Energy management for multimode software defined radio systems remains a daunting challenge. This brief develops a high level framework that generates a multiprocessor systems on chip architecture from a library of heterogeneous processing resources that can be reconfigured to support various modes of operation. The framework proposes joint task and core mapping with system level floorplanning. With the objective of minimizing energy, we develop an analytical probabilistic model that considers static, dynamic, configuration, and communication energy components for multiple applications characterized by probabilities of execution. Finally, a fast energy aware joint task and core mapping heuristic is proposed and performance is demonstrated on realistic benchmarks.