Due to the heavy reliance of millimeter-wave (mmWave) wireless systems on directional links, beamforming (BF) with high-dimensional arrays is essential for cellular systems in these frequencies. How to perform the array processing in a power efficient manner is a fundamental challenge. Analog and hybrid BF require fewer analog-to-digital and digital-to-analog converters (ADCs and DACs), but can only communicate in a small number of directions at a time, limiting directional search, spatial multiplexing and control signaling. Digital BF enables flexible spatial processing, but must be operated at a low quantization resolution to stay within reasonable power levels. This decrease in quantizer resolution introduces noise in the received signal and degrades the quality of the transmitted signal. To assess the effect of low-resolution quantization on cellular system, we present a simple additive white Gaussian noise (AWGN) model for quantization noise. Simulations with this model reveal that at moderate resolutions (3-4 bits per ADC), there is negligible loss in downlink cellular capacity from quantization. In essence, the low-resolution ADCs limit the high SNR, where cellular systems typically do not operate. For the transmitter, it is shown that DACs with 4 or more bits of resolution do not violate the adjacent carrier leakage limit set by 3-rd Generation Partnership Project (3GPP) New Radio (NR) standards for cellular operations. Further, this work studies the effect of low resolution quantization on the error vector magnitude (EVM) of the transmitted signal.In fact, our findings suggests that low-resolution fully digital BF architectures can be a power efficient alternative to analog or hybrid beamforming for both transmitters and receivers at millimeter wave.