Digital Systems: Fixed-Point and Floating-Point Arithmetic

This lecture covers the fundamentals of digital systems, focusing on number systems and arithmetic operations with fractional numbers. The instructor begins by reviewing fixed- and floating-point representations, explaining their structures and the IEEE 754 standard. The lecture details how to perform arithmetic operations, including addition, subtraction, and multiplication, for both fixed-point and floating-point numbers. Examples illustrate the processes involved in fixed-point arithmetic, highlighting potential issues such as overflow. The instructor also discusses the pros and cons of fixed-point representation, emphasizing its efficiency in certain applications. The lecture transitions to floating-point arithmetic, explaining the steps for addition and subtraction, including alignment and normalization of significands. Rounding methods, particularly the IEEE 754 rounding to nearest, are also covered, along with the implications of round-off errors. The instructor concludes by addressing the maximum round-off error in floating-point representation, providing a comprehensive overview of the arithmetic operations essential for digital systems.