Recent works propose neural network- (NN-) inspired analog-to-digital converters (NNADCs) and demonstrate their great potentials in many emerging applications. These NNADCs often rely on resistive random-access memory (RRAM) devices to realize the NN operations and require high-precision RRAM cells (6~12-bit) to achieve a moderate quantization resolution (4~8-bit). Such optimistic assumption of RRAM resolution, however, is not supported by fabrication data of RRAM arrays in large-scale production process. In this paper, we propose an NN-inspired super-resolution ADC based on low-precision RRAM devices by taking the advantage of a co-design methodology that combines a pipelined hardware architecture with a custom NN training framework. Results obtained from SPICE simulations demonstrate that our method leads to robust design of a 14-bit super-resolution ADC using 3-bit RRAM devices with improved power and speed performance and competitive figure-of-merits (FoMs). In addition to the linear uniform quantization, the proposed ADC can also support configurable high-resolution nonlinear quantization with high conversion speed and low conversion energy, enabling future intelligent analog-to-information interfaces for near-sensor analytics and processing.