Spectrum sensing is one of the most important tasks in cognitive radio system. In order to combat fading, cooperation among different sensing users is usually adopted. In our previous work , we quantified the performance gain of cooperative spectrum sensing by the notion of diversity. In addition, we have shown that even with local binary decisions, the cooperative spectrum sensing can achieve the maximum diversity by appropriately selecting local and fusion rules. However, there is a significant signal-to-noise ratio (SNR) loss compared with the soft information fusion scenario due to local binary quantization. Intuitively, increasing the number of bits of local quantization will improve the sensing performance. Most work in the literature on multi-bit cooperative sensing are mathematically intractable and can only be solved numerically with high complexity. In this paper, by jointly maximizing diversity and SNR gain, we provide a generalized multi-bit cooperative sensing strategy with the local and fusion decision rules in explicit closed form. Simulations show that even with small number of bits, our proposed cooperative sensing strategy can significantly improve the sensing performance.