The vast majority of neurons in the vertebrate nervous systems transmits information in a digital manner via action potentials. Yet, a detailed understanding of the advantages of digital communication in the brain is still lacking. In our study, we investigate synaptic transmission in terms of an optimization problem, where the space of solutions comprises the digital and the analog regime. We analyze a binomial synapse model connecting two neurons, where the probability of transmitter release, modeled by a transfer function, depends on the axonal membrane potential. We optimize the transfer function parameters and the number of vesicles to maximize information transmission about the presynaptic potential. We find that the information, measured as the mutual information between the pre- and the postsynaptic potential, increases with the number of vesicles and assumes a maximum for a smooth sigmoidal transfer function. This allows vesicle release to vary continuously in response to variations of the presynaptic potential, mimicking the analog communication seen in the ribbon synapses of the early visual and auditory processing stages where information rate is critical. Experimental studies corroborate this, showing sigmoidal relationships between transmitter release and light intensity for retinal cones [1] and between postsynaptic currents and the hair cell's membrane potential in the auditory pathway [2]. Adjusting the parameters of our model to optimize the ratio of transmitted information per energy changes the picture: the optimal number of vesicles is small and the transfer function becomes a step function, resulting in an all-or-none release of transmitter, leading to an effectively digital synaptic transmission. Moreover, the threshold of the release is shifted towards higher, less likely stimulus intensities to reduce the signaling energy. This sparse and effectively digital drive of synaptic transmission is prevalent in cortical synapses. Our results align with theoretical works showing that sparsity maximizes the ratio of information per energy in a priori spiking networks [3]. Overall, our study provides a normative account of the coupling between somatic nonlinearity and synaptic release probability, accurately predicting analog coupling when a high information rate is required and digital coupling when information efficiency is desirable.