Module 2

Outline Chapter 2

Chapter 2 Binary Values and Number Systems

2.1 Numbers and Computing

2.2 Positional Notation

Binary, Octal, and Hexadecimal

Arithmetic in Other Bases

Power-of-2 Number Systems

Converting from Base 10 to Other Bases

Binary Values and Computers

Ethical Issues: The FISA Court 49

Outline Chapter 3

Chapter 3 Data Representation

3.1 Data and Computers

Analog and Digital Data

Binary Representations

3.2 Representing Numeric Data

Representing Negative Values

Representing Real Numbers

3.3 Representing Text

The ASCII Character Set

The Unicode Character Set

Text Compression

3.4 Representing Audio Data

Audio Formats

The MP3 Audio Format

3.5 Representing Images and Graphics

Representing Color

Digitized Images and Graphics

Vector Representation of Graphics

3.6 Representing Video

Video Codecs

Ethical Issues: The Fallout from Snowden’s Revelations

Lesson

Day 1 (chapter 2)

• Lab review

• Chapter questions review

• DS

  • Sets, Relations, and Functions

    • Basic Concepts of Set Theory, Functions and Relations

      • Set - a collection of objects which are called the members or elements of that set

      • Relations - links existing between objects, like ‘is a subset of’

      • Functions - may be thought of as a “process” or as a correspondence

  • Logic

    • Truth table A table showing all possible input values and the associated output values

    • Introduction (more on this in chapter 4)

      • NOT (negation), AND (conjunction), OR (disjunction), IF (conditional)

      • List of logic symbols

      • Truth Table Generator

        • ¬A

        • A ∧ B

        • A ∨ B

        • A => B

• Algorithm

• Number systems

  • Converting with remainder method

  • Binary numbers are usually grouped with 8 digits, oct with 3, and hex with 4, using leading 0s when necessary.

• Computers interpret underlying patterns of 1s and 0s

• Binary

• Scratch Binary Bulbs

• 8 bit game

• Bring headphones to next class

Day 2 (chapter 3)

• Chapter questions review

• Representing Numeric Data

  • Floating Point

    • What Every Computer Scientist Should Know About Floating-Point Arithmetic

    • Floating Point Numbers - Computerphile (9:15)

    • Floating-point arithmetic may give inaccurate results in Excel

  • Overflow

    • StackOverflow

• Representing Text

  • Ascii table

  • HEX to ASCII

• Representing Audio

  • Audacity

  • Add custom audio to Scratch

  • Adobe Voco

    • VoCo. Adobe MAX video

• Representing Images

  • Paint - bmp, jpg, png, gif

  • Paint.NET

  • GIMP

  • Inkscape

    • Tutorials

• Representing Video

  • Containers and Codecs

    • Explained video (3:05)

    • 4K / VP9 / H.265

  • HandBrake

• Microsoft Digital Literacy

  • Digital Lifestyles

KA Topics:

• Sets, Relations, and Functions

  • Sets

    • Venn diagrams

    • Union, intersection, complement

    • Cartesian product

    • Power sets

    • Cardinality of finite sets

  • Relations

    • Reflexivity, symmetry, transitivity

    • Equivalence relations, partial orders

  • Functions

    • Surjections, injections, bijections

    • Inverses

    • Composition

• Basic Logic

  • Propositional logic (cross-reference: Propositional logic is also reviewed in IS/Knowledge Based Reasoning)

  • Logical connectives

  • Truth tables

  • Normal forms (conjunctive and disjunctive)

  • Validity of well-formed formula

  • Propositional inference rules (concepts of modus ponens and modus tollens)

  • Predicate logic

    • Universal and existential quantification

  • Limitations of propositional and predicate logic (e.g., expressiveness issues)

KA Learning Outcomes:

Sets, Relations, and Functions

1. Explain with examples the basic terminology of functions, relations, and sets. [Familiarity]

2. Perform the operations associated with sets, functions, and relations. [Usage]

3. Relate practical examples to the appropriate set, function, or relation model, and interpret the associated operations and terminology in context. [Assessment]

Basic Logic

1. Convert logical statements from informal language to propositional and predicate logic expressions. [Usage]

2. Apply formal methods of symbolic propositional and predicate logic, such as calculating validity of formulae and computing normal forms. [Usage]

3. Use the rules of inference to construct proofs in propositional and predicate logic. [Usage]

4. Describe how symbolic logic can be used to model real-life situations or applications, including those arising in computing contexts such as software analysis (e.g., program correctness), database queries, and algorithms. [Usage]

5. Apply formal logic proofs and/or informal, but rigorous, logical reasoning to real problems, such as predicting the behavior of software or solving problems such as puzzles. [Usage]

6. Describe the strengths and limitations of propositional and predicate logic. [Familiarity]