Understanding and Converting Base Number Systems

Base Number Systems

• Why learn about base number systems?
• What is a base number system?
• How does a base number system work?
  • Digits available
    • Counting in Decimal (Base₁₀)
    • Counting in Binary (Base₂)
    • Counting in Hexadecimal (Base₁₆)
    • Counting in Octal (Base₈)
    • Counting in different numbers systems
  • Values represented by column
    • Column values in Decimal (Base₁₀)
    • Column values in Binary (Base₂)
    • Column values in Hexadecimal (Base₁₆)
    • Column values in Octal (Base₈)
    • Differences in column values between number systems

Base Number System Practice Exercises

Binary (Base₂)

• Why learn the Binary (Base₂ ) number system?
• What is the Binary (Base₂ ) number system?
• How does the Binary (Base₂ ) number system work?
  • Counting in Binary (Base₂)
  • Column Values in Binary (Base₂)
  • Converting from Binary (Base₂) to Decimal (Base₁₀)
  • Converting from Decimal (Base₁₀) to Binary (Base₂)
  • Determining the number of bits needed to represent a given number of possible values
  • Masking binary numbers

Binary (Base₂) Practice Exercises

Hexadecimal (Base₁₆)

• Why learn the Hexadecimal (Base₁₆ ) number system?
• What is the Hexadecimal (Base₁₆ ) number system?
• How does the Hexadecimal (Base₁₆ ) number system work?
  • Counting in Hexadecimal (Base₁₆)
  • Column Values in Hexadecimal (Base₁₆)
  • Converting from Hexadecimal (Base₁₆) to Binary (Base₂)
  • Converting from Binary (Base₂) to Hexadecimal (Base₁₆)

Hexadecimal (Base₁₆) Practice Exercises

Octal (Base₈)

• Why learn the Octal (Base₈ ) number system?
• What is the Octal (Base₈ ) number system?
• How does the Octal (Base₈ ) number system work?
  • Counting in Octal (Base₈)
  • Column Values in Octal (Base₈)
  • Converting from Octal (Base₈) to Binary (Base₂)
  • Converting from Binary (Base₂) to Octal (Base₈)

Octal (Base₈) Practice Exercises

Resources

• Microsoft Windows Scientific Calculator
  • Start → Programs → Accessories → Calculator
    • View → Scientific
      • Hex = Hexadecimal
      • Dec = Decimal
      • Oct = Octal
      • Bin = Binary