POWERS
*5/15/1999 Version*

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2*^{64} 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
2^{32} or 2^{16}. 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:

2^{3}= 8

2^{5}= 32

2^{8}= 256

2^{10}= 1024
2^{64} is a lot larger than 1024^{6}. 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 2^{10} multiplied by itself six times is
close to (but a factor of 2^{4} smaller than) the 2^{64} quantity.

This all makes 2^{64} even bigger than 10^{3} times itself six times.

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