Sideband #28: 2 ^ 64, ‘K!

I’d planned to do this later, probably for Sideband #64, but in honor of my parents 64th wedding anniversary (2 parents, 64 years, okay!) this numerical rumination gets queue-bumped to now.

Just recently I wrote about 64-bit numbers and how 64 bits allows you to count to the (small, compared to where we’re going) number:

That’s 18 exabytes (or 18 giga-gigabyes). Just to put it into perspective, if we were counting seconds, it amounts to 584,942,417,355 years; more than 500 billion years! (That’s the American, short-scale billion.)

Now the number, 64, is a significant one to computer programmers. For one thing, it’s 8×8, a full chessboard. Among programmers, the numbers 2, 8, 64, 256  and 1024 may be the most significant, although all powers of two have some significance.

The number 2, of course, is central to computer programming. A bit–the fundamental information unit–has two values: zero and one. (Hence my second-favorite bumper sticker regarding computer science: Calm down! It’s just ones and zeros!) Everything is based on this, which is why powers of two have the significance they do.

The number 8 is also central to computing in that it’s (by far) the most common grouping of bits. The well known computer word, “byte,” by default means eight bits. (And it does get its name from being a “bite” of  data. The half-sized package of four bits, a half-bite of data, is known as a nybble.) In fact, the history of computing contains six-bit bytes and nine-bit bytes, so the term “octet” is used to remove ambiguity. But these days, byte pretty much means eight.

Eight bits allows you to count up to 256, which is why it’s a significant number in computing. But these days 256 isn’t as useful as it used to be. In the early (American) days, 256 was more than enough codes to represent all the letters (both upper- and lower-case), all ten digits, all the punctuation symbols and plenty left over for control codes and drawing symbols. There was even room for some non-American characters, such as ñ and ö and Ω.

Two to the power of eight is 256; eight to the power of two is 64. And 64 is the number of squares on a chessboard. It is also the number of bits used as a single package of data in many computers. (A 64-bit package is 8 8-bit bytes.)

And as mentioned above, a 64-bit number counts a good deal higher than an 8-bit number.  If you’re interested in the progression, it goes like this:

(Programmers tend to double things, which is why the powers go from 8 to 16 to 32 to 64.)

Which at least brings us to the point of this post! Two to the power of 64 counts to a rather big number, but it’s a number that has a name: 18+ exabytes. What if you had 64 K (65,536) bits?  How high would that count? First, here’s a  handful of ways to notate it:

And here it is written out (ready?):

Now that’s a big number!

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