Day 2 - Binary Representation of Numbers

Day 2: Binary Representation of Numbers

Learning Objectives

Essential Questions

Materials Needed

Vocabulary

Procedure (50 minutes)

Opening (8 minutes)

  1. Review and Connection (3 minutes)

    • Review binary conversion basics from previous lesson
    • Connect to today's focus on representing different types of numbers
  2. Warm-up Activity (5 minutes)

    • Quick binary conversion practice (2-3 problems)
    • Ask students to predict: "How might computers represent negative numbers?"

Main Activities (32 minutes)

  1. Lecture: Integer Representation (12 minutes)

    • Explain unsigned integers (positive numbers only)
    • Introduce the concept of fixed-bit representation (e.g., 8-bit integers)
    • Demonstrate the range of values in different bit lengths (8-bit: 0-255, etc.)
    • Explain signed integers and two's complement representation
    • Demonstrate converting between positive and negative numbers using two's complement
    • Discuss overflow errors when values exceed the range
  2. Hands-on Activity: Representing Integers (10 minutes)

    • Students work in pairs with 8-bit binary representation cards
    • Practice representing positive integers in 8 bits
    • Practice representing negative integers using two's complement
    • Identify cases where overflow would occur
  3. Group Work: Exploring Limitations (10 minutes)

    • Divide class into small groups (3-4 students)
    • Each group explores a scenario involving binary number limitations:
      • Group 1: What happens when adding two numbers causes overflow?
      • Group 2: What's the smallest/largest number representable in 8-bit signed binary?
      • Group 3: How does increasing bit length affect the range of representable numbers?
      • Group 4: Real-world examples of overflow errors
    • Groups document their findings and prepare to share

Closing (10 minutes)

  1. Brief Introduction to Real Numbers (5 minutes)

    • Explain the challenge of representing real numbers (infinite precision)
    • Introduce the concept of floating point representation
    • Briefly discuss how floating point uses bits for sign, exponent, and mantissa
    • Explain rounding errors and precision limitations
    • Preview that this is why some decimal calculations in computers seem "wrong"
  2. Exit Ticket and Preview (5 minutes)

    • Students complete a worksheet with binary number representation problems
    • Preview that next class will focus on text representation

Assessment

Differentiation

For Advanced Students

For Struggling Students

Homework/Extension

Teacher Notes