Brain-Computer Interface (BCI) systems create a bridge between the human brain and the outside world, potentially rendering traditional methods of information transmission obsolete in the not-so-distant future. One of the key research areas in BCI is the classification of brain activity in electroencephalographic (EEG) data. On the other hand, new memory-augmented neural networks, such as the Neural Turing Machine (NTM) and the Differentiable Neural Computer (DNC), have demonstrated their impressive abilities in solving complex tasks. Therefore, it is useful to evaluate the capability of memory-augmented neural networks to enhance the classification of brain activity within EEG signals. Previous methods have suffered from low accuracy and generalizability in classifying brain activities; primarily due to a lack of proper classification of Motor Imagery/Execution brain activities, an inability to extract valuable information at different time steps in time series data, and a failure to learn from longer dependencies. This article introduces TDMANN (Time-Distributed Memory Augmented Neural Network), a framework that leverages the principles of NTM and DNC for the binary classification of brain activities in EEG signals. The controller component of the memory-augmented neural network is enhanced with a time-distributed approach, which significantly improves the performance of the network in binary classification tasks involving motor imagery/execution brain activities by extracting valuable information at each time step. The benchmark datasets used in this study are EEGmmidb BCI2000 (Imagery/Execution), BCI IV 2B, and BCI IV 2A, all containing motor imagery/execution brain activity data in EEG format. The results demonstrate that the classification accuracy achieved by the proposed DNC@TDMANN method exhibits a maximum improvement of 23.03% compared to baseline research works. The NTM@TDMANN method also shows a maximum improvement accuracy of 22.5%.