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This lecture covers the representation of negative integers, starting with the concept of floating point and the need for controlled relative errors. It then explores the properties of integer representation, including the challenges of subtraction and the solution of using the Two's Complement. The lecture delves into practical examples of calculating the opposite of an integer using the Two's Complement, and how to represent negative numbers to replace subtraction with addition. It concludes with detailed explanations and examples of the Complement to 1 and Complement to 2 operations for integer representation.