Binary

Little Twelve Toes is a Schoolhouse Rock video. It doesn't just cover multiplying by twelve, it covers some very basic concepts connecting the fact that we have ten fingers and ten toes to the fact that earthbound humans use a base ten number system.

And it very quickly introduces what a base twelve number system would look like without getting bogged down or watering it down. It makes it clear that in a base twelve number system, one followed by zero is annotation for the number twelve, not the number ten.

Binary is a base two number system. One followed by zero is annotation for the number two.

Binary is an extremely important mathematical concept to be familiar with in the computer age because all computer systems are based on binary. That's what's under the hood and behind everything else computers do.

We use binary for computers because computers use electricity and there's an on state and an off state. So your on state equals the number one and your off state equals zero and if you use binary, that's sufficient information to build ANY number of ANY size when combined with stop and start codes so you know where your number begins and ends.

We also use that to build the alphabet.

Humans routinely use numbers and letters in substitution. Old fashioned rotary phones had three or four letters on every key with a number, so you can makeup a word and turn that into a phone number, though it works less well in the other direction. 

That was used to make it easy to remember important phone numbers. You can pick a number that you can figure out reliably if given a word or phrase where the letters correspond to the numbers in question on your keypad.

 

It works less well in the other direction. Being given a number and trying to figure out the word when every number corresponds to several letters is a guessing game, but a word or phrase reliably converts to a specific phone number.

Base ten means each digit in a string of numbers making up a larger number is a figure based on an exponential of the number ten, even the ones place.

So we have ten symbols for each place: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

And each time you add another place in a number, it's an order of magnitude larger. In other words, it's multipled by whatever your base number is.

In base ten, it's ones, tens, hundreds, thousands, etc.

In base two, those spaces are exponential values of the number two.

Two to the zero power is one.

Two to the first power is two.

Two to the second power is four.

Exponent means there's a little number written above it and to the right telling you how many times to multiply it by itself.

So the first ten values in binary are:

1

2

4

8

16

32

64

128

256

512

And if you want to count in binary on your fingers, the first five places are counted on the right hand and the second five are counted on the left hand.