I'm working on a series of blog posts that highlight some basic aspects of floating point arithmetic with examples in Julia. The first one, on bisecting floating point numbers, is available at
http://squishythinking.com/2014/02/22/bisecting-floats/ The intended audience is basically a version of me several years ago, early in physics grad. school. I wrote a fair amount of basic numerical code then, both for problem sets and for research, but no one ever sat me down and explained the nuts and bolts of how computers represent numbers. I thought that floating point numbers were basically rounded off real numbers that didn't quite work right all the time, but were usually fine. In the intervening years, I've had the chance to work on a few algorithms that leverage the detailed structure of floats, and I'd like to share some of the lessons I picked up along the way, in case there's anyone else reading who is now where I was then. Some of the material is drawn from a talk I gave at the Bay Area Julia Users meetup in January, on the motivations behind PowerSeries.jl
