In this paper, we analyze the operational flow of two hardware implementations of the Task Superscalar architecture. The Task Superscalar is an experimental task based dataflow scheduler that dynamically detects inter-task data dependencies, identifies task-level parallelism, and executes tasks in the out-of-order manner. In this paper, we present a base implementation of the Task Superscalar architecture, as well as a new design with improved performance. We study the behavior of processing some dependent and non-dependent tasks with both base and improved hardware designs and present the simulation results compared with the results of the runtime implementation.