1. The Problem

It's really easy to write integers as binary numbers in 2's complement form. It's a lot more difficult to express floating point numbers in a form that a computer can understand. The biggest problem, of course, is keeping track of the decimal point.

There are lots of possible ways to write floating point numbers as strings of binary digits. Here are some things that the original designers might have had to consider when picking a solution.

• Range
  To be useful, your method should allow very large positive and negative numbers.
  
  
• Precision
  Can you tell the difference between 1.7 and 1.8? How about between 1.700001 and 1.700002? How many decimal places should you remember?
  
  
• Time Efficiency
  Does your solution make comparisons and arithmetic operations fast and easy?
  
  
• Space Considerations
  An extremely precise representation of the square root of 3 is generally a wonderful thing, unless you require a megabyte to store it.
  
  
• 1-1 Relationships
  Your solution will be a lot simpler if each floating-point number can be written only one way, and vice versa.
  
  

Think for a moment about how you might attack this problem.

How did the IEEE ppl solve it? ->