Chen-Ho encoding
Encyclopedia
Chen-Ho encoding is an alternate system of binary
encoding for decimal
digits.
The traditional system of binary encoding for decimal digits, known as Binary-coded decimal
(BCD), uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth (since four bits can store 16 states and are being used to store only 10).
The concepts behind Chen-Ho encoding were first introduced in a memo from Tien Chi Chen to Dr. Irving T. Ho in 1971. Both men were working for IBM
at the time, although in different locations. Tien Chi Chen also consulted with Dr. Frank Tung to verify the results of his theories independently.
Tien Chi Chen noted that the digits zero through seven were simply encoded using three binary digits. He also postulated that one could use a flag
to identify a different encoding for the digits eight and nine, which would be encoded using a single bit.
The final version of Chen-Ho encoding was published in 1975 in the journal Communications of the Association for Computing Machinery (CACM). This version included several refinements, primarily related to the application of the encoding system.
Chen-Ho encoding is limited to encoding of sets of three decimal digits. One prominent application uses a 128-bit register to store 33 decimal digits with a three digit exponent.
published a further refinement of Chen-Ho encoding known as densely packed decimal encoding
in IEE Proceedings – Computers and Digital Techniques, which is summarized here.
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
encoding for decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
digits.
The traditional system of binary encoding for decimal digits, known as Binary-coded decimal
Binary-coded decimal
In computing and electronic systems, binary-coded decimal is a digital encoding method for numbers using decimal notation, with each decimal digit represented by its own binary sequence. In BCD, a numeral is usually represented by four bits which, in general, represent the decimal range 0 through 9...
(BCD), uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth (since four bits can store 16 states and are being used to store only 10).
The concepts behind Chen-Ho encoding were first introduced in a memo from Tien Chi Chen to Dr. Irving T. Ho in 1971. Both men were working for IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...
at the time, although in different locations. Tien Chi Chen also consulted with Dr. Frank Tung to verify the results of his theories independently.
Tien Chi Chen noted that the digits zero through seven were simply encoded using three binary digits. He also postulated that one could use a flag
Flag (computing)
In computer programming, flag can refer to one or more bits that are used to store a binary value or code that has an assigned meaning, but can refer to uses of other data types...
to identify a different encoding for the digits eight and nine, which would be encoded using a single bit.
Application
In practice, a series of boolean transformations are applied to the stream of input bits, compressing BCD encoded digits from 12 bits per three digits to 10 bits per three digits. Reversed transformations are used to decode the resulting coded stream to BCD. Equivalent results can also be achieved by the use of a look-up table.The final version of Chen-Ho encoding was published in 1975 in the journal Communications of the Association for Computing Machinery (CACM). This version included several refinements, primarily related to the application of the encoding system.
Chen-Ho encoding is limited to encoding of sets of three decimal digits. One prominent application uses a 128-bit register to store 33 decimal digits with a three digit exponent.
Related Systems of Encoding
In 2002, Mike CowlishawMike Cowlishaw
Mike Cowlishaw is a retired IBM Fellow, a Visiting Professor at the Department of Computer Science at the University of Warwick, and is a Fellow of the Royal Academy of Engineering , the Institute of Engineering and Technology , and the British Computer Society.- Career at IBM :Cowlishaw joined IBM...
published a further refinement of Chen-Ho encoding known as densely packed decimal encoding
Densely Packed Decimal
Densely packed decimal is a system of binary encoding for decimal digits.The traditional system of binary encoding for decimal digits, known as Binary-coded decimal , uses four bits to encode each digit, resulting in significant wastage of binary data bandwidth...
in IEE Proceedings – Computers and Digital Techniques, which is summarized here.