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Increasingly larger and better Transformer models keep advancing state-of-the-art accuracy and capability for Natural Language Processing applications. These models demand more computational power, storage, and energy. Mokey reduces the footprint of state-of-the-art 32-bit or 16-bit floating-point transformer models by quantizing all values to 4-bit indexes into dictionaries of representative 16-bit fixed-point centroids. Mokey does not need fine-tuning, an essential feature as often the training resources or datasets are not available to many. Exploiting the range of values that naturally occur in transformer models, Mokey selects centroid values to also fit an exponential curve. This unique feature enables Mokey to replace the bulk of the original multiply-accumulate operations with narrow 3b fixed-point additions resulting in an area- and energy-efficient hardware accelerator design. Over a set of state-of-the-art transformer models, the Mokey accelerator delivers an order of magnitude improvements in energy efficiency over a Tensor Cores-based accelerator while improving performance by at least $4\times$ and as much as $15\times$ depending on the model and on-chip buffering capacity. Optionally, Mokey can be used as a memory compression assist for any other accelerator, transparently stashing wide floating-point or fixed-point activations or weights into narrow 4-bit indexes. Mokey proves superior to prior state-of-the-art quantization methods for Transformers.