||Background: Ever since the seminal work by McCulloch and Pitts, the theory of neural computation and its philosophical foundation known as 'computationalism' have been central to brain-inspired artificial intelligence (AI) technologies. The present study describes neural dynamics and neural coding approaches to understand the mechanisms of neural computation. The primary focus is to characterize the multiscale nature of logic computations in the brain, which might occur at a single neuron level, between neighboring neurons via synaptic transmission, and at the neural circuit level. Results: For this, we begin the analysis with simple neuron models to account for basic Boolean logic operations at a single neuron level and then move on to the phenomenological neuron models to explain the neural computation from the viewpoints of neural dynamics and neural coding. The roles of synaptic transmission in neural computation are investigated using biologically realistic multi-compartment neuron models: two representative computational entities, CA1 pyramidal neuron in the hippocampus and Purkinje fiber in the cerebellum, are analyzed in the information-theoretic framework. We then construct two-dimensional mutual information maps, which demonstrate that the synaptic transmission can process not only basic AND/OR Boolean logic operations but also the linearly non-separable XOR function. Finally, we provide an overview of the evolutionary algorithm and discuss its benefits in automated neural circuit design for logic operations. Conclusions: This study provides a comprehensive perspective on the multiscale logic operations in the brain from both neural dynamics and neural coding viewpoints. It should thus be beneficial for understanding computational principles of the brain and may help design biologically plausible neuron models for AI devices.