Overview

You probably noticed that we’ve been very focused on integers and have been ignoring the idea of “floating point” or “real” numbers, such as 3.3333 or 1/6. That’s because they are really hard to work with! Today, we’ll just scratch the surface regarding their representation.

Basic Learning Objectives

Before class, you should be able to:

  • Explain the issue with representing real numbers in binary
  • Describe the high-level idea of floating-point representation
  • Summarize a historical example of a rounding error

Advanced Learning Objectives

After class, you should be able to:

  • Identify the parts of a floating-point binary sequence
  • Convert between floating point and binary

Resources

You should read the following in DIS:

Checks

Submit answers to the following on Moodle.

  1. Given the hexadecimal number 0x40533333, identify the sign, exponent, and mantissa/significand for these bits. Give your answer in hex or binary and indicate which it is.

  2. Convert that hexadecimal number 0x40533333 to decimal based on the IEEE standard 754.

  3. You can get additional practice with this calculator (and check your work, but I recommend doing it by hand first!)