This study proposes an innovative hierarchical binary classification approach based on scalp EEG data to predict comatose patients' Glasgow Outcome Scale (GOS).The dataset consists of continuous EEG recordings from 13 comatose patients classified into three GOS groups: GOS 1 (death), GOS 3 (severe disability), and GOS 5 (good recovery). Traditional machine learning (ML) and deep learning (DL) models, though effective in some instances, struggle to generalize across diverse patient populations, mainly when evaluated with leave-one-subject-out (LOSO) cross-validation. We introduce a two-step binary classification approach to address these challenges, utilizing Convolutional Neural Networks (CNNs) with spectrogram features for one classifier and Random Forest (RF) with Approximate Entropy (ApEn) for the other. By simplifying the multi-class classification task into two binary decisions, we achieve perfect classification performance for GOS 1 and GOS 5, while GOS 3 is inferred by exclusion. Importantly, we found that just 2 minutes of EEG data per subject was sufficient to achieve this level of performance, offering significant implications for clinical applications where data is often limited. Even considering the small dataset, our results prove that our method performs better than traditional approaches, providing a scalable, efficient solution for coma outcome prediction.