The binary numeration system is base 2, so the only possible digits are 0 and 1. This system is used extensively in computer programming. For example, the ASCII system converts letters to binary numbers.
http://en.wikipedia.org/wiki/ASCII
The letter A is represented by 65, which is 64 + 1 in terms of powers of 2:
65 = 1 (64) + 0(32) + 0(16) +0(8) + 0(4) + 0(2) +1(1) = 1000001.
B is given by 66, C is 67, etc.
The Flight of the Conchords have a binary solo in their song Robots:
https://www.youtube.com/watch?v=CTjolEUj00g
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