Floating point from scratch: Hard Mode (essenceia.github.io)

The article explains how IEEE 754 floating-point works by building intuition from the raw bit-level representation, covering tricky cases like signed zero, NaNs (including quiet vs signaling), infinities, and denormals with gradual underflow. It then discusses rounding modes and how they affect results when values fall outside a format’s representable range, setting up for a deeper “from scratch” and hardware/ASIC-focused implementation later.