In computer science, group code recording (GCR) refers to several distinct but related encoding methods for magnetic media. Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their The first, used in 6250 cpi magnetic tape, is an error-correcting code combined with a run length limited encoding scheme. Magnetic tape is a medium for Magnetic recording generally consisting of a thin magnetizable coating on a long and narrow strip of Plastic. In Telecommunication and Information theory, forward error correction (FEC is a System of Error control for Data transmission, whereby Run length limited or RLL coding is a technique that is used to store data on recordable media The others are different floppy disk encoding methods used in some microcomputers until the late 1980s. A floppy disk is an increasingly Obsolete data storage medium that is composed of a disk of thin flexible ("floppy" Magnetic storage medium encased microcomputer is a Computer with a Microprocessor as its Central processing unit.
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GCR for 9-track reel-to-reel tape
In order to reliably read and write to magnetic tape, several constraints on the signal to be written must be followed. The first is that two adjacent flux reversals must be separated by a certain distance on the media. The second is that there must be a flux reversal often enough to keep the reader's clock in phase with the written signal; that is, the signal must be self-clocking. In Telecommunications and Electronics, a self-clocking signal is one that can be decoded without the need for a separate Clock signal or other source Prior to 6250 cpi tapes, 1600 cpi tapes satisfied these constraints using a technique called phase encoding, which was only 50% efficient. In Telecommunication, Manchester code (also known as Phase Encoding, or PE) is a Line code in which the encoding of each data Bit For 6250 GCR tapes, a (0,2)RLL code is used. Run length limited or RLL coding is a technique that is used to store data on recordable media This code requires five bits to be written for every four bits of data. The code is structured so that no more than two zero bits (which are represented by lack of a flux reversal) can occur in a row, either within a code or between codes, no matter what the data was. This RLL code is applied independently to the data going to each of the 9 tracks.
Of the 32 5-bit patterns, 8 begin with two consecutive zero bits, 6 others end with two consecutive zero bits, and one more (10001) contains three consecutive zero bits. Removing the all-ones pattern (11111) from the remainder leaves 16 suitable code words.
The 6250 GCR RLL code:
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Because of the extremely high density of 6250 cpi tape, the RLL code is not sufficient to ensure reliable data storage. On top of the RLL code, an error-correcting code called the Optimal Rectangular Code (ORC) is applied. In Telecommunication and Information theory, forward error correction (FEC is a System of Error control for Data transmission, whereby This code is a combination of a parity track and polynomial code similar to a CRC, but structured for error correction rather than error detection. In Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations A cyclic redundancy check (CRC is a type of function that takes as input a data stream of any length and produces as output a value of a certain space commonly a 32-bit integer For every 7 bytes written to the tape (before RLL encoding), an 8th check byte is calculated and written to the tape. When reading, the parity is calculated on each byte and exclusive-or'd with the contents of the parity track, and the polynomial check code calculated and exclusive-or'd with the received check code, resulting in two 8-bit syndrome words. If these are both zero, the data is error free. Otherwise, error-correction logic in the tape controller corrects the data before it is forwarded to the host. The error correcting code is able to correct any number of errors in any single track, or in any two tracks if the erroneous tracks can be identified by other means.
IBM documents refer to the error correcting code itself as "group coded recording". However, GCR has come to refer to the recording format of 6250 cpi tape as a whole, and later to formats which use similar RLL codes without the error correction code.
GCR for floppy disks
Like magnetic tape drives, floppy disk drives have physical limits on the spacing of flux reversals (also called transitions, represented by 1 bits). A floppy disk is an increasingly Obsolete data storage medium that is composed of a disk of thin flexible ("floppy" Magnetic storage medium encased
For the Apple II floppy drive, Steve Wozniak invented a floppy controller which (along with the drive itself) imposed two constraints
- Between any two one bits, there may be a maximum of one zero bit.
- Each 8-bit byte must start with a one bit.
The simplest scheme to ensure compliance with these limits is to record an extra "clock" transition between each data bit. This scheme is called FM (Frequency Modulation) or "4 and 4", and allows only 10 256-byte sectors per track to be recorded on a single-density 5¼ floppy.
Wozniak realized that a more complex encoding scheme would allow each 8-bit byte on disk to hold 5 bits of useful data rather than 4 bits. This is because there are 34 bytes which have the top bit set and no two zero bits in a row. This encoding scheme became known as "5 and 3" encoding, and allowed 13 sectors per track; it was used for Apple DOS 3. Apple DOS refers to Operating systems for the Apple II series of microcomputers from 1979 through early 1983 1, 3. 2, and 3. 2. 1, as well as for the earliest version of Apple CP/M. Later, the design of the floppy drive controller was modified to allow a byte on disk to contain exactly one pair of zero bits in a row. This allowed each 8-bit byte to hold 6 bits of useful data, and allowed 16 sectors per track. This scheme is known as "6 and 2", and was used on Apple Pascal, Apple DOS 3. Apple Pascal was a language and operating system based on the UCSD Pascal system 3 and ProDOS, and later on the 400K and 800K 3½ disks on the Macintosh and Apple II. ProDOS (the Professional Disk Operating System) became the most popular Operating system for the Apple II series of Macintosh, commonly nicknamed Mac is a Brand name which covers several lines of Personal computers designed developed and marketed by Apple Inc Apple did not originally call this scheme "GCR", but the term was later applied to it to distinguish it from IBM PC floppies which used the MFM encoding scheme. This article is about Modified Frequency Modulation For other uses of MFM see the MFM (disambiguation
Independently, Commodore Business Machines created a Group Code Recording scheme for their Commodore 2040 floppy disk drive (launched in the spring of 1979). Commodore, the commonly used name for Commodore International, was a US-American Electronics company based in West Chester Pennsylvania Commodore 4040 and its sibling(s the 2040 and the European marketed 3040, were dual unit 5¼" Floppy disk drives for Commodore International The relevant constraint on the 2040 drive was that no more than two zero bits could occur in a row, with no special constraint on the first bit in a byte. This allowed the use of a scheme similar to that used in 6250 tape drives. Every 4 bits of data are translated into 5 bits on disk, according to the following table:
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Note no code starts with two zero bits, nor ends with two zero bits. This ensures that regardless of the input data, the encoded data will never contain more than two zero bits in a row. Also note that with this encoding not more than eight one bits in a row are possible. Therefore Commodore used sequences of ten or more one bits in a row as synchronization mark.
Partially because of this more efficient scheme, Commodore was able to fit 170KB on a standard single-density floppy, where Apple fit 140K (6 and 2) or 114K (5 and 3) and an FM-encoded floppy held only 88K.
See also
- Modified Frequency Modulation (MFM)
- Run Length Limited (RLL)
- Eight-to-Fourteen Modulation (EFM)
- Error-correcting code
- 8b/10b encoding
References
- Patel, A. This article is about Modified Frequency Modulation For other uses of MFM see the MFM (disambiguation Run length limited or RLL coding is a technique that is used to store data on recordable media Eight-to-Fourteen Modulation ( EFM) is a data encoding technique used by CDs and pre- Hi-MD MiniDiscs EFM and EFMPlus were both invented In Telecommunication and Information theory, forward error correction (FEC is a System of Error control for Data transmission, whereby In Telecommunications 8b/10b is a Line code that maps 8-bit symbols to 10-bit symbols to achieve DC-balance (see M and Hong, S. J, "Optimal Rectangular Code for High Density Magnetic Tapes", IBM Journal of Research and Development, 18, pp. 579-588 (1974)
- Hsiao, M. Y, et al, "Reliability, Availability, and Serviceability of IBM Computer Systems", IBM Journal of Research and Development, 25, p. 462 (1981) (mentions the 5/4 RLL code used on 6250 tape drives)
- Qualstar 34XX Technical Service Manual pp. 3-4. . 3-7 (additional detail on the GCR tape format)
- Lechner, Pieter and Worth, Don, Beneath Apple DOS ("5 and 3" and "6 and 2" details)
- Hildon, Karl, The Complete Commodore Inner Space Anthology, p. 49 (Commodore GCR codes -- but be warned that this reference erroneously claims that a 1 bit indicates a lack of a transition. )
- Williams, Gregg and Moore, Rob, "The Apple Story", Byte Interview with Steve Wozniak, where he describes creating the Apple version of GCR.
External links
- The PC Guide Frequency Modulation
- The Gallery of Old Iron A comment on the origin of the name "Group Coded Recording".
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