  In this paper, we give characterization of quadratic $\varepsilon-$canonical
number system ($\varepsilon-$CNS) polynomials for all values $\varepsilon
\in\lbrack0,1)$. Our characterization provides a unified view of the well-known
characterizations of the classical quadratic CNS polynomials ($\varepsilon=0$)
and quadratic SCNS polynomials ($\varepsilon=1/2$). This result is a
consequence of our new characterization results of $\varepsilon -$shift radix
systems ($\varepsilon-$SRS) in the two-dimensional case and their relation to
quadratic $\varepsilon-$CNS polynomials.
