true each product term in the above equation covers exactly two rows in the truth table; several rows are "covered" by more than one term

  20. Representations of Boolean Functions • Boolean Function: F = X + YZ Truth Table: Circuit Diagram: X Y Z F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

  21. Why Boolean Algebra/Logic Minimization? Logic Minimization: reduce complexity of the gate level implementation • reduce number of literals (gate inputs) • reduce number of gates • reduce number of levels of gates fewer inputs implies faster gates in some technologies fan-ins (number of gate inputs) are limited in some technologies fewer levels of gates implies reduced signal propagation delays number of gates (or gate packages) influences manufacturing costs

  22. Basic Boolean Identities: X + 0 = X * 1 = X + 1 = X * 0 = X + X = X * X = X + X = X * X = X =

  23. Basic Laws Commutative Law: X + Y = Y + X XY = YX Associative Law: X+(Y+Z) = (X+Y)+Z X(YZ)=(XY)Z Distributive Law: X(Y+Z) = XY + XZ X+YZ = (X+Y)(X+Z)

  24. Boolean Manipulations • Boolean Function: F = XYZ + XY + XYZ Truth Table: Reduce Function: X Y Z F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

  25. Advanced Laws (Absorbtion) • X+XY = • XY + XY = • X+XY = • X(X+Y) = • (X+Y)(X+Y) = • X(X+Y) =

  26. Boolean Manipulations (cont.) • Boolean Function: F = XYZ + XZ Truth Table: Reduce Function: X Y Z F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

  27. Boolean Manipulations (cont.) • Boolean Function: F = (X+Y+XY)(XY+XZ+YZ) Truth Table: Reduce Function: X Y Z F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

  28. X Y X Y X + Y X•Y 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 X Y X Y X•Y X + Y 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 DeMorgan’s Law (X + Y) = X * Y (X * Y) = X + Y DeMorgan's Law can be used to convert AND/OR expressions to OR/AND expressions Example: Z = A B C + A B C + A B C + A B C Z = (A + B + C) * (A + B + C) * (A + B + C) * (A + B + C)

  29. DeMorgan’s Law example • If F = (XY+Z)(Y+XZ)(XY+Z), F =

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