ECE 434 Advanced Digital Systems Electrical and Computer Engineering University of Western Ontario

General 1. Welcome remark Digital and analog Overview Note: 22/11/2018

Course Requirement Prerequisite and following courses Rules ECE339, ECE349, ECE489 Rules Attendance & Assignment Lab Midterm & final Note: 22/11/2018

Information Text book in library: Class notes and lab manual: 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 Note: 22/11/2018

Information (cont’d) Labs: Assignments: Drop-off box LOCKER #10 EB3107 Digital lab: EB3097 Assignments: Two weeks from the post date Drop-off box LOCKER #10 EB3107 Note: 22/11/2018

Wei Wang Office: EC 1006 Office hours: Thursday 3:00 to 5:00 pm Email: wwang@eng.uwo.ca Note: 22/11/2018

Digital and Analog Digital TV Amplifier 22/11/2018

History DSP, telecommunication, computer, microprocessor 22/11/2018

1947 transisitor 22/11/2018

Overview Digital system VHDL FPGA and CPLD Note: 22/11/2018

Review of Logic Design Fundamentals Outline Review of Logic Design Fundamentals Combinational Logic Boolean Algebra and Algebraic Simplifications Karnaugh Maps 22/11/2018

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 1 Negative Logic – low voltage corresponds to a logic 1, high voltage to a logic 0 22/11/2018

Basic Logic Gates 22/11/2018

Full Adder Module Truth table Algebraic expressions F(inputs for which the function is 1): Minterms m-notation 22/11/2018

Full Adder (cont’d) Module Truth table Algebraic expressions F(inputs for which the function is 0): Maxterms M-notation 22/11/2018

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? 22/11/2018

Laws and Theorems of Boolean Algebra 22/11/2018

Laws and Theorems of Boolean Algebra 22/11/2018

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’) 22/11/2018

Theorems to Apply to Exclusive-OR (Commutative law) (Associative law) (Distributive law) 22/11/2018

Karnaugh Maps 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 Location of minterms Based on AND and OR 22/11/2018

Karnaugh Maps (cont’d) Example 22/11/2018

Sum-of-products Representation Function consists of a sum of prime implicants Prime implicant a group of one, two, four, eight 1s on a map represents 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 Why? K-map and SOP and POS, why?  AND and OR gates 22/11/2018

Selection of Prime Implicants Two minimum forms 22/11/2018

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 22/11/2018

Products of Sums F(1) = {0, 2, 3, 5, 6, 7, 8, 10, 11} F(X) = {14, 15} 22/11/2018

To Do Textbook Read Chapter 1.1, 1.2 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 22/11/2018