Lecture Notes: IP Subnetting and Binary Calculations

Introduction to Binary Numbers

• Binary System: A numbering system using two digits, 0 and 1.
  • Each digit is called a bit.
  • Byte/Octet: A group of 8 bits.
• Importance: Essential for understanding IP subnetting and conversions between decimal and binary.

Creating a Binary-Decimal Conversion Chart

• Chart Construction:
  1. Start with 1 on the right.
  2. Double each subsequent number moving left:
     • 1, 2, 4, 8, 16, 32, 64, 128, etc.
  3. Can extend beyond 128 to 256, 512, etc.
• Purpose: Used for conversions between binary and decimal.

Binary to Decimal Conversion

• Example 1: Binary 00000010
  • Conversion chart: 1, 2, 4, 8, 16, 32, 64, 128
  • Only the 2 position has a 1.
  • Sum: 2 (Decimal)
• Example 2: Binary 10000010
  • 1s in 128 and 2 positions.
  • Sum: 128 + 2 = 130 (Decimal)
• Example 3: Binary 11111111
  • 1s in all positions.
  • Sum: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 (Decimal)

Decimal to Binary Conversion

• Example: Decimal 154 to Binary
  • Use conversion chart, starting from the largest value.
  • Check if each value is less than or equal to the remaining decimal number:
    • 128 fits (1), 64 does not (0), 32 does not (0), 16 fits (1), 8 fits (1), 4 does not (0), 2 fits (1), 1 does not (0)
  • Binary result: 10011010

Increasing Bit and Decimal Options

• Binary Expansion:
  • More bits = more decimal possibilities.
  • Examples:
    • 2 bits: 4 outcomes (00, 01, 10, 11) → Decimal: 0-3
    • 3 bits: 8 outcomes
    • 4 bits: 16 outcomes
    • 5 bits: 32 outcomes
    • 6 bits: 64 outcomes
    • 7 bits: 128 outcomes
    • 8 bits: 256 outcomes
• Power of Two:
  • Fundamental concept for understanding binary.
  • Examples:
    • 2^0 = 1
    • 2^1 = 2
    • 2^2 = 4
    • 2^3 = 8

Conclusion

• Mastery of binary-decimal conversions is crucial for IP subnetting.
• Understanding and using the conversion chart effectively aids in accurate calculations and understanding of network configurations.