Bit
The amount of information D in a discrete valued variable with N distinct states is measured in units of bits as
D = log2N bits
A binary variable(?) conveys log22 = 1 bit of information. Indeed, the word bit is short for binary digit.
Bit Definition
A bit is two discrete values of information
Not to be confused with positions in binary numbers. Or how many bits of a binary number does it take to include this value.
One digit - is zero information! Fine!
From: Harris D. M., Harris S. L. - Digital Design and Computer Architecture, 2nd Edition - 2012
1.4.6 Signed Binary Numbers - 8 page