College Notebook: When I Was Taught Floating-Point

In my article “Floating-Point Questions Are Endless on stackoverflow.com” I showed examples of the many questions asked that demonstrate lack of knowledge of the most basic property of floating-point — that not all decimal values are representable in binary. In response to a reader’s comment on my article I wrote:

It would be interesting to know how it’s taught today (it’s been a very long time since I was taught it). I can’t imagine though that the person teaching it wouldn’t say — within a sentence or two of saying “floating-point” — that it “can’t represent all decimal numbers accurately”.

That prompted me to look through my box of thirty plus year old college (undergraduate) notebooks. I found notebooks for four classes in which I was taught floating-point. The notes from three of those classes confirm what I thought — that we were warned early of the decimal/binary mismatch. But in the first class of the four — the beginner’s class — it’s less clear what we were told. I’ll show you images of the relevant excerpts from my notes. (I notice I had some elements of cursive in my handwriting back then.)

Exploring Binary On My Apple II

I’m reading Steve Wozniak’s 2006 book “iWoz” and this line got me wondering about my own Apple II:

“In every speech I give, I talk to people who are still running Apple IIs, and they say those machines are still running after this many years.”

So I got it out of the attic and powered it up. The dozen or so dead keys notwithstanding, it still works — after 30 years!

My Goals for Exploring Binary in 2009

Well, it’s been one year! I’m very happy about how things are going, even if I didn’t meet any of my goals! (See below for how I did in 2009.)

This post was motivated by the article “What Are Your Internet Goals for 2009?”, by Daniel Scocco.

Since I am new to blogging (I just started this blog a month ago), my internet goals for 2009 are my goals for Exploring Binary specifically. I’d like to get this blog off the ground before I try anything else!

I’ve been maintaining a long list of things I want to accomplish with this blog, but I whittled it down to the most important goals — all challenging but realistically attainable:

Exploring Binary is Live!

After months of toiling with this site off-line I’ve decided it’s time to go live!

If you want to get an idea of what this site is about, you can read the following articles:

The Origins of This Site

My name is Rick Regan and I am the author of this site. I have a B.S., M.S., and Ph.D. in computer science (and no, not from Binary University College 🙂 ). All told, I have been using, studying, and programming computers for almost 30 years. OK, so that qualifies me to write about binary. But why do I want to?

My Plan For This Site

This Web site is for anyone who wants to know more about the underlying technology of computers, which, in a word, is binary. It will cover three main topics: binary numbers, binary code, and binary logic. My hope is that it becomes a reference for beginners and professionals alike, a clearinghouse for binary if you will.

We will discuss binary as it exists both inside and outside of computers; for example, binary numbers. Binary numbers are what computers generally use to do arithmetic. There are all sorts of engineering issues related to their implementation in computers: how big to make them, how to represent negative numbers, how to approximate real numbers. etc. Binary numbers were invented long before computers were; they were just a mathematical construct. It’s enlightening to study them in this pure form, and that we’ll do.