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As datasets continue to grow, vector-based search becomes more storage and compute intensive, requiring large-scale systems to support retrieval. Proposed solutions range from quantization techniques that balance speed and accuracy, to hashing methods that learn compact binary representations. This paper promotes the use of hyperbolic space for its compact nature whilst overcoming its slow retrieval via binarization. Specifically, we address hyperbolic space's inherent slowness by proving that its complex similarity calculations can be equated to a binary XOR operation. Our approach allows for 90% less storage and at least 4.7 times faster search while maintaining performance of full-precision Euclidean embeddings.