We propose a new experimental realization of a periodic oscillator that we term Boolean phase oscillator (BPO) [1]. One of the important features of our design is that it allows us to tune the coupling strength using only Boolean signals. Our BPO is realized on a field-programmable gate array(FPGA) in its autonomous mode of operation. It consists of a ring oscillator with state-dependent delay taking two discrete values depending on an external coupling signal. We demonstrate experimentally and numerically that two uni- and bidirectionally coupled BPOs can exhibit phase synchronization. We characterize the synchronization regions as a function of the frequency detuning between two BPOs and a quantity related to the variation of state-dependent delay. We notice that the synchronization regions become larger when the second quantity is increased. This allows us to conclude that this quantity is an effective coupling strength in BPOs. We gratefully acknowledge the financial support of the U.S. Army Research Office Grant W911NF12-1-0099 and National Science Foundation IGERT Grant DGE-1068871.