Digital Systems: Fixed and Floating Point Arithmetic

This lecture covers the fundamentals of digital systems, focusing on fixed-point and floating-point representations. It begins with a review of number systems, including the concept of radix points in binary. The instructor explains how to perform arithmetic operations such as addition, subtraction, and multiplication in both fixed-point and floating-point formats. Key topics include the IEEE 754 standard for floating-point representation, the significance of precision, resolution, and dynamic range, as well as the implications of rounding errors. The lecture provides examples to illustrate the arithmetic processes, emphasizing the differences between fixed-point and floating-point calculations. The instructor also discusses the advantages and disadvantages of fixed-point representation, particularly in terms of efficiency and complexity in determining the binary point's position. The session concludes with a detailed examination of floating-point arithmetic, including alignment, normalization, and rounding techniques, ensuring a comprehensive understanding of how these systems operate in digital computing.