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The trend toward multicore processors is moving the emphasis in computation from sequential to parallel processing. However, not all applications can be parallelized and benefit from multiple cores. Such applications lead to under-utilization of parallel resources, hence sub-optimal performance/watt. They may however, benefit from powerful uniprocessors. On the other hand, not all applications can take advantage of more powerful uniprocessors. To address competing requirements of diverse applications, we propose a heterogeneous multicore architecture with a Dynamic Core Morphing (DCM) capability. Depending on the computational demands of the currently executing applications, the resources of a few tightly coupled cores are morphed at runtime. We present a simple hardware-based algorithm to monitor the time-varying computational needs of the application and when deemed beneficial, trigger reconfiguration of the cores at fine-grain time scales to maximize the performance/watt of the application. The proposed dynamic scheme is then compared against a baseline static heterogeneous multicore configuration and an equivalent homogeneous configuration. Our results show that dynamic morphing of cores can provide performance/watt gains of 43% and 16% on an average, when compared to the homogeneous and baseline heterogeneous configurations, respectively.