Homework 2

• Bases other than 10
  • Convert 31040₅ to base 10.
  • Convert 2023 (base 10) to base 7.
  • Convert 12012₃ to base 4.
  • In what base(s) is 4×5=32?
  • If a number is represented as 1234 in base a and as 1002003004 in base b for some positive a and b, what can you say about bases a and b?
  • State and provide brief justifications for a few divisibility tests in base 12. (Try to find as many as you can, but at least three different ones are expected. For example, you could have one divisibility test that looks at the last digit, one that looks at the last two or three digits, and one that looks at the sum of the digits.)