Binary Floating Point Multiplication and Division

Understanding how computers handle fractional numbers is essential for anyone pursuing low-level programming, computer architecture, or hardware design. At the processor level, multiplying and dividing decimal values requires precise manipulation of binary representations. This text-based course guides you through the mechanics of binary floating-point arithmetic without needing complex hardware simulators. You will start by mastering foundational concepts, including the anatomy of floating-point representations, binary fractions, and normalized scientific notation. From there, you will learn to execute step-by-step arithmetic operations by manually calculating sign bits, adjusting exponents, and multiplying or dividing mantissas. What you'll learn: Understand the core structure of binary floating-point numbers including sign, exponent, and mantissa fields; Apply normalization rules and handle biased exponents during binary calculations; Multiply binary floating-point numbers by adding exponents and multiplying mantissas; Divide binary floating-point numbers by subtracting exponents and dividing mantissas; Practice rounding, handling overflow and underflow, and identifying precision limits; Analyze modern IEEE floating-point standards and common edge cases. The course begins with essential definitions and binary-to-decimal conversions, then guides you through structured written exercises that build confidence in manual arithmetic. This course is designed for beginner computer science students, aspiring hardware engineers, and curious software developers with no prior experience in binary arithmetic. Start reading today to demystify how processors calculate fractional numbers.