Introduction:

The following lessons introduce the topic of number systems with a focus on binary numbers and binary arithmetic. Each lesson includes a set of review questions which test the important concepts from the lesson and provide practice problems. After reading each lesson, you should work the review questions before proceeding to the next lesson. Use the navigation bar at the top of this page to view the lessons and access the review questions. Each lesson page has a link on the navigation bar which will take you to the review questions for that lesson. To begin your study, click at the top of this page.

Lessons:

  1. Introduction to Binary Numbers
  2. Understanding Number Systems
    1. Binary to Decimal Conversion
    2. Decimal to Binary Conversion
    3. Converting Fractions
  3. Binary Arithmetic
    1. Binary Addition
      1. Adding Two Binary Numbers
      2. Adding Multiple Binary Numbers
      3. Adding Binary Fractions
    2. Binary Subtraction
    3. Binary Multiplication
    4. Binary Division
  4. Signed numbers
    1. One's complement
    2. Two's complement
  5. Subtraction with Signed Numbers
    1. Subtraction with One's complement
    2. Subtraction with Two's complement
  6. Hexadecimal and Octal Numbers
  7. Comparing Number Systems
  8. Summary

Learning objectives:

  • Convert between binary and decimal numbers
  • Add, subtract, multiply, and divide binary numbers
  • Represent signed binary numbers with 1 and 2's complement
  • Add and subtract signed binary numbers