It's the simplest number I could think of that contains any finite binary code in its digits: $$\begin{align} c &= 0.0100011011000001010011100101110111...\\ &= 0.\;0\;1\;00\;01\;10\;11\;000\;001\;010\;011\;100\;101\;110\;111\;0000\;0001... \end{align}$$ Is there any name for this constant?
I found a reference to that constant in this book (Chance: The Life of Games & the Game of Life, Joaquim P. Marques de Sá, p. 120):
A few numbers are known to be normal. One of them, somewhat obvious, was presented by the economist David Champernowne (1920–2000) and corresponds to concatenating the distinct binary blocks of length 1, 2, 3, etc.: $$0.0100011011000001010011100101110111...$$
There is a related number called Champernowne constant for base 2: $$ C_2 = (0.11011100101110111...)_2 $$ but it's not the same as the one cited by that book.
It might sound silly to ask about the name of such constant, but in 2006 I asked about $0.739085...$ and in 2007 it was named Dottie Number, so... who knows?