UTPA STEM/CBI Courses/Microprocessor Systems/Number Representation

Course Title: Microprocessor Systems

Lecture Topic: Number Representation

Instructor: Jun Peng

Institution: UTPA

Backwards Design

Course Objectives

• Primary Objectives- By the next class period students will be able to:
  • Convert numbers in different representations

• Sub Objectives- The objectives will require that students be able to:
  • Understand the base of number representation

• Difficulties- Students may have difficulty:
  • Using a system other than the commonly used decimal system used in everyday life.

• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
  • Almost all data is in digital format now and this material will help students understand digital data.

Model of Knowledge

• Concept Map
  • Numbers
  • Decimal numbers
  • Other number systems such as binary and hexadecimal numbers
  • The conversion between them

• Content Priorities
  • Enduring Understanding
    • Number representation.

• • Important to Do and Know
    • Convert numbers in different representations.

• • Worth Being Familiar with
    • Calculating in various number systems

Assessment of Learning

• Formative Assessment
  • In Class (groups)
    • Quizzes
    • Questions and answers.

• • Homework (individual)
    • Homework problems

• Summative Assessment
  • Tests
  • Labs

Legacy Cycle

OBJECTIVE

By the next class period, students will be able to:

• Convert numbers in different representations

The objectives will require that students be able to:

• Understand number representations

THE CHALLENGE

If you were a computer, how would you like the numbers to be represented?

GENERATE IDEAS

Ask students to play the role of a computer to do data storage and processing.

MULTIPLE PERSPECTIVES

Discuss students' ideas and "designs".

RESEARCH & REVISE

Explain how numbers are represented in computers and how they might be presented in different representations to human beings.

TEST YOUR METTLE

Give students quizzes on number representation and conversion.

GO PUBLIC

Give students tests. Ask students write a program to convert numbers in different representations.

Pre-Lesson Quiz

1. What is a decimal number?
2. Why do we like decimal numbers?
3. Why do computers like numbers with a base of 2?
4. What does the base of a number system exactly mean?

Test Your Mettle Quiz

1. Convert decimal 18 to a binary number.
2. Convert decimal 18 to a hexadecimal number.
3. Convert hexadecimal AB to a decimal number.
4. Convert hexadecimal AB to a binary number.
5. Add two hexadecimal numbers AB and CD.
6. What is ABH in decimal if it represents a 2's complement binary number?
7. Why do computers like 2's complement numbers?
8. Do you think with the evolution of science and technology, computers in the future may store data in a different representation from binary? Why and why not?