Information Representation: Real Numbers and Errors

This lecture covers the representation of information, focusing on natural numbers, integers, reals, alphabets, and images. It explains how real numbers are represented in base 10 and binary, with examples of conversion and discretization errors. The consequences of a finite number of digits on precision are discussed, along with fixed-point and floating-point representations. The lecture also delves into the errors associated with discretization and the normalization of numbers. Examples of floating-point representation are provided, emphasizing the significance of the most significant digit. The implications of uniform relative error in scientific notation and the three parts of floating-point representation are explored.