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Squarers are widely used in communication and DSP applications. In this letter, two approximate squarers (ABFS1 and ABFS2) are proposed. Specifically, a novel approximate Booth-folding encoding is designed to generate approximate partial product arrays. Several approximate compressors with precision recovery circuits are proposed. In the ABFS1, a novel approximate 4-2 compressor with an accurate compensation circuit is utilized. Moreover, the proposed approximate 4-2 compressor with constant compensation is used in the ABFS2 to improve the performance of squarer. In addition, this letter presents the logic synthesizing result of the two approximate squarers with the 45 nm technology. The comparison with state-of-the-art approximate squarers demonstrates the proposed designs reduce the 58.1% PDP while maintaining a similar or even better accuracy. Finally, the proposed approximate squarers are verified by the K-means clustering application.

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