POWERS
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.