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We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).