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ECE 434 Advanced Digital Systems

ECE 434 Advanced Digital Systems. Electrical and Computer Engineering University of Western Ontario. General. 1. Welcome remark Digital and analog Overview. Course Requirement. Prerequisite and following courses ECE339, ECE349, ECE489 Rules Attendance & Assignment Lab Midterm & final.

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ECE 434 Advanced Digital Systems

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  1. ECE 434Advanced Digital Systems Electrical and Computer EngineeringUniversity of Western Ontario

  2. General 1. Welcome remark • Digital and analog • Overview

  3. Course Requirement • Prerequisite and following courses • ECE339, ECE349, ECE489 • Rules • Attendance & Assignment • Lab • Midterm & final

  4. Information • Text book in library: • Digital Systems Design Using VHDL, Charles H. Roth, Jr., PWS Publishing, 1998 (ISBN: 0-534-95099-X). • S. Brown and Z. Vranesic, Fundamentals of Digital Logic with VHDL Design, McGraw Hill, 1999/2000 (Book should contain CD-ROM from Altera Corp). • Class notes and lab manual: www.engga.uwo.ca/people/wwang

  5. Information (cont’d) • Labs: • Digital lab: EB3097 • Assignments: • Two weeks from the post date • Drop-off box LOCKER #10 EB3107

  6. Wei Wang Office: EC 1006 Office hours: Thursday 3:00 to 5:00 pm Email: wwang@eng.uwo.ca

  7. Digital and Analog

  8. Overview • Digital system • VHDL • FPGA and CPLD

  9. Outline Review of Logic Design Fundamentals • Combinational Logic • Boolean Algebra and Algebraic Simplifications • Karnaugh Maps

  10. Combinational Logic • Has no memory =>present state depends only on the present input X = x1 x2... xn Z = z1 z2... zm x1 z1 x2 z2 xn zm Note: Positive Logic – low voltage corresponds to a logic 0, high voltage to a logic 1Negative Logic – low voltage corresponds to a logic 1, high voltage to a logic 0

  11. Basic Logic Gates

  12. Full Adder Module Truth table Algebraic expressionsF(inputs for which the function is 1): Minterms m-notation

  13. Full Adder (cont’d) Module Truth table Algebraic expressionsF(inputs for which the function is 0): Maxterms M-notation

  14. Boolean Algebra • Basic mathematics used for logic design • Laws and theorems can be used to simplify logic functions • Why do we want to simplify logic functions?

  15. Laws and Theorems of Boolean Algebra

  16. Laws and Theorems of Boolean Algebra

  17. Simplifying Logic Expressions • Combining terms • Use XY+XY’=X, X+X=X • Eliminating terms • Use X+XY=X • Eliminating literals • Use X+X’Y=X+Y • Adding redundant terms • Add 0: XX’ • Multiply with 1: (X+X’)

  18. Theorems to Apply to Exclusive-OR (Commutative law) (Associative law) (Distributive law)

  19. Convenient way to simplify logic functions of 3, 4, 5, (6) variables Four-variable K-map each square corresponds to one of the 16 possible minterms 1 - minterm is present; 0 (or blank) – minterm is absent; X – don’t care the input can never occur, or the input occurs but the output is not specified adjacent cells differ in only one value =>can be combined Karnaugh Maps Location of minterms

  20. Karnaugh Maps (cont’d) • Example

  21. Sum-of-products Representation • Function consists of a sum of prime implicants • Prime implicant • a group of one, two, four, eight 1s on a maprepresents a prime implicant if it cannot be combined with another group of 1s to eliminate a variable • Prime implicant is essential if it contains a 1 that is not contained in any other prime implicant

  22. Selection of Prime Implicants Two minimum forms

  23. Procedure for min Sum of products • 1. Choose a minterm (a 1) that has not been covered yet • 2. Find all 1s and Xs adjacent to that minterm • 3. If a single term covers the minterm and all adjacent 1s and Xs, then that term is an essential prime implicant, so select that term • 4. Repeat steps 1, 2, 3 until all essential prime implicants have been chosen • 5. Find a minimum set of prime implicants that cover the remaining 1s on the map. If there is more than one such set, choose a set with a minimum number of literals

  24. Products of Sums • F(1) = {0, 2, 3, 5, 6, 7, 8, 10, 11}F(X) = {14, 15}

  25. To Do • Textbook • Chapter 1.1, 1.2 • Read • Altera’s MAX+plus II and the UP1 Educational board:A User’s Guide, B. E. Wells, S. M. Loo • Altera University Program Design Laboratory Package

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