Epilepsy diagnosis based on Interictal Epileptiform Discharges (IEDs) in scalp electroencephalograms (EEGs) is laborious and often subjective. Therefore, it is necessary to build an effective IED detector and an automatic method to classify IED-free versus IED EEGs. In this study, we evaluate features that may provide reliable IED detection and EEG classification. Specifically, we investigate the IED detector based on convolutional neural network (ConvNet) with different input features (temporal, spectral, and wavelet features). We explore different ConvNet architectures and types, including 1D (one-dimensional) ConvNet, 2D (two-dimensional) ConvNet, and noise injection at various layers. We evaluate the EEG classification performance on five independent datasets. The 1D ConvNet with preprocessed full-frequency EEG signal and frequency bands (delta, theta, alpha, beta) with Gaussian additive noise at the output layer achieved the best IED detection results with a false detection rate of 0.23/min at 90% sensitivity. The EEG classification system obtained a mean EEG classification Leave-One-Institution-Out (LOIO) cross-validation (CV) balanced accuracy (BAC) of 78.1% (area under the curve (AUC) of 0.839) and Leave-One-Subject-Out (LOSO) CV BAC of 79.5% (AUC of 0.856). Since the proposed classification system only takes a few seconds to analyze a 30-min routine EEG, it may help in reducing the human effort required for epilepsy diagnosis.