  The understanding of the Chern insulator and anomalous quantum Hall effect
(AQHE) in terms of chiral edge states in confined systems is the first aim of
the paper. The model we use consists in a diatomic square lattice with hopping
to the next-nearest-neighbors and broken time-reversal symmetry, which exhibits
edge states in the absence of an external magnetic field. The question of
chiral edge states is approached in the ribbon and plaquette geometries with
different atomic connectivities at the boundaries. Insulating and semi-metallic
phases are revealed, the resulting phase diagram being richer than in Haldane's
model. The transmission coefficients and the Hall resistance $R_H$ are
calculated for the finite size system in the Landauer-B\"{u}ttiker formalism.
The quantized values $R_H=\pm h/e^2$, specific to the Chern insulator, are
manifest in the energy range occupied by the chiral edge states, corresponding
to the unique gap existing in the energy spectrum. Our second aim is to examine
the disorder-induced properties of the model, and, as a novelty, we prove the
disorder-driven AQHE in the semi-metallic phase.
