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?