Hexadecimal Introduction

Hexadecimal Numbering System

175 -> 10100101 -> AF

• Number base systems

  • Base 10 (decimal)
  • Base 2 (binary)
  • Base 16 (hexadecimal)

• A = 10

• B = 11

• C = 12

• D = 13

• E = 14

• F = 15

Place Value

• Base 10 (decimal)
  • 10 possibilities
    • 0 1 2 3 4 5 6 7 8 9
  • Each place value multiplies by 10
• Base 2 (binary)
  • 2 possibilities
    • 0 1
  • Each place value multiplies by 2
• Base 16 (hexadecimal)
  • 16 possibilities
    • 0 1 2 3 4 5 6 7 8 9 A B C D E F
      • A=10 B=11 C=12
      • D=13 E=14 D=15

Calculating Values

• Calculate:
  • 175: 100 + 70 + 5 = 175
  • 10010101: 128 + 32 + 8 + 4 + 2 + 1 = 175
  • AF: 160 + 15 = 175
• If we want to write 175 into binary
  1. Take the biggest bits you can burn first
     • 128
     • Subtract: 175 - 128
  2. Take the second biggest bits you can burn first
     • 32
     • Subtract: 175 - 128 - 32
  3. Repeat...

Comparing Values

• FF = 255
  • 15 * 16 + 15 = 255