Flipping the Last Bit

Everyone understands binary math now, right? I've had my head inside a computer for almost fifty years, so I can't entirely trust my sense of what non-nerds do, and don't know, but I'm thinking that the basics of bits and bytes are common knowledge this far into the 21st century.

Certainly everyone understands the idea of place value as it applies to regular, decimal numbers; that the two in $205 is "bigger" than the five in the same number because the two is a number of hundreds and not a number of ones.

In decimals, each digit position to the left increases in value by a factor of ten. Put differently, each position represents a power of ten: 205 is (2 x 10^2) + (0 x 10^1) + (5 x 10^0).

Binary numbers work the same way, of course, so that the first one in 101 has a greater value than the second one.

In binary, each digit position to the left increases in value by a factor of two: each represents a power of two. So that binary 101 is equal to (1 x 2^2) + (0 x 2^1) + (1 x 2^0) = 4 + 0 + 1 = 5.

Excuse me for repeating what everyone probably already knows. I'm done now.

I'm 64 today. That's two raised to the sixth power.

(I've wondered if I could shoehorn significance into the flipping of each successive bit, or if it would be too forced. I've tried it and it almost works, but not quite: that jump from 32 to 64 spans a lot of birth and death and living and other things that deserve more than a simple "times two." So I'll resist the temptation.)

So, not really the last bit, I fervently hope, but merely the left-most that any human gets to flip. I hope to keep revisiting a lot of bits I've flipped before. But that's out of my hands, and every bit is a blessing. I'll take what I can get.

I wish you all a wonderful day.

Hank