Why your 32nd birthday is a momentous ordeal

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 100
Ten 0010 101
One hundred 0100 102
One thousand 1000 103

Whereas in the binary system, we have:

One 0001 20
Two 0010 21
Four 0100 22
Eight 1000 23

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 210-1 = 1023, a huge improvement!

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

0
00000 00000

Lift your right thumb and you have the number 20=1:

00000 00001
00000 00001

Lift just your right index-finger. Now you have 21 = 2

00000 00010
00000 00010

How about the number ten? That’s 23 + 21 = 8 + 2 = 10, so you say:

00000 01010
00000 01010

which is kind of a funny bunny hand signal.

What about the universal rock hand-symbol?

00000 10010
00000 10010

That’s 16 + 2 = 18

Middle finger?

00000 00100
00000 00100

That’s four.

Middle finger with thumb out?

00000 00101
00000 00101

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 32nd 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

00000 11111
00000 11111

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

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

00001 00000
00001 00000 = 32

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

00010 11001
00010 11001

= 1+8+16+64 = 89

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

11111 11111
11111 11111

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

Happy new year everyone.

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