Binary Introduction

Binary Numbering System

175 -> 10100101

• Number base systems
  • Base 10 (decimal)
    • Each digit space has a maximum value, in decimal it is 9.
  • Base 2 (binary)
    • In binary it is 1.

Place Value

• Base 10 (decimal)

  • 10 possibilities
    • 0 1 2 3 4 5 6 7 8 9 10
  • Each place value multiplies by 10

• Base 2 (binary)

  • 2 possibilities
    • 0 1
  • Each place value multiplies by 2

• Byte = 8 bits.
  • 256 combinations
• Calculate:
  • 100 + 70 + 5 = 175
  • 128 + 32 + 8 + 4 + 2 + 1 = 175

What range of values can we make with 8 bits? 256

• 255 = 11111111
• 0 = 00000000