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binary
| There are 10 kinds of people in the world, those who understand binary math, and those who don't. |
| —anonymous |
The simplest positional number system and the natural one to use when dealing with computers; it employs just two symbols, 0 and 1, which correspond to the possible states of an off-on switch. Binary arithmetic was first investigated by Gottfried Leibniz in 1672, though he didn't publish anything about it until 1701.
Each place to the left in a binary number represents the next highest power of two. The binary number 101102, for example, means 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20, or 2210 in the familiar decimal notation. Non-integers can be represented by using negative powers, which are set off from the other digits by means of a radix point (called a decimal point in base 10). The binary number 11.012 thus means 1 × 21 + 1 × 20 + 0 × 2-1 + 1 × 2-2 which equals 3.2510. A number that terminates in decimal doesn't necessarily do so in binary (for example, 0.310 = 0.0100110011001...2), and vice versa. An irrational number, however, is non-periodic in both systems; for example, π = 3.1415926...10 = 11.001001000011111...2.
As the scientist-hero of Fred Hoyle's science fiction novel A For Andromeda explains:
It's arithmetic expressed entirely by the figures 0 and 1, instead of the figures 1 to 10, which we normally use and which we call denary. 0 and 1, you see, could be dot and dash... the binary system is basic; it's based on positive and negative, yes and no ... – it's universal.It is generally accepted that binary may represent a lingua franca for communication between technological civilizations in the Galaxy.
Related category
• MATHEMATICS
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