My programming career started with Webmonkey's PHP tutorial[1], when it was first published some years ago. It doesn't talk about floating point operations or binary representations. Instead, you first learn how to print "I am the CHICKEN MAN" in your browser. Shortly after, you're taught to use forms, and by then you've created something that takes input and processes it.
You type your stuff in, click the button, and it shows up in the browser. The code you wrote -- this strange language that seems like magic -- clearly works. You've made the machine do something. Just to make sure, you type something else in, click the button, and there it is. That's what inspired me to become a programmer. The ones and zeros came later.
[1] http://www.webmonkey.com/2010/02/php_tutorial_for_beginners/ (I don't recommend this tutorial to anyone learning to program. It was useful when it was written, but it's not up to date, and some of the examples are broken. In 2011, there are lots of good beginner books.)