Quantization for Convolutional Neural Network (CNN) has shown significant progress with the intention of reducing the cost of computation and storage with low-bitwidth data inputs. There are, however, no systematic studies on how an existing full-bitwidth processing unit, such as CPUs and DSPs, can be better utilized to carry out significantly higher computation throughput for convolution under various quantized bitwidths. In this study, we propose HiKonv, a unified solution that maximizes the compute throughput of a given underlying processing unit to process low-bitwidth quantized data inputs through novel bitwise parallel computation. We establish theoretical performance bounds using a full-bitwidth multiplier for highly parallelized low-bitwidth convolution, and demonstrate new breakthroughs for high-performance computing in this critical domain. For example, a single 32-bit processing unit can deliver 128 binarized convolution operations (multiplications and additions) under one CPU instruction, and a single 27× 18 DSP core can deliver eight convolution operations with 4-bit inputs in one cycle. We demonstrate the effectiveness of HiKonv on CPU and FPGA for both convolutional layers or a complete DNN model. For a convolutional layer quantized to 4-bit, HiKonv achieves a 3.17× latency improvement over the baseline implementation using C++ on CPU. Compared to the DAC-SDC 2020 champion model for FPGA, HiKonv achieves a 2.37×: throughput improvement and 2.61× DSP efficiency improvement, respectively.