Number Systems: Fixed and Floating Point Representations

This lecture covers the representation of numbers in digital systems, focusing on fixed-point and floating-point representations. It begins with a review of previous concepts, including arithmetic operations with decimal and binary numbers, and the importance of understanding how digital systems represent fractional numbers. The instructor explains fixed-point representation, detailing its components, precision, resolution, range, and accuracy. Examples illustrate how to compute values for fixed-point numbers, including both unsigned and signed representations. The lecture then transitions to floating-point representation, discussing its structure, including the significand and exponent, and the advantages it offers over fixed-point representation, such as a larger dynamic range and better precision. The IEEE Standard 754 is introduced, outlining how floating-point numbers are represented in computing systems. Throughout the lecture, the instructor emphasizes the trade-offs between fixed and floating-point representations, providing insights into their applications in scientific and engineering contexts.