Number Systems: Fixed and Floating-Point Representations

This lecture covers the fundamentals of number systems, focusing on fixed-point and floating-point representations. It begins by reviewing arithmetic operations with decimal and binary numbers, including algorithms for addition, subtraction, and multiplication. The instructor explains the concepts of radix point, precision, resolution, range, accuracy, and dynamic range, highlighting the differences between fixed-point and floating-point representations. The lecture details how to represent numbers in both formats, including the IEEE 754 standard for floating-point representation. Examples illustrate the conversion between decimal and binary formats, as well as the advantages and disadvantages of each representation. The discussion includes the significance of the significand, exponent, and the concept of biased representation in floating-point numbers. The lecture concludes with an overview of rounding methods and the handling of special values such as zero, infinity, and NaN (not a number). Overall, this lecture provides a comprehensive understanding of how digital systems represent and manipulate numbers.