Deep Neural Networks (DNNs) have emerged as the method of choice for solving a wide range of machine learning tasks. The enormous computational demands posed by DNNs have most commonly been addressed through the design of custom accelerators. However, these accelerators are prohibitive in many design scenarios (e.g., wearable devices and IoT sensors), due to stringent area/cost constraints. Accelerating DNNs on these low-power systems, comprising of mainly the general-purpose processor (GPP) cores, requires new approaches. We improve the performance of DNNs on GPPs by exploiting a key attribute of DNNs, i.e., sparsity. We propose Sparsity aware Core Extensions (SparCE)- a set of micro-architectural and ISA extensions that leverage sparsity and are minimally intrusive and low-overhead. We dynamically detect zero operands and skip a set of future instructions that use it. Our design ensures that the instructions to be skipped are prevented from even being fetched, as squashing instructions comes with a penalty. SparCE consists of 2 key micro-architectural enhancements- a Sparsity Register File (SpRF) that tracks zero registers and a Sparsity aware Skip Address (SASA) table that indicates instructions to be skipped. When an instruction is fetched, SparCE dynamically pre-identifies whether the following instruction(s) can be skipped and appropriately modifies the program counter, thereby skipping the redundant instructions and improving performance. We model SparCE using the gem5 architectural simulator, and evaluate our approach on 6 image-recognition DNNs in the context of both training and inference using the Caffe framework. On a scalar microprocessor, SparCE achieves 19%-31% reduction in application-level. We also evaluate SparCE on a 4-way SIMD ARMv8 processor using the OpenBLAS library, and demonstrate that SparCE achieves 8%-15% reduction in the application-level execution time.