Number Systems: Fixed and Floating-Point Representations

This lecture covers the fundamentals of number systems in digital systems, focusing on fixed-point and floating-point representations. The instructor begins by reviewing previous concepts related to arithmetic operations with decimal and binary numbers, including algorithms for addition, subtraction, and multiplication. The lecture then introduces the notion of the radix point and explains how digital systems represent numbers with fractional parts. Key learning outcomes include understanding fixed-point representation, evaluating precision, resolution, range, accuracy, and dynamic range, as well as comparing the advantages and disadvantages of fixed and floating-point representations. The instructor elaborates on the IEEE 754 standard for floating-point representation, detailing the components of significand and exponent, and discussing rounding methods. The lecture concludes with examples illustrating the conversion between decimal and floating-point formats, emphasizing the importance of these representations in scientific and engineering applications.