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Nearest neighbor (NN) search is an essential operation in many applications, such as one/few-shot learning and image classification. As such, fast and low-energy hardware support for accurate NN search is highly desirable. Ternary content-addressable memories (TCAMs) have been proposed to accelerate NN search for few-shot learning tasks by implementing $L_\infty$ and Hamming distance metrics, but they cannot achieve software-comparable accuracies. This paper proposes a novel distance function that can be natively evaluated with multi-bit content-addressable memories (MCAMs) based on ferroelectric FETs (FeFETs) to perform a single-step, in-memory NN search. Moreover, this approach achieves accuracies comparable to floating-point precision implementations in software for NN classification and one/few-shot learning tasks. As an example, the proposed method achieves a 98.34% accuracy for a 5-way, 5-shot classification task for the Omniglot dataset (only 0.8% lower than software-based implementations) with a 3-bit MCAM. This represents a 13% accuracy improvement over state-of-the-art TCAM-based implementations at iso-energy and iso-delay. The presented distance function is resilient to the effects of FeFET device-to-device variations. Furthermore, this work experimentally demonstrates a 2-bit implementation of FeFET MCAM using AND arrays from GLOBALFOUNDRIES to further validate proof of concept.