Subsection 6.5.3 The IEEE floating point standard
A colleague of ours, Sid Chatterjee, share the below video on IEEE Standard floating point arithmetic. While we choose to abtract away from the details, It is important to be aware of them.
Unfortunately, we have not figured out how to embed this video, so you will have to access it via the following link: Lecture by Prof. Sid Chatterjee (the lecture starts around the 1:15 minute mark).