Turning 32 may not seem like a very exciting* *birthday, but it is! In fact, it is the most momentous birthday of all, because it’s the first time in your life that you can’t show your age on a single hand.

## Counting in binary.

First, a refresher. Binary, (popularly known as the number system of computers which think in terms of ons and offs, as represented by ones and zeros) is base-2, whereas good old decimal is base-10.

This means that in the decimal system, we have:

One | 0001 | 10^{0} |

Ten | 0010 | 10^{1} |

One hundred | 0100 | 10^{2} |

One thousand | 1000 | 10^{3} |

Whereas in the binary system, we have:

One | 0001 | 2^{0} |

Two | 0010 | 2^{1} |

Four | 0100 | 2^{2} |

Eight | 1000 | 2^{3} |

In decimal, there are 10 characters: 0,1,2,3,4,5,6,7,8, and 9. We can easily count to ten on our fingers with each finger representing the next character. But you can’t reach any number higher than ten. In binary, each finger contains all possibilities of each character (0 or 1, up or down) so you can have each finger represent the next power of two instead of the other characters. In effect, with ten fingers, you an represent all numbers up to 2^{10}-1 = 1023, a huge improvement!

Hold your closed fists in front of you, nails facing you. You can think of ten bits, like this:

Lift your right thumb and you have the number 2^{0}=1:

Lift just your right index-finger. Now you have 2^{1} = 2

How about the number ten? That’s 2^{3} + 2^{1} = 8 + 2 = 10, so you say:

which is kind of a funny bunny hand signal.

What about the universal rock hand-symbol?

That’s 16 + 2 = 18

Middle finger?

That’s four.

Middle finger with thumb out?

is five. So next time your five year old gives you the finger, and says, “I’m this many!” you know he or she is counting in a powerful numbering system. Congratulations!

## The momentous 32^{nd} birthday.

Now you can see why 32 is such a momentous birthday. If you hold all your fingers up on one hand, you’re expressing

= 1+2+4+8+16 = 31

So once you turn 32 you have to show your left pinky and a right fist:

So when you’re 89, you can still show it on your 2 hands!

= 1+8+16+64 = 89

If you reach the ripe old age of 1023, you’re this many:

It’s no coincidence, then, that one of my favorite numbers is 645.

Happy new year everyone.