Abstract: A method and apparatus for a varying-radix numeration system is described. A method includes receiving a first sequence of values, determining a number of positions for a second sequence of values, and generating the second sequence of values, each value of the second sequence corresponding to a radix, the radix for each value of the second sequence varying over the second sequence in relation to an application value, the application value corresponding to a position in the second sequence and a sum of a set of values in the second sequence.

Abstract: A method and apparatus for a varying-radix numeration system is described. A method comprises receiving a first sequence of values, determining a number of positions for a second sequence of values, and generating the second sequence of values, each value of the second sequence corresponding to a radix, the radix for each value of the second sequence varying over the second sequence in relation to an application value, the application value corresponding to a position in the second sequence and a sum of a set of values in the second sequence.

Abstract: The methods and apparatus described herein encrypt an unencrypted binary string using an encryption key and a varying-radix conversion method. The encryption key is used to parse the unencrypted binary string into unencrypted sub-strings. The varying-radix conversion method is used to transform the unencrypted sub-strings into encrypted sub-strings. The encrypted sub-strings may then be concatenated together to produce an encrypted binary string. In addition, the reverse process is employed to recover the unencrypted binary string from the encrypted binary string. For example, the decryption process may occur after the encrypted binary string is transmitted over a network communications system.

Abstract: A method includes receiving an original string of bits where each of the bits represents one of two possible logic levels. The string of bits also carries information. A new string is formed, based on the original string, which contains all of the information of the original string by using fewer bits of one of the logic levels.

Abstract: A method and apparatus for a varying-radix numeration system is described. A method comprises receiving a first sequence of values, determining a number of positions for a second sequence of values, and generating the second sequence of values, each value of the second sequence corresponding to a radix, the radix for each value of the second sequence varying over the second sequence in relation to an application value, the application value corresponding to a position in the second sequence and a sum of a set of values in the second sequence.