In recent years, physical limitations in the integration of transistors in computers have forced the search for low‐computational‐power alternatives in hardware design. Although doubts may arise regarding the limit of the relationship between performance and power consumption in computers, these disappear when considering the brain, which is one of the most efficient computing systems. In this way, bioinspired applications try to benefit from the low‐power consumption present in the biological nervous system. Previous work has shown the feasibility of implementing spiking neural networks that operate in a Boolean manner on digital platforms, such as SpiNNaker, using basic logic gates and a spiking memory, which suggests the potential for constructing a low‐power consumption spiking computer. This work takes a first step in the implementation of a spiking central processing unit by developing an arithmetic logic unit, which is an essential block for instruction execution, demonstrating its correct operation on Dynap‐SE1. The results confirm the feasibility of using this Boolean approach on this platform, despite certain limitations in the number of inputs and operating frequencies of the blocks, and pave the way for the construction of a spiking computer.