Floating Point Numbers: Representation and Errors

This lecture discusses the representation of floating point numbers, focusing on ensuring a uniform relative error within a given domain. It explores examples using scientific notation with a fixed number of significant digits, highlighting the trade-off between precision and range. The instructor explains the concept of relative error and its implications, emphasizing the importance of maintaining consistency in error distribution. Additionally, the lecture covers the representation of floating point numbers in binary, detailing the structure of a floating point number in base 2. It also addresses the maximum relative error in binary representation and compares it to decimal representation. The discussion includes practical examples and visual aids to illustrate the concepts effectively.