Monostable multivibrators are simple timers which are easily implemented using counters in digital hardware and can be interpreted as non-biologically inspired spiking neurons. We show how fully binarized event-driven recurrent networks of monostable multivibrators can be trained to solve classification tasks. We mitigate an important bottleneck in neuromorphic hardware concepts by circumventing synaptic addition within the network. Here rather, input signals to a neuron are simply OR-ed together. Temporally overlapping input events are resolved at the neuron level. We demonstrate our approach on the MNIST handwritten digits, Google Soli radar gestures, IBM DVS128 gestures and Yin-Yang classification tasks, all with excellent results. The estimated energy consumption for the MNIST handwritten digits task, excluding the final readout layer, is 855pJ per inference for a test accuracy of 98.61% for a reconfigurable network of 500 units that was mapped to a 28nm process.