ECE 434 Advanced Digital Systems

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ECE 434Advanced Digital Systems

• Electrical and Computer EngineeringUniversity of
  Western Ontario

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General

• 1. Welcome remark
• Digital and analog
• Overview

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Course Requirement

1. Prerequisite and following courses
2. ECE339, ECE349, ECE489
3. Rules
4. Attendance Assignment
5. Lab
6. Midterm final

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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

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Information (contd)

• Labs
• Digital lab EB3097
• Assignments
• Two weeks from the post date
• Drop-off box
• LOCKER 10 EB3107

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Wei Wang

• Office EC 1006
• Office hours Thursday
• 300 to 500 pm
• Email wwang_at_eng.uwo.ca

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Digital and Analog
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Overview

• Digital system
• VHDL
• FPGA and CPLD

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Outline

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

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Combinational Logic

• Has no memory gtpresent 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
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Basic Logic Gates
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Full Adder
Module
Truth table
Algebraic expressionsF(inputs for which the
function is 1)
Minterms
m-notation
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Full Adder (contd)
Module
Truth table
Algebraic expressionsF(inputs for which the
function is 0)
Maxterms
M-notation
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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?

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Laws and Theorems of Boolean Algebra
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Laws and Theorems of Boolean Algebra
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Simplifying Logic Expressions

• Combining terms
• Use XYXYX, XXX
• Eliminating terms
• Use XXYX
• Eliminating literals
• Use XXYXY
• Adding redundant terms
• Add 0 XX
• Multiply with 1 (XX)

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Theorems to Apply to Exclusive-OR
(Commutative law)
(Associative law)
(Distributive law)
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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 dont care
• the input can never occur, or
• the input occurs but the output is not specified
• adjacent cells differ in only one value gtcan be
  combined

Location of minterms
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Karnaugh Maps (contd)

• Example

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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

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Selection of Prime Implicants
Two minimum forms
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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

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Products of Sums

• F(1) 0, 2, 3, 5, 6, 7, 8, 10, 11F(X) 14,
  15

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To Do

• Textbook
• Chapter 1.1, 1.2
• Read
• Alteras MAXplus II and the UP1 Educational
  boardA Users Guide, B. E. Wells, S. M. Loo
• Altera University Program Design Laboratory
  Package