Dynamic Flowgraph Methodology (DFM) is a new approach developed to integrate the modeling and analysis of the hardware and software components of an embedded system. The objective is to complement the traditional approaches which generally follow the philosophy of separating out the hardware and software portions of the assurance analysis. In this paper, the DFM approach is demonstrated using the Titan 2 Space Launch Vehicle Digital Flight Control System. The hardware and software portions of this embedded system are modeled in an integrated framework. In addition, the time dependent behavior and the switching logic can be captured by this DFM model. In the modeling process, it is found that constructing decision tables for software subroutines is very time consuming. A possible solution is suggested. This approach makes use of a well-known numerical method, the Newton-Raphson method, to solve the equations implemented in the subroutines in reverse. Convergence can be achieved in a few steps. Yau, M. and Guarro, S. and Apostolakis, G. Unspecified Center COMPUTER PROGRAMS; COMPUTERIZED SIMULATION; MATHEMATICAL MODELS; NEWTON-RAPHSON METHOD; SUBROUTINES; SWITCHING CIRCUITS; SYSTEMS ANALYSIS; TIME DEPENDENCE; DIGITAL SYSTEMS; EMBEDDING; FLIGHT CONTROL; RELIABILITY ANALYSIS; TITAN LAUNCH VEHICLES...