# Bit

A binary unit of information, numerically equal to the amount of information obtained during a trial with two mutually exclusive equally probable alternatives ( $p _ {1} = p _ {2} = 1/2$):

$$I (p _ {1} , p _ {2} ) = \ p _ {1} \mathop{\rm log} _ {2} p _ {1} - p _ {2} \mathop{\rm log} _ {2} p _ {2} = \ \mathop{\rm log} _ {2} 2 = 1 \ \ \textrm{ \BQT bit\EQT } ,$$

the logarithms being taken to the base 2. The bit is the most frequently used unit, but other units of information are also employed — the "Hartley" or the "nit" , the definitions of which involve decimal and natural logarithms respectively.