Lecture on IP Subnetting and Binary Calculations

Introduction to Binary

• Binary uses two numbers: 0 and 1.
• Each 0 or 1 is known as a bit.
• Byte consists of 8 bits, sometimes called an octet.

Conversion Chart for Binary to Decimal

• Important for converting between binary and decimal.
• Start with 1 on the right, and double moving left:
  • 1, 2, 4, 8, 16, 32, 64, 128, etc.
• Useful for binary to decimal conversions.

Binary to Decimal Conversion Examples

Example 1: Binary 00000010

• Conversion chart: 1, 2, 4, 8, 16, 32, 64, 128
• Only binary 1 in column 2, so 2 in decimal.
• Result: 2 in decimal.

Example 2: Binary 10000010

• Conversion chart used.
• Binary 1s in columns 128 and 2.
• Sum: 128 + 2 = 130 in decimal.

Example 3: Binary 11111111

• All positions have binary 1.
• Sum: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 in decimal.

Decimal to Binary Conversion Example

Example: Decimal 154

• Start with a conversion chart.
• Determine positions of binary 1 by checking column sums:
  • 128 is less than 154: binary 1.
  • 128 + 16 (144) is less than 154: binary 1.
  • 128 + 16 + 8 (152) is less than 154: binary 1.
  • 128 + 16 + 8 + 2 = 154: binary 1.
• Result: 10011010 in binary.

Understanding Binary Length and Decimal Range

• With 8 bits, can convert numbers from 0 to 255.
• More bits increase possible decimal options:
  • 2 bits: 4 outcomes (0, 1, 2, 3)
  • 3 bits: 8 outcomes
  • 4 bits: 16 outcomes
  • 5 bits: 32 outcomes
  • 6 bits: 64 outcomes
  • 7 bits: 128 outcomes

Powers of Two

• Each binary place represents a power of two:
  • $2^0 = 1$
  • $2^1 = 2$
  • $2^2 = 4$
  • $2^3 = 8$, etc.
• Increasing the power increases the maximum decimal value.

Conclusion

• Understanding binary and its conversions is crucial for IP subnetting and network calculations.
• Practice converting to solidify understanding of binary and decimal relationships.