Skip to main content

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:

And as a picture:

Comments

Popular posts from this blog

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

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 rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr. 

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…