Binary 1: Clocks

There are 10 types of people: Those who know binary and those who don't. old joke**"There are 10 types of people: those who know ternary, those who don't and those who were expecting the binary joke."Mathematical joke

To anyone who might have been raised on the decimal system, to anyone who counts to 10 on their fingers, different number systems can seem intimidating. What makes out the charm of the above joke is that we can be quick to take it for granted that numbers are supposed to look the way they look in the decimal system. A 10 that really means a 2 is confusing, or at its worst an insult to many of those among us who celebrate 10th, 30th and 50th birthday parties in ways we wouldn't celebrate our 43rd.

I'm inclined to consider this a long-term effect of a math class dominated by fear.

Since in the meantime a math of a perfectly harmless (even friendly) nature has become something I like tinkering with, I have talked to people of various different backgrounds and levels of education about this or the other mathematical topic and would often be met by the shield of "I'm no good at math" to spare the person wielding it the embarassment of not understanding a particular idea (or otherwise - in some cases, surely - to get me to stop talking to them and leave them alone; thank you, scary math teachers, for making this ambiguous).

There is however nothing inherently threatening about binary numbers, at least not to those of us who know how to read digital clocks. We see a 59 and expect it to be followed by 0, and 23 is followed by 0 (and Sunday, btw, is followed by Monday).

We cycle through our seconds from 0 to 59 (base-60), and another minute cycles through its own base-60 system, which upon completion grants the hour a step ahead toward 23 or a return to 0 (base-24), and in just the same way do we cycle from 0 to 9 (base-10 or decimal system) when we, for example, count sheep, or compose lists of commandments that we hand down to our creations (supposedly).

The point being, if you can count from 0 to 59, from 0 to 23 and from 0 to 9 then you can also count from 0 to 1.

Binary alarm clock

1111 is 15 in the decimal system by the way, or F in a base-16 (hexadecimal) system that cycles from 0 through 9 and A to F.

That's all for now.

 

HOMEWORK
Try to fall asleep while counting sheep in binary.

Binary 1: Clocks .pat