Review Questions for Floating Point Representation

  1. Convert a decimal number to binary.
  2. Convert a binary number to decimal.
  3. What are the differences between floating point and fixed point representation?
  4. Given a real number, how would you store it as a machine number?
  5. Given a real number, what is the rounding error involved in storing it as a machine number? What is the relative error?
  6. Explain the different parts of a floating-point number: sign, significand, and exponent.
  7. How is the exponent of a machine number actually stored?
  8. What is machine epsilon?
  9. What is underflow (UFL)?
  10. What is overflow?
  11. Why is underflow sometimes not a problem?
  12. Given a toy floating-point system, determine machine epsilon and UFL for that system.
  13. How do you store zero as a machine number?
  14. What are subnormal numbers?
  15. How are subnormal numbers represented in a machine?
  16. Why are subnormal numbers sometimes helpful?
  17. What are some drawbacks to using subnormal numbers?