Existing works are dedicated to untangling atomized numerical components (features) from the hidden states of Large Language Models (LLMs). However, they typically rely on autoencoders constrained by some training-time regularization on single training instances, without an explicit guarantee of global sparsity among instances, causing a large amount of dense (simultaneously inactive) features, harming the feature sparsity and atomization. In this paper, we propose a novel autoencoder variant that enforces minimal entropy on minibatches of hidden activations, thereby promoting feature independence and sparsity across instances. For efficient entropy calculation, we discretize the hidden activations to 1-bit via a step function and apply gradient estimation to enable backpropagation, so that we term it as Binary Autoencoder (BAE) and empirically demonstrate two major applications: (1) Feature set entropy calculation. Entropy can be reliably estimated on binary hidden activations, which can be leveraged to characterize the inference dynamics of LLMs. (2) Feature untangling. Compared to typical methods, due to improved training strategy, BAE avoids dense features while producing the largest number of interpretable ones among baselines.