The SEmulation system provides four modes of operation: (1) Software Simulation, (2) Simulation via Hardware Acceleration, (3) In-Circuit Emulation (ICE), and (4) Post-Simulation Analysis. At a high level, the present invention may be embodied in each of the above four modes or various combinations of these modes. At the core of these modes is a software kernel which controls the overall operation of this system. The main control loop of the kernel executes the following steps: initialize system, evaluate active test-bench processes/components, evaluate clock components, detect clock edge, update registers and memories, propagate combinational components, advance simulation time, and continue the loop as long as active test-bench processes are present. The Memory Mapping aspect of the invention provides a structure and scheme where the numerous memory blocks associated with the user's design is mapped into the SRAM memory devices in the Simulation system instead of inside the logic devices, which are used to configure and model the user's design. The Memory Mapping or Memory Simulation system includes a memory state machine, an evaluation state machine, and their associated logic to control and interface with: (1) the main computing system and its associated memory system, (2) the SRAM memory devices coupled to the FPGA buses in the Simulation system, and (3) the FPGA logic devices which contain the configured and programmed user design that is being debugged.