Chapter 1: Data Representation

NOTES

1.1 Number Systems

Summary

• Binary System: A number system using only 0 and 1 (base-2).
• Denary System: The standard number system using 0-9 (base-10).
• Hexadecimal System: A number system using 0-9 and A-F (base-16).
• MAC Address: A unique identifier assigned to a network device, partially represented in hexadecimal.
• IP Address: Internet Protocol address identifying devices on a network.
• Overflow: When the result of a binary addition exceeds the storage limit of the system.
• Logical Shift: A binary operation that shifts digits left or right, multiplying or dividing by 2.

Conversions:

1. Binary to Denary:

• Multiply each binary digit by its place value (2^position) and sum the results.
• Example: Binary 1101
  • (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 8 + 4 + 0 + 1 = 13

2.Binary to Hexadecimal:

• Group binary digits in sets of 4 (starting from the right). Add leading zeros if needed.
• Convert each group to hexadecimal using a binary-to-hexa table.
• Example: Binary 11011110
  • Split: 1101 (D in hex) and 1110 (E in hex).
  • Result: DE

3.Denary to Binary: