  Let $T:= T(A, {\mathcal D})$ be a disk-like self-affine tile generated by an
integral expanding matrix $A$ and a consecutive collinear digit set ${\mathcal
D}$, and let $f(x)=x^{2}+px+q$ be the characteristic polynomial of $A$. In the
paper, we identify the boundary $\partial T$ with a sofic system by
constructing a neighbor graph and derive equivalent conditions for the pair
$(A,{\mathcal D})$ to be a number system. Moreover, by using the graph-directed
construction and a device of pseudo-norm $\omega$, we find the generalized
Hausdorff dimension $\dim_H^{\omega} (\partial T)=2\log \rho(M)/\log |q|$ where
$\rho(M)$ is the spectral radius of certain contact matrix $M$. Especially,
when $A$ is a similarity, we obtain the standard Hausdorff dimension $\dim_H
(\partial T)=2\log \rho/\log |q|$ where $\rho$ is the largest positive zero of
the cubic polynomial $x^{3}-(|p|-1)x^{2}-(|q|-|p|)x-|q|$, which is simpler than
the known result.
