5/15/1999 Version

264 is an extemely large quantity. Still it is very close in a way to other powers of 2 that are at the heart of digital computers. Consider a number like 232 or 216. Those both represent the length of computer words as numbers of binary digits in some digital systems.

In computing it is useful to know certain powers of 2. A few of the most useful are:

23= 8

25= 32

28= 256

210= 1024 264 is a lot larger than 10246. That's true because when we multiply things with the same lower or base quantity, we add their exponents. This is easy to check by rewriting 100 and 1000 using exponents (compare with acquiring a hundred thousand dollar bills). So 210 multiplied by itself six times is close to (but a factor of 24 smaller than) the 264 quantity.

This all makes 264 even bigger than 103 times itself six times.

In other words, the number of grains for the last chessboard square exceeds a billion billion.