Method and apparatus for encoding and decoding data in residue number system

A decoding method for demodulating RNS data composed of residue data of a plurality of moduli into binary data by a Mixed Radix Conversion Method (MRC) using a multiplicative inverse element of a value of one modulus for that of another modulus to reduce the number of residue data, comprising the steps of:

• selecting one of said moduli to be a value represented by the power of 2 and said moduli has residue data value R.sub.i or residue data value R.sub.j of moduli m.sub.i or m.sub.j, respectively,
• applying to residue data scale-down processing performed in parallel pertaining to said one of said moduli represented by said power of 2 and said residue scale-down processing having a value R.sub.ji represented by the expression R.sub.ji ={(R.sub.i -R.sub.j)X.sub.ij }MOD m.sub.i, wherein X.sub.ij is a multiplicative inverse element of the modulus m.sub.j, and
• applying to said residue data scale-down processing pertaining to each of the remaining of said plurality of moduli.

A decoder method for demodulating RNS data into binary data, comprising the steps of:

• scale-down processing the RNS data of a plurality of fixed moduli for obtaining a plurality of residue data corresponding to each of said moduli of the RNS data, said scale-down processing using multiplicative inverse values of the RNS set to the values of said moduli,
• addition processing said residue data with said fixed moduli, respectively, to obtain addition data, thereby demodulating the RNS data into binary data, said addition processing adding data D.sub.i which are bit-shifted by l bits, and
• adding the value 1 to a fixed bit of said RNS data to achieve fixed data intermediate said scale-down processing and said addition processing for discriminating positive and negative numbers.

A decoder circuit for converting RNS data into unipolar binary data comprising:

• a data converting circuit for converting said RNS data into unipolar binary data;
• a discriminating circuit for adding a first fixed value to said binary data output from said data converting circuit and outputting the most significant bit of the result of said adding for discriminating between positive and negative numbers by the most significant bit, and
• an adder for adding a second fixed value to said unipolar binary data and outputting the result thereof as said bipolar binary data.

A decoder circuit comprising:

• a first data converting circuit for converting RNS data into binary data;
• an adder for adding the value 1 to a fixed bit of said binary data for discriminating between positive and negative numbers by the most significant bit, and
• a second data converting circuit for adding a fixed value to said binary data including said fixed bit added with the value 1, thereby converting said binary data into bipolar binary data.