Field-programmable gate array (FPGA)-based accelerators for convolutional neural network (CNN) inference have received significant attention in recent years. The reported designs tend to adopt a similar underlying approach based on multiplier-accumulator (MAC) arrays, which yields strong demand for the available on-chip DSP blocks, while leaving FPGA logic and memory resources underutilized. The practical outcome is that the computational roof of the accelerator is bound by the number of DSP blocks offered by the target FPGA. In addition, integrating the CNN accelerator with other functional units that may also need DSP blocks would degrade the inference performance. Leveraging the robustness of inference accuracy to limited arithmetic precision, we propose a transformation to the convolution computation, which leads to transformation of the accelerator design space and relaxes the pressure on the required DSP resources. Through analytical and empirical evaluations, we demonstrate that our approach enables us to strike a favorable balance between utilization of the FPGA on-chip memory, logic, and DSP resources, due to which, our accelerator considerably outperforms state of the art. We report the effectiveness of our approach on a variety of FPGA devices, including Cyclone-V, Stratix-V, and Arria-10, which are used in large number of applications, ranging from embedded settings to high performance computing. Our proposed technique yields 1.5x throughput improvement and 4x DSP resource reduction compared to the best frequency domain convolution-based accelerator, and 2.5x boost in raw arithmetic performance and 8.4x saving in DSPs compared to a state-of-the-art sparse convolution-based accelerator.