We present an in vitro neuronal network with controlled topology capable of performing basic Boolean computations, such as NAND and OR. Neurons cultured within polydimethylsiloxane (PDMS) microstructures on high-density microelectrode arrays (HD-MEAs) enable precise interaction through extracellular voltage stimulation and spiking activity recording. This system allows for the investigation of input-output relationships that define non-linear biological activation functions. Additionally, we analyze various output encoding schemes, comparing the limitations of rate coding with the potential advantages of spike-timing-based coding strategies. This work contributes to the advancement of hybrid intelligence and biocomputing by offering insights into neural information encoding and decoding with the potential to directly validate bio-inspired computational mechanisms used in artificial intelligence (AI) systems.