The power and powers of 2

I'm not a mathematician, but I like numbers. The powers of 2 are particularly interesting, whether in base 10 or binary. Here are some examples:

exponent	base 10	binary
0	1	1
1	2	10
2	4	100
3	8	1000
4	16	10000
5	32	100000
6	64	1000000
7	128	10000000
8	256	100000000
9	512	10000000000
10	1024	10000000000

Wikipedia has this to say:

Powers of 2 are important in computer science; for example, there are 2ⁿ possible values for a variable that takes n bits to store in memory. They occur so commonly that SI prefixes are commonly reinterpreted to refer to them: 1 kilobyte = 2¹⁰ = 1024 bytes. As the standard meanings of the prefixes also occur, confusion may result, and in 1998 the International Electrotechnical Commission approved a set of binary prefixes. For instance, the prefix for multiples of 1024 is kibi-, so 1024 bytes is 1 kibibyte. Other prefixes are mebi-, gibi-, and tebi-.

What about 2 itself? The word two has two homonyms - to & too. 2 is the only even prime number. Two's company. Paul McCartney wrote a song called One And One Is Two, and another called Two Of Us. The Eurythmics put out an album called We Too Are One that featured a song called We Two Are One. Canada has a $2 coin.

Some more factoids from Wikipedia:

• Despite being a prime, two is also a highly composite number, because it has more divisors than one. The next highly composite number is four.
• Two is a factor of ten, so vulgar fractions with 2 in the denominator do not yield infinite decimal expansions, as is the case with most primes.
• Two is the base of the simplest numeral system in which natural numbers can be written concisely, the binary system widely used in computers.
• The square root of 2 was the first known irrational number.
• The designation of the Trans-Canada Highway in most of the province of New Brunswick is 2.
• Two is the DVD region in Europe, South Africa, the Middle East and Japan.
• Two is the first digit of international telephone dialing codes primarily for countries in Africa. On most phones, the 2 key is associated with the letters A, B, and C, but on the BlackBerry it is the key for T and Y.
• The atomic number of helium [my favourite element] is 2.

There are so many interesting things about the number 2!