The design of a cortical neuron with carbon nanotube circuit elements that performs nonlinear dendritic computations with excitatory and inhibitory post-synaptic potentials is presented. The inhibitory synapse with controllable parameters that implement plasticity is described in detail. The circuit design was simulated using carbon nanotube spice models. Simulations show that the neuron fires as long as the inhibitory post-synaptic potential is weak or absent. Strong inhibitory post-synaptic potentials prevent the neuron from firing.