We propose a Virtual Generalizing Random Access Memory (VG-RAM) Weightless Neural Network (WNN) Computer (V'Ger Computer for short). VG-RAM WNNs are very effective pattern recognition tools, offering fast training (one shot training) and competitive recognition performance, if compared with other current techniques. The V'Ger Computer architecture was inspired on the organization of the human neocortex and is composed of hierarchically organized and recurrently interconnected layers of VG-RAM WNN neurons. One layer is connected to another in a way similar to cortico-cortical feed-forward and feedback connections between functionally adjacent and hierarchically organized areas. We have "programmed" the V'Ger Computer for counting from 0 to 9 three times. Our preliminary experimental results showed that V'Ger is capable of executing this sequence of actions in spite of strong interferences.