Binary Math Lessons: The Secret Origin

Unschooling? How did my last post have anything to do with unschooling? As soon as I saw the title on the screen, I cringed. The benefits of binary math, check, anything to do with unschooling? Nada.

As it turns out, I’d started in the middle of the story. Our six year-old, No. 1, and I started heading towards binary math—in more proper unschooling form—because she wandered into the room one day and said, “Dad, I want to learn what you do at work.”

All I do at work is test machines whose sole job it is to move ones and zeroes around: microprocessors and other digital devices also known as computer chips in the vernacular. So, since one and zero are pretty simple concepts, and as it turns out, the logic gate building blocks of digital devices are also really simple, off we went!

The first thing we need to nail down were the handful of logic gates I encounter. What’s a logic gate you ask? It’s just an electrical embodiment of a logical construct, (you know like the one’s you had in philosophy 101). Take the ‘and’ gate we started out with for example. The device takes two inputs that can be either a one or a zero, and outputs a single number in return, again either one or zero. If both the inputs are 1, (known as logical true in the vernacular), then the device outputs a one, if not, then the device outputs a 0,(a logical false value). Hence, if one output AND the other are both true, the ‘and’ gate gives a true output aka 1. Otherwise its output is 0, aka false .

No. 1 and I made up some homework sheets for her to play around with. Her homework was to fill in the logic gates on the page with any sets of inputs and outputs from the table.

Did I mention we talk about this stuff all the time too?
"Hey, what's 1 AND 1?"
"1"
"What's 1 AND 0?"
"0 Dad," and so on.

I personally think our constant conversations drive things home more than the homework, but who knows? In any event, there are a lot of MUNI riders who know more about logic gates than they used to or maybe wanted to.

In case you wanted to play along:

Homework pages as pdf

And as a picture:

Comments

More Cowbell! Record Production using Google Forms and Charts

First, the what : This article shows how to embed a new Google Form into any web page. To demonstrate ths, a chart and form that allow blog readers to control the recording levels of each instrument in Blue Oyster Cult's "(Don't Fear) The Reaper" is used. HTML code from the Google version of the form included on this page is shown and the parts that need to be modified are highlighted. Next, the why : Google recently released an e-mail form feature that allows users of Google Documents to create an e-mail a form that automatically places each user's input into an associated spreadsheet. As it turns out, with a little bit of work, the forms that are created by Google Docs can be embedded into any web page. Now, The Goods: Click on the instrument you want turned up, click the submit button and then refresh the page. Through the magic of Google Forms as soon as you click on submit and refresh this web page, the data chart will update immediately. Turn up the:

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

Now available as a Kindle ebook for 99 cents ! Get a spiffy ebook, and fund more physics The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems , there seem to be fewer explanations of the procedure for deriving the conversion, so here goes! What do we actually want? To convert the Cartesian nabla to the nabla for another coordinate system, say… cylindrical coordinates. What we’ll need: 1. The Cartesian Nabla: 2. A set of equations relating the Cartesian coordinates to cylindrical coordinates: 3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system: How to do it: Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables. The chain

The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1. While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero. This is typically explained in the following way. While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare. That doesn't stop us from looking for them though! Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2]. Cabrera was utilizing a loop type of magnetic monopole detector. Its operation is in concept very sim

Copasetic Flow

Search This Blog