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.)

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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!

Some BASIC Commands I Tried On My Keyboard-Challenged But Otherwise Still Working Apple II
Some BASIC Commands I Tried On My Keyboard-Challenged But Otherwise Still Working Apple II

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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:

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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?

The Apple II I Used in High School.
The Apple II I Used in High School.

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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.

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