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As we begin to see low-powered computing paradigms (Neuromorphic Computing, Spiking Neural Networks, etc.) becoming more popular, learning binary word embeddings has become increasingly important for supporting NLP applications at the edge. Existing binary word embeddings are mostly derived from pretrained real-valued embeddings through different simple transformations, which often break the semantic consistency and the so-called ``arithmetic'' properties learned by the original, real-valued embeddings. This paper aims to address this limitation by introducing a new approach to learn binary embeddings from scratch, preserving the semantic relationships between words as well as the arithmetic properties of the embeddings themselves. To achieve this, we propose a novel genetic algorithm to learn the relationships between words from existing word analogy data-sets, carefully making sure that the arithmetic properties of the relationships are preserved. Evaluating our generated 16, 32, and 64-bit binary word embeddings on Mikolov's word analogy task shows that more than 95% of the time, the best fit for the analogy is ranked in the top 5 most similar words in terms of cosine similarity."