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A new technique for Residue Number System (RNS) Digital-to-Binary or Digital-to-Analog conversion based on the Chinese Remainder Theorem allows conversion with only one level of ROM and one level of Adders. The ROM's are small (e.g., 256 x 8) and the Adders use standard binary adders. Compared to previous Chinese Remainder Theorem or Mixed-Radix-Conversion Techniques, the new technique offers conversion times which are independent of the number of Residue Number System moduli and conversion times are usually much faster than competative techniques. The new technique also allows for rounding or truncation to fewer bits and sign-detection by simple modifications to the procedure. These modifications yield particularly simple and fast hardware.