This chapter of the book "Computer Arithmetic Algorithms" by Israel Koren, in its second edition, covers conventional number systems and their representations. It begins with an introduction to binary number systems, explaining how numbers are represented in fixed-length sequences of bits and the interpretation rules for these sequences. The chapter then discusses machine representations of numbers, distinguishing between conventional and unconventional number systems. It highlights the importance of nonredundant, weighted, and positional number systems, and explains the concept of radix conversion, which involves translating numbers between different number systems. The chapter delves into the representation of negative numbers, presenting two common methods: signed-magnitude and complement representations. The signed-magnitude method represents the sign and magnitude separately, while the complement representations (radix complement and diminished-radix complement) use a single sequence to represent both positive and negative numbers. The chapter provides detailed explanations and examples for each method, including the calculation of numerical values from binary representations. Additionally, the chapter covers addition and subtraction operations in these number systems, discussing overflow conditions and the arithmetic shift operations, which are useful in multiplication and division algorithms. The chapter concludes with exercises that reinforce the concepts discussed, such as finding fixed-point representations, verifying procedures for obtaining complements, and proving extensions of signed numbers to infinite sequences.This chapter of the book "Computer Arithmetic Algorithms" by Israel Koren, in its second edition, covers conventional number systems and their representations. It begins with an introduction to binary number systems, explaining how numbers are represented in fixed-length sequences of bits and the interpretation rules for these sequences. The chapter then discusses machine representations of numbers, distinguishing between conventional and unconventional number systems. It highlights the importance of nonredundant, weighted, and positional number systems, and explains the concept of radix conversion, which involves translating numbers between different number systems. The chapter delves into the representation of negative numbers, presenting two common methods: signed-magnitude and complement representations. The signed-magnitude method represents the sign and magnitude separately, while the complement representations (radix complement and diminished-radix complement) use a single sequence to represent both positive and negative numbers. The chapter provides detailed explanations and examples for each method, including the calculation of numerical values from binary representations. Additionally, the chapter covers addition and subtraction operations in these number systems, discussing overflow conditions and the arithmetic shift operations, which are useful in multiplication and division algorithms. The chapter concludes with exercises that reinforce the concepts discussed, such as finding fixed-point representations, verifying procedures for obtaining complements, and proving extensions of signed numbers to infinite sequences.