This paper investigates antenna selection at a base station with large antenna arrays and low-resolution analog-to-digital converters. For downlink transmit antenna selection for narrowband channels, we show (1) a selection criterion that maximizes sum rate with zero-forcing precoding equivalent to that of a perfect quantization system; (2) maximum sum rate increases with number of selected antennas; (3) derivation of the sum rate loss function from using a subset of antennas; and (4) unlike high-resolution converter systems, sum rate loss reaches a maximum at a point of total transmit power and decreases beyond that point to converge to zero. For wideband orthogonal-frequency-division-multiplexing (OFDM) systems, our results hold when entire subcarriers share a common subset of antennas. For uplink receive antenna selection for narrowband channels, we (1) generalize a greedy antenna selection criterion to capture tradeoffs between channel gain and quantization error; (2) propose a quantization-aware fast antenna selection algorithm using the criterion; and (3) derive a lower bound on sum rate achieved by the proposed algorithm based on submodular functions. For wideband OFDM systems, we extend our algorithm and derive a lower bound on its sum rate. Simulation results validate theoretical analyses and show increases in sum rate over conventional algorithms.