The problem of digital finite communication bandwidth (DFCB) control has come to the attention of the research community in connection with a growing interest in the development of distributed and/or networked control systems. In these systems, actuators, sensors, and other components are connected via data-rate constrained links such as wireless radio, etc. In this paper, we consider a scalar model of DFCB control that accommodates time-varying data-rate constraints, such as might occur with intermittent network congestion, and asynchronism of sampling and control actuation. Because of the possibly unpredictable fluctuation of the data-rate, we are interested in feedback control designs that will tolerate significantly constrained data-rates on feedback loops, while providing acceptable performance when such data-rate constraints are not in force. In light of a very basic notion of acceptable performance, we show that control designs with different number of quantization levels tolerate constrained data-rates differently. This leads to the conclusion that binary control represents the most robust control quantization under data-rate constraints imposed by time-varying congestion on the feedback communication channel. The advantage margin of binary control is further investigated numerically with and without the sampling-control asynchronism being considered. We show that the advantage margin is more substantial when the sampling-control asynchronism is significant. A design of quantized (binary) feedback with side channel information is proposed, and stability properties are discussed. We conclude the paper by examining performance limitations of our binary coding in the presence of noise.