An apparatus for displaying a state of a multiplexing system of a power plant, the multiplexing system provided with a plurality of modules comprising at least one main module and at least one sub-module, wherein a main module and a sub-module are distinguished by providing a priority of each module, the apparatus comprising: at least one controller (10, 11) configured to determine priorities of the plurality of modules of the system of the power plant; checking units (20, 21) configured to check an operation state of each module, wherein the at least one controller (10, 11) is configured to determine the priorities of the plurality of modules based on the check results of the checking units (20, 21) and to generate preset information according to the determined priorities, and wherein the at least one controller (10, 11) is configured to determine the priority of the plurality of modules by comparing penalty scores of the modules with each other and the penalty scores are calculated based on the check results by the checking units (20, 21), display units (30, 31) configured to display a preset information on the plurality of modules, wherein the displayed preset information is first information preset according to priorities preset to the modules or, in case the priorities determined by the controller based on the checking result by the checking units (20, 21) are different from the preset priorities, second information preset according to the determined priorities, the at least one controller (10,11) is disposed at one of the plurality of modules of the multiplexing system and each of the checking units (20, 21) and each of the display units (30, 31) is disposed at a respective one of the plurality of modules of the multiplexing system, and the preset information displayed on each of the display units (30, 31) indicates whether the respective module is a main module or a sub-module. at least one controller (10, 11) configured to determine priorities of the plurality of modules of the system of the power plant; checking units (20, 21) configured to check an operation state of each module, wherein the at least one controller (10, 11) is configured to determine the priorities of the plurality of modules based on the check results of the checking units (20, 21) and to generate preset information according to the determined priorities, and wherein the at least one controller (10, 11) is configured to determine the priority of the plurality of modules by comparing penalty scores of the modules with each other and the penalty scores are calculated based on the check results by the checking units (20, 21), display units (30, 31) configured to display a preset information on the plurality of modules, wherein the displayed preset information is first information preset according to priorities preset to the modules or, in case the priorities determined by the controller based on the checking result by the checking units (20, 21) are different from the preset priorities, second information preset according to the determined priorities, the at least one controller (10,11) is disposed at one of the plurality of modules of the multiplexing system and each of the checking units (20, 21) and each of the display units (30, 31) is disposed at a respective one of the plurality of modules of the multiplexing system, and the preset information displayed on each of the display units (30, 31) indicates whether the respective module is a main module or a sub-module.