Number Systems

Warmup

• Deconstruct the number 134. What does the 1 mean? What does the 3 mean? What does the 4 mean?
• What is the significance of increasing the digits in a number? Why do we go from single digit at 9 to double digit at 10?

Tracking Sheet

Create a chart like the one below to keep track of each number system:

Base-10 (decimal)

• Uses the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Digits carry over to the next place when 9 becomes 0
• One digit can represent 10 unique numbers
• Two digits represent 100 unique numbers
• Moving right to left, positions represent:
  • 10^0 = 1
  • 10^1 = 10 (“tens”)
  • 10^2 = 100 (“hundreds”)
  • 10^3 = 1000 (“thousands”)

Base-2 (binary)

• Uses the symbols 0 and 1 only
• Digits carry over to the next place when 1 becomes 0
• One digit can represent only two unique numbers
• Two digits can represent only four unique numbers
• Moving right to left, positions represent:
  • 2^0 = 1
  • 2^1 = 2
  • 2^2 = 4
  • 2^3 = 8

Base-16 (hexadecimal)

• Uses the symbols 0 through 9 then A, B, C, D, E, F
• Digits carry over to the next place when F becomes 0
• One digit can represent sixteen unique numbers
• Two digits can represent 256 unique numbers
• Moving right to left, positions represent:
  • 16^0 = 1
  • 16^1 = 16
  • 16^2 = 256
  • 16^3 = 4096

Base-8 (octal)

• Uses the symbols 0, 1, 2, 3, 4, 5, 6, and 7
• Digits carry over to the next place when 7 becomes 0
• One digit can represent eight unique numbers
• Two digits can represent 64 unique numbers
• Moving right to left, positions represent:
  • 8^0 = 1
  • 8^1 = 8
  • 8^2 = 64
  • 8^3 = 512

Practice: Counting

Practice: Subtracting