|On, On, Off, Off, On = 16+8+1=25|
B is for BinaryI loved teaching about binary numbers when I used to teach basic computer courses. What's going on inside that box? Lots of little electronic switches are going on and off, and that's enough to represent any number (and anything else you put in a translation table). The switches are not the mechanical sort you see to the right; they're microscopic.
On=1, Off=0. Start on the right with the ones position (20), double each time for the twos (21) place, fours (22), eights (23), sixteens (24), and further. One byte in a computer is 8 bits (bit is short for binary digit), so the highest-valued binary digit in a byte is worth 27 or 128, and a byte can take on any value from 0 to 255. For instance, I'm 54 - that's 32+16+4+2, or 00110110.
Rick Regan really digs binary, and his blog, Exploring Binary, says it all. Much of it is too technical for me, but I've enjoyed a number of his articles. How I Taught My Mother Binary Numbers looks like a good starting point, along with One Hundred Cheerios in Binary. His post on the look and sound of binary numbers is delightful, as is The Binary Marble Adding Machine.
Here's one more fun site for binary numbers: Computer Science Unplugged.
Outside of math, I think we too often think in binary terms - good or bad, left or right, boy or girl, etc. I like it when I can break out of those boxes and find a third path. But in math, binary is fun.