Boundary layer transition on fluid flows holds significant implications on the aerodynamic drag imposed on aircrafts due to the high coefficient of friction of turbulent boundary layers. The presence of gaps, small rectangular cavities, on the surface of the vehicle can accelerate transition. Stability analyses of the flow over gaps demonstrate that the interaction between two-dimensional unstable Rossiter modes and three-dimensional unstable centrifugal modes plays an important role in the boundary layer transition process. In this project, we evaluate the stability of two-dimensional compressible fluid flows past asymmetric rectangular gap configurations, i.e., gaps with trailing edge at a different height than the leading edge. We apply direct numerical simulation (DNS) of the compressible Navier-Stokes equations and linear stability theory (LST) using in-house algorithms. The analyses reveals that varying the trailing edge height of the gap affects the interaction between the two-dimensional mode and the mixing layer of the flow. Increases in the height of the trailing edge enhanced the stability of the two-dimensional mode, while lower trailing edges had the opposite effect and contributed to a significant increase in flow instability. It was observed that lower trailing edges also contributed to increased acoustic emission and circulation inside the gap.