With the rapid growth of image and video data on the web, hashing has been extensively studied for image or video search in recent years. Benefiting from recent advances in deep learning, deep hashing methods have shown superior performance over the traditional hashing methods. However, there are some limitations of previous deep hashing methods (e.g., the semantic information is not fully exploited). In this paper, we develop a general deep supervised discrete hashing framework based on the assumption that the learned binary codes should be ideal for classification. Both the similarity information and the classification information are used to learn the hash codes within one stream framework. We constrain the outputs of the last layer to be binary codes directly, which is rarely investigated in deep hashing algorithms. Besides, both the pairwise similarity information and the triplet ranking information are exploited in this paper. In addition, two different loss functions are presented: l2 loss and hinge loss, which are carefully designed for the classification term under the one stream framework. Because of the discrete nature of hash codes, an alternating minimization method is used to optimize the objective function. Experimental results have shown that our approach outperforms current state-of-the-art methods on benchmark datasets.