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In this article, we present and analyze a new family of fixed-point data formats for signal processing applications. These formats represent compressed two's complement data formats where compression on the sign bit is undertaken on a sample by sample basis. The extra room provided by sign-bit compression is utilized to retain more bits of precision for each individual sample. Compressed two's complement data formats are shown to provide greater dynamic range and improved noise performance over traditional fixed-point data formats such as sign-magnitude, offset binary, and traditional two's complement. Traditional two's complement is shown to be a member of the compressed two's complement family where the compression factor (CF) is equal to one. The dynamic range of a compressed two's complement data format is shown to approach the dynamic range of a non compressed data format raised to the power of the CF. Improved performance for digital signal processing (DSP) applications such as digital filters and transforms is presented for specific instances of this family.