One of the most interesting and still growing scientific fields is neuromorphic engineering, which is focused on studying and designing hardware and software with the purpose of mimicking the basic principles of biological nervous systems. Currently, there are many research groups developing practical applications based on neuroscientific knowledge. This work provides researchers with a novel toolkit of building blocks based on Spiking Neural Networks that emulate the behavior of different logic gates. These could be very useful in many spike-based applications, since logic gates are the basis of digital circuits. The designs and models proposed are presented and implemented on a SpiNNaker hardware platform. Different experiments were performed in order to validate the expected behavior, and the obtained results are discussed. The functionality of traditional logic gates and the proposed blocks is studied, and the feasibility of the presented approach is discussed.