Methods, apparatus, and articles of manufacture to encode auxiliary data into numeric data and methods, apparatus, and articles of manufacture to obtain encoded data from numeric data

An apparatus to encode auxiliary information into numeric data, comprising:

• a data unit group assignor to assign source data to one of a plurality of groups, the source data comprising a numeric value;
• a symbol group assignor to assign a symbol to be added to the source data to the one of the plurality of groups;
• and
• a data unit encoder to generate encoded data by selectively modifying the numeric value of the source data to be representative of the symbol.

A computer readable storage medium comprising computer readable instructions which, when executed, cause a processor to at least:

• assign source data to one of a plurality of groups, the source data comprising a numeric value;
• identify a symbol to be added to the source data based on an assigned group of the source data;
• and
• generate encoded data by selectively modifying the numeric value of the source data to be representative of the symbol.