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This lecture covers the sign-and-magnitude representation of integers, where the set of integers Z includes natural numbers and their negatives. It explains how addition and subtraction are performed in sign-and-magnitude and one's-complement representations, highlighting the advantages of the latter. The lecture also introduces the two's-complement representation, comparing it with one's complement. Additionally, it discusses the Excess-N representation and the concepts of overflow and underflow in integer arithmetic. The presentation concludes with a brief overview of binary multiplication methods.