View source for Group coded recording

{{Short description|Encoding methods for representing data on magnetic media}}
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{{Use list-defined references|date=December 2021}}

In [[Computer science|computer science]], '''group coded recording''' or '''group code recording''' ('''GCR''') refers to several distinct but related encoding methods for representing data on magnetic media. The first, used in {{val|6250}}&nbsp;bpi [[Physics:Magnetic tape|magnetic tape]] since 1973, is an error-correcting code combined with a [[Run-length limited|run-length limited]] (RLL) encoding scheme, belonging into the group of modulation codes.<ref name="Patel_1988_MR"/> The others are different [[Mainframe computer|mainframe]] hard disk as well as [[Floppy disk|floppy disk]] encoding methods used in some [[Microcomputer|microcomputer]]s until the late 1980s. GCR is a modified form of a NRZI code, but necessarily with a higher transition density.<ref name="Patel_1988_MR"/>

== {{anchor|Tape|IBM}}Magnetic tape ==
Group coded recording was first used for [[Physics:Magnetic-tape data storage|magnetic-tape data storage]] on [[Engineering:9-track tape|9-track]] reel-to-reel tape.<ref name="Patel_1988_MR"/> The term was coined during the development of the IBM 3420 Model 4/6/8 Magnetic Tape Unit<ref name="CW_1973_IBM"/> and the corresponding 3803 Model&nbsp;2 Tape Control Unit,<ref name="OldIron_2004_IBM3803"/><ref name="CW_1973_IBM"/> both introduced in 1973.<ref name="CW_1973_IBM"/><ref name="Harris_1981_IBM"/> [[Company:IBM|IBM]] referred to the error correcting code itself as "group coded recording". However, GCR has come to refer to the recording format of {{val|6250}}&nbsp;bpi (250&nbsp;bits/mm<ref name="Patel_1988_MR"/>) tape as a whole, and later to formats which use similar RLL codes without the error correction code.

In order to reliably read and write to [[Physics:Magnetic tape|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, defined by the magnetic properties of the media itself. The second is that there must be a reversal often enough to keep the reader's clock in phase with the written signal; that is, the signal must be [[Self-clocking signal|self-clocking]] and most importantly to keep the playback output high enough as this is proportional to the density of flux transitions. Prior to {{val|6250}}&nbsp;bpi tapes, {{val|1600}}&nbsp;bpi tapes satisfied these constraints using a technique called phase encoding (PE), which was only 50% efficient. For {{val|6250}}&nbsp;bpi GCR tapes, a (0,&nbsp;2)&nbsp;RLL code is used, or more specifically a <small>{{sfrac|4|5}}</small>&nbsp;(0,&nbsp;2) [[Block code|block code]]<ref name="Patel_1988_MR"/> sometimes also referred to as ''GCR (4B-5B)'' encoding.<ref name="Geoffroy_2002"/> This code requires five bits to be written for every four bits of data.<ref name="Patel_1988_MR"/> 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,<ref name="Patel_1988_MR"/> 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 nine tracks.

Of the 32 five-bit patterns, eight begin with two consecutive zero bits, six 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 {{val|6250}}&nbsp;bpi GCR RLL code:<ref name="Keong_GCR"/><ref name="Watkinson_1990"/><ref name="Savard_2006"/><ref name="Geoffroy_2002"/>
{|
|
{|class="wikitable" style="text-align:center;"
! colspan="2"|4-bit value !! colspan="2"|GCR code<ref name="Keong_GCR"/><ref name="Watkinson_1990"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x0 || 0000 || 1.1001 || 0x19
|-
| 0x1 || 0001 || 1.1011 || 0x1B
|-
| 0x2 || 0010 || 1.0010 || 0x12
|-
| 0x3 || 0011 || 1.0011 || 0x13
|-
| 0x4 || 0100 || 1.1101 || 0x1D
|-
| 0x5 || 0101 || 1.0101 || 0x15
|-
| 0x6 || 0110 || 1.0110 || 0x16
|-
| 0x7 || 0111 || 1.0111 || 0x17
|}
|
{|class="wikitable" style="text-align:center;"
! colspan="2"|4-bit value !! colspan="2"|GCR code<ref name="Keong_GCR"/><ref name="Watkinson_1990"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x8 || 1000 || 1.1010 || 0x1A
|-
| 0x9 || 1001 || 0.1001 || 0x09
|-
| 0xA || 1010 || 0.1010 || 0x0A
|-
| 0xB || 1011 || 0.1011 || 0x0B
|-
| 0xC || 1100 || 1.1110 || 0x1E
|-
| 0xD || 1101 || 0.1101 || 0x0D
|-
| 0xE || 1110 || 0.1110 || 0x0E
|-
| 0xF || 1111 || 0.1111 || 0x0F
|}
|}
11 of the [[Nibble|nibble]]s (other than xx00 and 0001) have their code formed by prepending the complement of the [[Most significant bit|most significant bit]]; i.e. abcd is encoded as {{overline|a}}abcd. The other five values are assigned codes beginning with 11. Nibbles of the form ab00 have codes 11ba{{overline|a}}, i.e. the bit reverse of the code for ab11. The code 0001 is assigned the remaining value 11011.

Because of the back then extremely high density of {{val|6250}}&nbsp;bpi 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.<ref name="Patel_1974_ORC"/> This code is a combination of a [[Parity bit|parity]] track and [[Polynomial|polynomial]] code similar to a CRC, but structured for error correction rather than error detection. For every seven bytes written to the tape (before RLL encoding), an eighth check byte is calculated and written to the tape. When reading, the parity is calculated on each byte and exclusive-ORed with the contents of the parity track, and the polynomial check code calculated and exclusive-ORed 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.

In newer IBM half-inch 18-track tape drives recording at {{val|24000}}&nbsp;bpi, <small>{{sfrac|4|5}}</small>&nbsp;(0,&nbsp;2) GCR was replaced by a more efficient <small>{{sfrac|8|9}}</small>&nbsp;(0,&nbsp;3) modulation code, mapping eight bits to nine bits.<ref name="Patel_1988_MR"/>

== {{anchor|Hard disk|Sperry}}Hard disks ==
In the mid-1970s, Sperry Univac, ISS Division was working on large hard drives for the [[Mainframe computer|mainframe]] business using group coding.<ref name="Jacoby_1977_3PM"/>

== {{anchor|Floppy}}Floppy disks ==
Like magnetic tape drives, [[Floppy disk|floppy disk]] drives have physical limits on the spacing of flux reversals (also called transitions, represented by one-bits).

=== Micropolis ===<!-- used in redirects -->
Offering GCR-compatible diskette drives and floppy disk controllers (like the 100163-51-8 and 100163-52-6<ref>{{Cite web |url=https://www.micropolis.com/support/floppy-drives/100163 |title=Micropolis 100163 Intelligent Controller |access-date=2022-06-26 |website=Micropolis }})</ref>), [[Company:Micropolis Corporation|Micropolis]] endorsed data encoding with group coded recording<ref name="McClelland_1979_GCR"/> on 5¼-inch 100&nbsp;tpi 77-track diskette drives to store twelve 512-byte sectors per track<!-- 462 KiB per side --> since 1977 or 1978.<ref name="Micropolis_1978"/><ref name="Micropolis_1979_DiskMaint"/><ref name="IW_1980_Micropolis"/><ref name="Guzis_2015_Multi"/>

=== Micro Peripherals ===<!-- used in redirects -->
Micro Peripherals, Inc. (MPI) marketed double-density 5¼-inch disk drives (like the single-sided B51<!-- 250K with encoding ? --> and double-sided B52 drives<!-- 500K with encoding ? -->) and a controller solution implementing GCR since <!-- at least -->early 1978.<ref name="Allen_1978_Byte"/><ref name="CW_1979_MPI"/>

=== Durango ===<!-- used in redirects -->
The [[Company:Durango Systems|Durango Systems]] [[Engineering:Durango F-85|F-85]] (introduced in September 1978<ref name="Schultz_1978_Durango"/><ref name="Hendrie_2003_Comstock"/>) used single-sided 5¼-inch 100&nbsp;tpi diskette drives providing 480&nbsp;KB utilizing a proprietary high-density 4/5 group coded encoding. The machine was using a Western Digital FD1781 floppy disk controller, designed by a former Sperry ISS engineer,<ref name="Guzis_2015_Multi"/> with 77-track Micropolis drives.<ref name="Guzis_2009_Micropolis"/> In later models such as the Durango 800<ref name="Durango_800"/> series this was expanded to a double-sided option for 960&nbsp;KB (946&nbsp;KB formatted<ref name="Durango_800"/><ref group="nb" name="NB_On-line_capacity"/>) per diskette.<ref name="Hendrie_2003_Comstock"/><ref name="Guzis_2006_F85"/><ref name="Guzis_2009_Micropolis"/><ref name="Micropolis_1978"/>

=== Apple ===<!-- used in redirects -->
For the Apple II floppy drive, [[Biography:Steve Wozniak|Steve Wozniak]] invented a floppy controller which (along with the Disk II 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.

{{anchor|4 and 4}}The simplest scheme to ensure compliance with these limits is to record an extra "clock" transition before each data bit according to differential Manchester encoding or (digital) FM (Frequency Modulation). Known as '''4-and-4 encoding''', the resulting Apple implementation allowed only ten 256-byte sectors per track to be recorded on a single-density 5¼-inch floppy. It uses two bytes for each byte.
{{Col-begin|class=mw-collapsible mw-collapsed}}, 
|+'''4-and-4 encoding table'''
{{Col-4}}
{|class="wikitable" style="text-align:center;"
! colspan="2"|Value !! colspan="2"|Code<ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x00 || 0000.0000 || 1010.1010 1010.1010 || 0xAA 0xAA
|-
| 0x01 || 0000.0001 || 1010.1010 1010.1011 || 0xAA 0xAB
|-
| 0x02 || 0000.0010 || 1010.1011 1010.1010 || 0xAB 0xAA
|-
| 0x03 || 0000.0011 || 1010.1011 1010.1011 || 0xAB 0xAB
|-
| 0x04 || 0000.0100 || 1010.1010 1010.1110 || 0xAA 0xAE
|-
| 0x05 || 0000.0101 || 1010.1010 1010.1111 || 0xAA 0xAF
|-
| 0x06 || 0000.0110 || 1010.1011 1010.1110 || 0xAB 0xAE
|-
| 0x07 || 0000.0111 || 1010.1011 1010.1111 || 0xAB 0xAF
|-
| 0x08 || 0000.1000 || 1010.1110 1010.1010 || 0xAE 0xAA
|-
| 0x09 || 0000.1001 || 1010.1110 1010.1011 || 0xAE 0xAB
|-
| 0x0A || 0000.1010 || 1010.1111 1010.1010 || 0xAF 0xAA
|-
| 0x0B || 0000.1011 || 1010.1111 1010.1011 || 0xAF 0xAB
|-
| 0x0C || 0000.1100 || 1010.1110 1010.1110 || 0xAE 0xAE
|-
| 0x0D || 0000.1101 || 1010.1110 1010.1111 || 0xAE 0xAF
|-
| 0x0E || 0000.1110 || 1010.1111 1010.1110 || 0xAF 0xAE
|-
| 0x0F || 0000.1111 || 1010.1111 1010.1111 || 0xAF 0xAF
|-
| 0x10 || 0001.0000 || 1010.1010 1011.1010 || 0xAA 0xBA
|-
| 0x11 || 0001.0001 || 1010.1010 1011.1011 || 0xAA 0xBB
|-
| 0x12 || 0001.0010 || 1010.1011 1011.1010 || 0xAB 0xBA
|-
| 0x13 || 0001.0011 || 1010.1011 1011.1011 || 0xAB 0xBB
|-
| 0x14 || 0001.0100 || 1010.1010 1011.1110 || 0xAA 0xBE
|-
| 0x15 || 0001.0101 || 1010.1010 1011.1111 || 0xAA 0xBF
|-
| 0x16 || 0001.0110 || 1010.1011 1011.1110 || 0xAB 0xBE
|-
| 0x17 || 0001.0111 || 1010.1011 1011.1111 || 0xAB 0xBF
|-
| 0x18 || 0001.1000 || 1010.1110 1011.1010 || 0xAE 0xBA
|-
| 0x19 || 0001.1001 || 1010.1110 1011.1011 || 0xAE 0xBB
|-
| 0x1A || 0001.1010 || 1010.1111 1011.1010 || 0xAF 0xBA
|-
| 0x1B || 0001.1011 || 1010.1111 1011.1011 || 0xAF 0xBB
|-
| 0x1C || 0001.1100 || 1010.1110 1011.1110 || 0xAE 0xBE
|-
| 0x1D || 0001.1101 || 1010.1110 1011.1111 || 0xAE 0xBF
|-
| 0x1E || 0001.1110 || 1010.1111 1011.1110 || 0xAF 0xBE
|-
| 0x1F || 0001.1111 || 1010.1111 1011.1111 || 0xAF 0xBF
|-
| 0x20 || 0010.0000 || 1011.1010 1010.1010 || 0xBA 0xAA
|-
| 0x21 || 0010.0001 || 1011.1010 1010.1011 || 0xBA 0xAB
|-
| 0x22 || 0010.0010 || 1011.1011 1010.1010 || 0xBB 0xAA
|-
| 0x23 || 0010.0011 || 1011.1011 1010.1011 || 0xBB 0xAB
|-
| 0x24 || 0010.0100 || 1011.1010 1010.1110 || 0xBA 0xAE
|-
| 0x25 || 0010.0101 || 1011.1010 1010.1111 || 0xBA 0xAF
|-
| 0x26 || 0010.0110 || 1011.1011 1010.1110 || 0xBB 0xAE
|-
| 0x27 || 0010.0111 || 1011.1011 1010.1111 || 0xBB 0xAF
|-
| 0x28 || 0010.1000 || 1011.1110 1010.1010 || 0xBE 0xAA
|-
| 0x29 || 0010.1001 || 1011.1110 1010.1011 || 0xBE 0xAB
|-
| 0x2A || 0010.1010 || 1011.1111 1010.1010 || 0xBF 0xAA
|-
| 0x2B || 0010.1011 || 1011.1111 1010.1011 || 0xBF 0xAB
|-
| 0x2C || 0010.1100 || 1011.1110 1010.1110 || 0xBE 0xAE
|-
| 0x2D || 0010.1101 || 1011.1110 1010.1111 || 0xBE 0xAF
|-
| 0x2E || 0010.1110 || 1011.1111 1010.1110 || 0xBF 0xAE
|-
| 0x2F || 0010.1111 || 1011.1111 1010.1111 || 0xBF 0xAF
|-
| 0x30 || 0011.0000 || 1011.1010 1011.1010 || 0xBA 0xBA
|-
| 0x31 || 0011.0001 || 1011.1010 1011.1011 || 0xBA 0xBB
|-
| 0x32 || 0011.0010 || 1011.1011 1011.1010 || 0xBB 0xBA
|-
| 0x33 || 0011.0011 || 1011.1011 1011.1011 || 0xBB 0xBB
|-
| 0x34 || 0011.0100 || 1011.1010 1011.1110 || 0xBA 0xBE
|-
| 0x35 || 0011.0101 || 1011.1010 1011.1111 || 0xBA 0xBF
|-
| 0x36 || 0011.0110 || 1011.1011 1011.1110 || 0xBB 0xBE
|-
| 0x37 || 0011.0111 || 1011.1011 1011.1111 || 0xBB 0xBF
|-
| 0x38 || 0011.1000 || 1011.1110 1011.1010 || 0xBE 0xBA
|-
| 0x39 || 0011.1001 || 1011.1110 1011.1011 || 0xBE 0xBB
|-
| 0x3A || 0011.1010 || 1011.1111 1011.1010 || 0xBF 0xBA
|-
| 0x3B || 0011.1011 || 1011.1111 1011.1011 || 0xBF 0xBB
|-
| 0x3C || 0011.1100 || 1011.1110 1011.1110 || 0xBE 0xBE
|-
| 0x3D || 0011.1101 || 1011.1110 1011.1111 || 0xBE 0xBF
|-
| 0x3E || 0011.1110 || 1011.1111 1011.1110 || 0xBF 0xBE
|-
| 0x3F || 0011.1111 || 1011.1111 1011.1111 || 0xBF 0xBF
|}
{{Col-4}}
{|class="wikitable" style="text-align:center;"
! colspan="2"|Value !! colspan="2"|Code<ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x40 || 0100.0000 || 1010.1010 1110.1010 || 0xAA 0xEA
|-
| 0x41 || 0100.0001 || 1010.1010 1110.1011 || 0xAA 0xEB
|-
| 0x42 || 0100.0010 || 1010.1011 1110.1010 || 0xAB 0xEA
|-
| 0x43 || 0100.0011 || 1010.1011 1110.1011 || 0xAB 0xEB
|-
| 0x44 || 0100.0100 || 1010.1010 1110.1110 || 0xAA 0xEE
|-
| 0x45 || 0100.0101 || 1010.1010 1110.1111 || 0xAA 0xEF
|-
| 0x46 || 0100.0110 || 1010.1011 1110.1110 || 0xAB 0xEE
|-
| 0x47 || 0100.0111 || 1010.1011 1110.1111 || 0xAB 0xEF
|-
| 0x48 || 0100.1000 || 1010.1110 1110.1010 || 0xAE 0xEA
|-
| 0x49 || 0100.1001 || 1010.1110 1110.1011 || 0xAE 0xEB
|-
| 0x4A || 0100.1010 || 1010.1111 1110.1010 || 0xAF 0xEA
|-
| 0x4B || 0100.1011 || 1010.1111 1110.1011 || 0xAF 0xEB
|-
| 0x4C || 0100.1100 || 1010.1110 1110.1110 || 0xAE 0xEE
|-
| 0x4D || 0100.1101 || 1010.1110 1110.1111 || 0xAE 0xEF
|-
| 0x4E || 0100.1110 || 1010.1111 1110.1110 || 0xAF 0xEE
|-
| 0x4F || 0100.1111 || 1010.1111 1110.1111 || 0xAF 0xEF
|-
| 0x50 || 0101.0000 || 1010.1010 1111.1010 || 0xAA 0xFA
|-
| 0x51 || 0101.0001 || 1010.1010 1111.1011 || 0xAA 0xFB
|-
| 0x52 || 0101.0010 || 1010.1011 1111.1010 || 0xAB 0xFA
|-
| 0x53 || 0101.0011 || 1010.1011 1111.1011 || 0xAB 0xFB
|-
| 0x54 || 0101.0100 || 1010.1010 1111.1110 || 0xAA 0xFE
|-
| 0x55 || 0101.0101 || 1010.1010 1111.1111 || 0xAA 0xFF
|-
| 0x56 || 0101.0110 || 1010.1011 1111.1110 || 0xAB 0xFE
|-
| 0x57 || 0101.0111 || 1010.1011 1111.1111 || 0xAB 0xFF
|-
| 0x58 || 0101.1000 || 1010.1110 1111.1010 || 0xAE 0xFA
|-
| 0x59 || 0101.1001 || 1010.1110 1111.1011 || 0xAE 0xFB
|-
| 0x5A || 0101.1010 || 1010.1111 1111.1010 || 0xAF 0xFA
|-
| 0x5B || 0101.1011 || 1010.1111 1111.1011 || 0xAF 0xFB
|-
| 0x5C || 0101.1100 || 1010.1110 1111.1110 || 0xAE 0xFE
|-
| 0x5D || 0101.1101 || 1010.1110 1111.1111 || 0xAE 0xFF
|-
| 0x5E || 0101.1110 || 1010.1111 1111.1110 || 0xAF 0xFE
|-
| 0x5F || 0101.1111 || 1010.1111 1111.1111 || 0xAF 0xFF
|-
| 0x60 || 0110.0000 || 1011.1010 1110.1010 || 0xBA 0xEA
|-
| 0x61 || 0110.0001 || 1011.1010 1110.1011 || 0xBA 0xEB
|-
| 0x62 || 0110.0010 || 1011.1011 1110.1010 || 0xBB 0xEA
|-
| 0x63 || 0110.0011 || 1011.1011 1110.1011 || 0xBB 0xEB
|-
| 0x64 || 0110.0100 || 1011.1010 1110.1110 || 0xBA 0xEE
|-
| 0x65 || 0110.0101 || 1011.1010 1110.1111 || 0xBA 0xEF
|-
| 0x66 || 0110.0110 || 1011.1011 1110.1110 || 0xBB 0xEE
|-
| 0x67 || 0110.0111 || 1011.1011 1110.1111 || 0xBB 0xEF
|-
| 0x68 || 0110.1000 || 1011.1110 1110.1010 || 0xBE 0xEA
|-
| 0x69 || 0110.1001 || 1011.1110 1110.1011 || 0xBE 0xEB
|-
| 0x6A || 0110.1010 || 1011.1111 1110.1010 || 0xBF 0xEA
|-
| 0x6B || 0110.1011 || 1011.1111 1110.1011 || 0xBF 0xEB
|-
| 0x6C || 0110.1100 || 1011.1110 1110.1110 || 0xBE 0xEE
|-
| 0x6D || 0110.1101 || 1011.1110 1110.1111 || 0xBE 0xEF
|-
| 0x6E || 0110.1110 || 1011.1111 1110.1110 || 0xBF 0xEE
|-
| 0x6F || 0110.1111 || 1011.1111 1110.1111 || 0xBF 0xEF
|-
| 0x70 || 0111.0000 || 1011.1010 1111.1010 || 0xBA 0xFA
|-
| 0x71 || 0111.0001 || 1011.1010 1111.1011 || 0xBA 0xFB
|-
| 0x72 || 0111.0010 || 1011.1011 1111.1010 || 0xBB 0xFA
|-
| 0x73 || 0111.0011 || 1011.1011 1111.1011 || 0xBB 0xFB
|-
| 0x74 || 0111.0100 || 1011.1010 1111.1110 || 0xBA 0xFE
|-
| 0x75 || 0111.0101 || 1011.1010 1111.1111 || 0xBA 0xFF
|-
| 0x76 || 0111.0110 || 1011.1011 1111.1110 || 0xBB 0xFE
|-
| 0x77 || 0111.0111 || 1011.1011 1111.1111 || 0xBB 0xFF
|-
| 0x78 || 0111.1000 || 1011.1110 1111.1010 || 0xBE 0xFA
|-
| 0x79 || 0111.1001 || 1011.1110 1111.1011 || 0xBE 0xFB
|-
| 0x7A || 0111.1010 || 1011.1111 1111.1010 || 0xBF 0xFA
|-
| 0x7B || 0111.1011 || 1011.1111 1111.1011 || 0xBF 0xFB
|-
| 0x7C || 0111.1100 || 1011.1110 1111.1110 || 0xBE 0xFE
|-
| 0x7D || 0111.1101 || 1011.1110 1111.1111 || 0xBE 0xFF
|-
| 0x7E || 0111.1110 || 1011.1111 1111.1110 || 0xBF 0xFE
|-
| 0x7F || 0111.1111 || 1011.1111 1111.1111 || 0xBF 0xFF
|}
{{Col-4}}
{|class="wikitable" style="text-align:center;"
! colspan="2"|Value !! colspan="2"|Code<ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x80 || 1000.0000 || 1110.1010 1010.1010 || 0xEA 0xAA
|-
| 0x81 || 1000.0001 || 1110.1010 1010.1011 || 0xEA 0xAB
|-
| 0x82 || 1000.0010 || 1110.1011 1010.1010 || 0xEB 0xAA
|-
| 0x83 || 1000.0011 || 1110.1011 1010.1011 || 0xEB 0xAB
|-
| 0x84 || 1000.0100 || 1110.1010 1010.1110 || 0xEA 0xAE
|-
| 0x85 || 1000.0101 || 1110.1010 1010.1111 || 0xEA 0xAF
|-
| 0x86 || 1000.0110 || 1110.1011 1010.1110 || 0xEB 0xAE
|-
| 0x87 || 1000.0111 || 1110.1011 1010.1111 || 0xEB 0xAF
|-
| 0x88 || 1000.1000 || 1110.1110 1010.1010 || 0xEE 0xAA
|-
| 0x89 || 1000.1001 || 1110.1110 1010.1011 || 0xEE 0xAB
|-
| 0x8A || 1000.1010 || 1110.1111 1010.1010 || 0xEF 0xAA
|-
| 0x8B || 1000.1011 || 1110.1111 1010.1011 || 0xEF 0xAB
|-
| 0x8C || 1000.1100 || 1110.1110 1010.1110 || 0xEE 0xAE
|-
| 0x8D || 1000.1101 || 1110.1110 1010.1111 || 0xEE 0xAF
|-
| 0x8E || 1000.1110 || 1110.1111 1010.1110 || 0xEF 0xAE
|-
| 0x8F || 1000.1111 || 1110.1111 1010.1111 || 0xEF 0xAF
|-
| 0x90 || 1001.0000 || 1110.1010 1011.1010 || 0xEA 0xBA
|-
| 0x91 || 1001.0001 || 1110.1010 1011.1011 || 0xEA 0xBB
|-
| 0x92 || 1001.0010 || 1110.1011 1011.1010 || 0xEB 0xBA
|-
| 0x93 || 1001.0011 || 1110.1011 1011.1011 || 0xEB 0xBB
|-
| 0x94 || 1001.0100 || 1110.1010 1011.1110 || 0xEA 0xBE
|-
| 0x95 || 1001.0101 || 1110.1010 1011.1111 || 0xEA 0xBF
|-
| 0x96 || 1001.0110 || 1110.1011 1011.1110 || 0xEB 0xBE
|-
| 0x97 || 1001.0111 || 1110.1011 1011.1111 || 0xEB 0xBF
|-
| 0x98 || 1001.1000 || 1110.1110 1011.1010 || 0xEE 0xBA
|-
| 0x99 || 1001.1001 || 1110.1110 1011.1011 || 0xEE 0xBB
|-
| 0x9A || 1001.1010 || 1110.1111 1011.1010 || 0xEF 0xBA
|-
| 0x9B || 1001.1011 || 1110.1111 1011.1011 || 0xEF 0xBB
|-
| 0x9C || 1001.1100 || 1110.1110 1011.1110 || 0xEE 0xBE
|-
| 0x9D || 1001.1101 || 1110.1110 1011.1111 || 0xEE 0xBF
|-
| 0x9E || 1001.1110 || 1110.1111 1011.1110 || 0xEF 0xBE
|-
| 0x9F || 1001.1111 || 1110.1111 1011.1111 || 0xEF 0xBF
|-
| 0xA0 || 1010.0000 || 1111.1010 1010.1010 || 0xFA 0xAA
|-
| 0xA1 || 1010.0001 || 1111.1010 1010.1011 || 0xFA 0xAB
|-
| 0xA2 || 1010.0010 || 1111.1011 1010.1010 || 0xFB 0xAA
|-
| 0xA3 || 1010.0011 || 1111.1011 1010.1011 || 0xFB 0xAB
|-
| 0xA4 || 1010.0100 || 1111.1010 1010.1110 || 0xFA 0xAE
|-
| 0xA5 || 1010.0101 || 1111.1010 1010.1111 || 0xFA 0xAF
|-
| 0xA6 || 1010.0110 || 1111.1011 1010.1110 || 0xFB 0xAE
|-
| 0xA7 || 1010.0111 || 1111.1011 1010.1111 || 0xFB 0xAF
|-
| 0xA8 || 1010.1000 || 1111.1110 1010.1010 || 0xFE 0xAA
|-
| 0xA9 || 1010.1001 || 1111.1110 1010.1011 || 0xFE 0xAB
|-
| 0xAA || 1010.1010 || 1111.1111 1010.1010 || 0xFF 0xAA
|-
| 0xAB || 1010.1011 || 1111.1111 1010.1011 || 0xFF 0xAB
|-
| 0xAC || 1010.1100 || 1111.1110 1010.1110 || 0xFE 0xAE
|-
| 0xAD || 1010.1101 || 1111.1110 1010.1111 || 0xFE 0xAF
|-
| 0xAE || 1010.1110 || 1111.1111 1010.1110 || 0xFF 0xAE
|-
| 0xAF || 1010.1111 || 1111.1111 1010.1111 || 0xFF 0xAF
|-
| 0xB0 || 1011.0000 || 1111.1010 1011.1010 || 0xFA 0xBA
|-
| 0xB1 || 1011.0001 || 1111.1010 1011.1011 || 0xFA 0xBB
|-
| 0xB2 || 1011.0010 || 1111.1011 1011.1010 || 0xFB 0xBA
|-
| 0xB3 || 1011.0011 || 1111.1011 1011.1011 || 0xFB 0xBB
|-
| 0xB4 || 1011.0100 || 1111.1010 1011.1110 || 0xFA 0xBE
|-
| 0xB5 || 1011.0101 || 1111.1010 1011.1111 || 0xFA 0xBF
|-
| 0xB6 || 1011.0110 || 1111.1011 1011.1110 || 0xFB 0xBE
|-
| 0xB7 || 1011.0111 || 1111.1011 1011.1111 || 0xFB 0xBF
|-
| 0xB8 || 1011.1000 || 1111.1110 1011.1010 || 0xFE 0xBA
|-
| 0xB9 || 1011.1001 || 1111.1110 1011.1011 || 0xFE 0xBB
|-
| 0xBA || 1011.1010 || 1111.1111 1011.1010 || 0xFF 0xBA
|-
| 0xBB || 1011.1011 || 1111.1111 1011.1011 || 0xFF 0xBB
|-
| 0xBC || 1011.1100 || 1111.1110 1011.1110 || 0xFE 0xBE
|-
| 0xBD || 1011.1101 || 1111.1110 1011.1111 || 0xFE 0xBF
|-
| 0xBE || 1011.1110 || 1111.1111 1011.1110 || 0xFF 0xBE
|-
| 0xBF || 1011.1111 || 1111.1111 1011.1111 || 0xFF 0xBF
|}
{{Col-4}}
{|class="wikitable" style="text-align:center;"
! colspan="2"|Value !! colspan="2"|Code<ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0xC0 || 1100.0000 || 1110.1010 1110.1010 || 0xEA 0xEA
|-
| 0xC1 || 1100.0001 || 1110.1010 1110.1011 || 0xEA 0xEB
|-
| 0xC2 || 1100.0010 || 1110.1011 1110.1010 || 0xEB 0xEA
|-
| 0xC3 || 1100.0011 || 1110.1011 1110.1011 || 0xEB 0xEB
|-
| 0xC4 || 1100.0100 || 1110.1010 1110.1110 || 0xEA 0xEE
|-
| 0xC5 || 1100.0101 || 1110.1010 1110.1111 || 0xEA 0xEF
|-
| 0xC6 || 1100.0110 || 1110.1011 1110.1110 || 0xEB 0xEE
|-
| 0xC7 || 1100.0111 || 1110.1011 1110.1111 || 0xEB 0xEF
|-
| 0xC8 || 1100.1000 || 1110.1110 1110.1010 || 0xEE 0xEA
|-
| 0xC9 || 1100.1001 || 1110.1110 1110.1011 || 0xEE 0xEB
|-
| 0xCA || 1100.1010 || 1110.1111 1110.1010 || 0xEF 0xEA
|-
| 0xCB || 1100.1011 || 1110.1111 1110.1011 || 0xEF 0xEB
|-
| 0xCC || 1100.1100 || 1110.1110 1110.1110 || 0xEE 0xEE
|-
| 0xCD || 1100.1101 || 1110.1110 1110.1111 || 0xEE 0xEF
|-
| 0xCE || 1100.1110 || 1110.1111 1110.1110 || 0xEF 0xEE
|-
| 0xCF || 1100.1111 || 1110.1111 1110.1111 || 0xEF 0xEF
|-
| 0xD0 || 1101.0000 || 1110.1010 1111.1010 || 0xEA 0xFA
|-
| 0xD1 || 1101.0001 || 1110.1010 1111.1011 || 0xEA 0xFB
|-
| 0xD2 || 1101.0010 || 1110.1011 1111.1010 || 0xEB 0xFA
|-
| 0xD3 || 1101.0011 || 1110.1011 1111.1011 || 0xEB 0xFB
|-
| 0xD4 || 1101.0100 || 1110.1010 1111.1110 || 0xEA 0xFE
|-
| 0xD5 || 1101.0101 || 1110.1010 1111.1111 || 0xEA 0xFF
|-
| 0xD6 || 1101.0110 || 1110.1011 1111.1110 || 0xEB 0xFE
|-
| 0xD7 || 1101.0111 || 1110.1011 1111.1111 || 0xEB 0xFF
|-
| 0xD8 || 1101.1000 || 1110.1110 1111.1010 || 0xEE 0xFA
|-
| 0xD9 || 1101.1001 || 1110.1110 1111.1011 || 0xEE 0xFB
|-
| 0xDA || 1101.1010 || 1110.1111 1111.1010 || 0xEF 0xFA
|-
| 0xDB || 1101.1011 || 1110.1111 1111.1011 || 0xEF 0xFB
|-
| 0xDC || 1101.1100 || 1110.1110 1111.1110 || 0xEE 0xFE
|-
| 0xDD || 1101.1101 || 1110.1110 1111.1111 || 0xEE 0xFF
|-
| 0xDE || 1101.1110 || 1110.1111 1111.1110 || 0xEF 0xFE
|-
| 0xDF || 1101.1111 || 1110.1111 1111.1111 || 0xEF 0xFF
|-
| 0xE0 || 1110.0000 || 1111.1010 1110.1010 || 0xFA 0xEA
|-
| 0xE1 || 1110.0001 || 1111.1010 1110.1011 || 0xFA 0xEB
|-
| 0xE2 || 1110.0010 || 1111.1011 1110.1010 || 0xFB 0xEA
|-
| 0xE3 || 1110.0011 || 1111.1011 1110.1011 || 0xFB 0xEB
|-
| 0xE4 || 1110.0100 || 1111.1010 1110.1110 || 0xFA 0xEE
|-
| 0xE5 || 1110.0101 || 1111.1010 1110.1111 || 0xFA 0xEF
|-
| 0xE6 || 1110.0110 || 1111.1011 1110.1110 || 0xFB 0xEE
|-
| 0xE7 || 1110.0111 || 1111.1011 1110.1111 || 0xFB 0xEF
|-
| 0xE8 || 1110.1000 || 1111.1110 1110.1010 || 0xFE 0xEA
|-
| 0xE9 || 1110.1001 || 1111.1110 1110.1011 || 0xFE 0xEB
|-
| 0xEA || 1110.1010 || 1111.1111 1110.1010 || 0xFF 0xEA
|-
| 0xEB || 1110.1011 || 1111.1111 1110.1011 || 0xFF 0xEB
|-
| 0xEC || 1110.1100 || 1111.1110 1110.1110 || 0xFE 0xEE
|-
| 0xED || 1110.1101 || 1111.1110 1110.1111 || 0xFE 0xEF
|-
| 0xEE || 1110.1110 || 1111.1111 1110.1110 || 0xFF 0xEE
|-
| 0xEF || 1110.1111 || 1111.1111 1110.1111 || 0xFF 0xEF
|-
| 0xF0 || 1111.0000 || 1111.1010 1111.1010 || 0xFA 0xFA
|-
| 0xF1 || 1111.0001 || 1111.1010 1111.1011 || 0xFA 0xFB
|-
| 0xF2 || 1111.0010 || 1111.1011 1111.1010 || 0xFB 0xFA
|-
| 0xF3 || 1111.0011 || 1111.1011 1111.1011 || 0xFB 0xFB
|-
| 0xF4 || 1111.0100 || 1111.1010 1111.1110 || 0xFA 0xFE
|-
| 0xF5 || 1111.0101 || 1111.1010 1111.1111 || 0xFA 0xFF
|-
| 0xF6 || 1111.0110 || 1111.1011 1111.1110 || 0xFB 0xFE
|-
| 0xF7 || 1111.0111 || 1111.1011 1111.1111 || 0xFB 0xFF
|-
| 0xF8 || 1111.1000 || 1111.1110 1111.1010 || 0xFE 0xFA
|-
| 0xF9 || 1111.1001 || 1111.1110 1111.1011 || 0xFE 0xFB
|-
| 0xFA || 1111.1010 || 1111.1111 1111.1010 || 0xFF 0xFA
|-
| 0xFB || 1111.1011 || 1111.1111 1111.1011 || 0xFF 0xFB
|-
| 0xFC || 1111.1100 || 1111.1110 1111.1110 || 0xFE 0xFE
|-
| 0xFD || 1111.1101 || 1111.1110 1111.1111 || 0xFE 0xFF
|-
| 0xFE || 1111.1110 || 1111.1111 1111.1110 || 0xFF 0xFE
|-
| 0xFF || 1111.1111 || 1111.1111 1111.1111 || 0xFF 0xFF
|}
{{Col-end}}
{{anchor|5 and 3}}Close to a month prior to the shipment of the disk drive in spring 1978,<ref name="Williams_1985_Byte"/> Wozniak realized that a more complex encoding scheme would allow each eight-bit byte on disk to hold five bits of useful data rather than four 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 [[Software:Apple DOS|Apple DOS 3.1]], 3.2, and [[Software:Apple DOS|3.2.1]], as well as for the earliest version of {{ill|Apple CP/M|de}}:<ref name="Lechner_1982_Beneath_Apple_DOS"/>
{{Col-begin|class=mw-collapsible mw-collapsed}}, 
|+'''5-and-3 encoding table'''
{{Col-2}}
{|class="wikitable" style="text-align:center;"
! colspan="2"|5-bit value !! colspan="2"|GCR code<ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Sather_1983_Understanding_Apple_II"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x00 || 0.0000 || 1010.1011 || 0xAB
|-
| 0x01 || 0.0001 || 1010.1101 || 0xAD
|-
| 0x02 || 0.0010 || 1010.1110 || 0xAE
|-
| 0x03 || 0.0011 || 1010.1111 || 0xAF
|-
| 0x04 || 0.0100 || 1011.0101 || 0xB5
|-
| 0x05 || 0.0101 || 1011.0110 || 0xB6
|-
| 0x06 || 0.0110 || 1011.0111 || 0xB7
|-
| 0x07 || 0.0111 || 1011.1010 || 0xBA
|-
| 0x08 || 0.1000 || 1011.1011 || 0xBB
|-
| 0x09 || 0.1001 || 1011.1101 || 0xBD
|-
| 0x0A || 0.1010 || 1011.1110 || 0xBE
|-
| 0x0B || 0.1011 || 1011.1111 || 0xBF
|-
| 0x0C || 0.1100 || 1101.0110 || 0xD6
|-
| 0x0D || 0.1101 || 1101.0111 || 0xD7
|-
| 0x0E || 0.1110 || 1101.1010 || 0xDA
|-
| 0x0F || 0.1111 || 1101.1011 || 0xDB
|}
{{Col-2}}
{|class="wikitable" style="text-align:center;"
! colspan="2"|5-bit value !! colspan="2"|GCR code<ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Sather_1983_Understanding_Apple_II"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x10 || 1.0000 || 1101.1101 || 0xDD
|-
| 0x11 || 1.0001 || 1101.1110 || 0xDE
|-
| 0x12 || 1.0010 || 1101.1111 || 0xDF
|-
| 0x13 || 1.0011 || 1110.1010 || 0xEA
|-
| 0x14 || 1.0100 || 1110.1011 || 0xEB
|-
| 0x15 || 1.0101 || 1110.1101 || 0xED
|-
| 0x16 || 1.0110 || 1110.1110 || 0xEE
|-
| 0x17 || 1.0111 || 1110.1111 || 0xEF
|-
| 0x18 || 1.1000 || 1111.0101 || 0xF5
|-
| 0x19 || 1.1001 || 1111.0110 || 0xF6
|-
| 0x1A || 1.1010 || 1111.0111 || 0xF7
|-
| 0x1B || 1.1011 || 1111.1010 || 0xFA
|-
| 0x1C || 1.1100 || 1111.1011 || 0xFB
|-
| 0x1D || 1.1101 || 1111.1101 || 0xFD
|-
| 0x1E || 1.1110 || 1111.1110 || 0xFE
|-
| 0x1F || 1.1111 || 1111.1111 || 0xFF
|}
{{Col-end}}
Reserved GCR-codes: 0xAA and 0xD5.<ref name="Lechner_1982_Beneath_Apple_DOS"/>

Wozniak called the system "my most incredible experience at [[Company:Apple Inc.|Apple]] and the finest job I did".<ref name="Williams_1985_Byte"/>

{{anchor|6 and 2}}Later, the design of the floppy drive controller was modified to allow a byte on disk to contain up to one pair of zero bits in a row. This allowed each eight-bit byte to hold six bits of useful data, and allowed 16 sectors per track. This scheme is known as '''6-and-2 encoding''',<ref name="Lechner_1982_Beneath_Apple_DOS"/> and was used on [[Software:Apple Pascal|Apple Pascal]], [[Software:Apple DOS|Apple DOS 3.3]]<ref name="Lechner_1982_Beneath_Apple_DOS"/> and [[Software:Apple ProDOS|ProDOS]],<ref name="Lechner_1985_Beneath_Apple_ProDOS"/> and later with [[Engineering:Apple FileWare|Apple FileWare]] drives in the [[Engineering:Apple Lisa|Apple Lisa]] and the 400K and 800K 3½-inch disks on the Macintosh and Apple II.<ref name="Feichtinger_1987"/><ref name="IWM_1982"/> Apple did not originally call this scheme "GCR", but the term was later applied to it<ref name="IWM_1982"/> to distinguish it from [[Engineering:IBM Personal Computer|IBM PC]] floppies which used the [[Modified Frequency Modulation|MFM]] encoding scheme.
{{Col-begin|class=mw-collapsible mw-collapsed}}, 
|+'''6-and-2 encoding table'''
{{Col-4}}
{| class="wikitable"
! colspan="2"|6-bit value !! colspan="2"|GCR code<ref name="Feichtinger_1987"/><ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Lechner_1985_Beneath_Apple_ProDOS"/><ref name="Sather_1983_Understanding_Apple_II"/><ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x00 || 00.0000 || 1001.0110 || 0x96
|-
| 0x01 || 00.0001 || 1001.0111 || 0x97
|-
| 0x02 || 00.0010 || 1001.1010 || 0x9A
|-
| 0x03 || 00.0011 || 1001.1011 || 0x9B
|-
| 0x04 || 00.0100 || 1001.1101 || 0x9D
|-
| 0x05 || 00.0101 || 1001.1110 || 0x9E
|-
| 0x06 || 00.0110 || 1001.1111 || 0x9F
|-
| 0x07 || 00.0111 || 1010.0110 || 0xA6
|-
| 0x08 || 00.1000 || 1010.0111 || 0xA7
|-
| 0x09 || 00.1001 || 1010.1011 || 0xAB
|-
| 0x0A || 00.1010 || 1010.1100 || 0xAC
|-
| 0x0B || 00.1011 || 1010.1101 || 0xAD
|-
| 0x0C || 00.1100 || 1010.1110 || 0xAE
|-
| 0x0D || 00.1101 || 1010.1111 || 0xAF
|-
| 0x0E || 00.1110 || 1011.0010 || 0xB2
|-
| 0x0F || 00.1111 || 1011.0011 || 0xB3
|}
{{Col-4}}
{| class="wikitable"
! colspan="2"|6-bit value !! colspan="2"|GCR code<ref name="Feichtinger_1987"/><ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Lechner_1985_Beneath_Apple_ProDOS"/><ref name="Sather_1983_Understanding_Apple_II"/><ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x10 || 01.0000 || 1011.0100 || 0xB4
|-
| 0x11 || 01.0001 || 1011.0101 || 0xB5
|-
| 0x12 || 01.0010 || 1011.0110 || 0xB6
|-
| 0x13 || 01.0011 || 1011.0111 || 0xB7
|-
| 0x14 || 01.0100 || 1011.1001 || 0xB9
|-
| 0x15 || 01.0101 || 1011.1010 || 0xBA
|-
| 0x16 || 01.0110 || 1011.1011 || 0xBB
|-
| 0x17 || 01.0111 || 1011.1100 || 0xBC
|-
| 0x18 || 01.1000 || 1011.1101 || 0xBD
|-
| 0x19 || 01.1001 || 1011.1110 || 0xBE
|-
| 0x1A || 01.1010 || 1011.1111 || 0xBF
|-
| 0x1B || 01.1011 || 1100.1011 || 0xCB
|-
| 0x1C || 01.1100 || 1100.1101 || 0xCD
|-
| 0x1D || 01.1101 || 1100.1110 || 0xCE
|-
| 0x1E || 01.1110 || 1100.1111 || 0xCF
|-
| 0x1F || 01.1111 || 1101.0011 || 0xD3
|}
{{Col-4}}
{| class="wikitable"
! colspan="2"|6-bit value !! colspan="2"|GCR code<ref name="Feichtinger_1987"/><ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Lechner_1985_Beneath_Apple_ProDOS"/><ref name="Sather_1983_Understanding_Apple_II"/><ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x20 || 10.0000 || 1101.0110 || 0xD6
|-
| 0x21 || 10.0001 || 1101.0111 || 0xD7
|-
| 0x22 || 10.0010 || 1101.1001 || 0xD9
|-
| 0x23 || 10.0011 || 1101.1010 || 0xDA
|-
| 0x24 || 10.0100 || 1101.1011 || 0xDB
|-
| 0x25 || 10.0101 || 1101.1100 || 0xDC
|-
| 0x26 || 10.0110 || 1101.1101 || 0xDD
|-
| 0x27 || 10.0111 || 1101.1110 || 0xDE
|-
| 0x28 || 10.1000 || 1101.1111 || 0xDF
|-
| 0x29 || 10.1001 || 1110.0101 || 0xE5
|-
| 0x2A || 10.1010 || 1110.0110 || 0xE6
|-
| 0x2B || 10.1011 || 1110.0111 || 0xE7
|-
| 0x2C || 10.1100 || 1110.1001 || 0xE9
|-
| 0x2D || 10.1101 || 1110.1010 || 0xEA
|-
| 0x2E || 10.1110 || 1110.1011 || 0xEB
|-
| 0x2F || 10.1111 || 1110.1100 || 0xEC
|}
{{Col-4}}
{| class="wikitable"
! colspan="2"|6-bit value !! colspan="2"|GCR code<ref name="Feichtinger_1987"/><ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Lechner_1985_Beneath_Apple_ProDOS"/><ref name="Sather_1983_Understanding_Apple_II"/><ref name="CP_1989_CopyII"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x30 || 11.0000 || 1110.1101 || 0xED
|-
| 0x31 || 11.0001 || 1110.1110 || 0xEE
|-
| 0x32 || 11.0010 || 1110.1111 || 0xEF
|-
| 0x33 || 11.0011 || 1111.0010 || 0xF2
|-
| 0x34 || 11.0100 || 1111.0011 || 0xF3
|-
| 0x35 || 11.0101 || 1111.0100 || 0xF4
|-
| 0x36 || 11.0110 || 1111.0101 || 0xF5
|-
| 0x37 || 11.0111 || 1111.0110 || 0xF6
|-
| 0x38 || 11.1000 || 1111.0111 || 0xF7
|-
| 0x39 || 11.1001 || 1111.1001 || 0xF9
|-
| 0x3A || 11.1010 || 1111.1010 || 0xFA
|-
| 0x3B || 11.1011 || 1111.1011 || 0xFB
|-
| 0x3C || 11.1100 || 1111.1100 || 0xFC
|-
| 0x3D || 11.1101 || 1111.1101 || 0xFD
|-
| 0x3E || 11.1110 || 1111.1110 || 0xFE
|-
| 0x3F || 11.1111 || 1111.1111 || 0xFF
|}
{{Col-end}}
Reserved GCR-codes: 0xAA and 0xD5.<ref name="Lechner_1982_Beneath_Apple_DOS"/><ref name="Lechner_1985_Beneath_Apple_ProDOS"/>

=== {{anchor|GCR 4/5|Commodore}}Commodore ===
Independently, Commodore Business Machines (CBM) created a group coded recording scheme for their Commodore 2040 floppy disk drive (launched in the spring of 1979). The relevant constraints on the 2040 drive were that no more than two zero bits could occur in a row; the drive imposed no special constraint on the first bit in a byte. This allowed the use of a scheme similar to that used in {{val|6250}}&nbsp;bpi tape drives. Every four bits of data are translated into five bits on disk, according to the following table:
{|
|
{| class="wikitable"
! colspan="2"|4-bit value !! colspan="2"|GCR code<ref name="Hildon_1985_Anthology"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x0 || 0000 || 0.1010 || 0x0A
|-
| 0x1 || 0001 || 0.1011 || 0x0B
|-
| 0x2 || 0010 || 1.0010 || 0x12
|-
| 0x3 || 0011 || 1.0011 || 0x13
|-
| 0x4 || 0100 || 0.1110 || 0x0E
|-
| 0x5 || 0101 || 0.1111 || 0x0F
|-
| 0x6 || 0110 || 1.0110 || 0x16
|-
| 0x7 || 0111 || 1.0111 || 0x17
|}
|
{| class="wikitable"
! colspan="2"|4-bit value !! colspan="2"|GCR code<ref name="Hildon_1985_Anthology"/>
|-
! hex !! bin !! bin !! hex
|-
| 0x8 || 1000 || 0.1001 || 0x09
|-
| 0x9 || 1001 || 1.1001 || 0x19
|-
| 0xA || 1010 || 1.1010 || 0x1A
|-
| 0xB || 1011 || 1.1011 || 0x1B
|-
| 0xC || 1100 || 0.1101 || 0x0D
|-
| 0xD || 1101 || 1.1101 || 0x1D
|-
| 0xE || 1110 || 1.1110 || 0x1E
|-
| 0xF || 1111 || 1.0101 || 0x15
|}
|}
Each code starts and ends with at most one zero bit, ensuring that even when the codes are concatenated, the encoded data will never contain more than two zero bits in a row. With this encoding at most eight one bits in a row are possible. Therefore, Commodore used sequences of ten or more one bits in a row as synchronization mark.

This more efficient GCR scheme, combined with an approach at constant bit-density recording by gradually increasing the clock rate (zone constant angular velocity, ZCAV) and storing more physical sectors on the outer tracks than on the inner ones ([[Engineering:Zone bit recording|zone bit recording]], ZBR), enabled Commodore to fit 170&nbsp;kB on a standard single-sided single-density 5.25-inch floppy, where Apple fit 140&nbsp;kB (with 6-and-2 encoding) or 114&nbsp;kB (with 5-and-3 encoding) and an FM-encoded floppy held only 88&nbsp;kB.

=== {{anchor|Victor|Sirius}}Sirius/Victor ===
Similar, the 5.25-inch floppy drives of the Victor&nbsp;9000 aka Sirius&nbsp;1, designed by Chuck Peddle in 1981/1982, used a combination of ten-bit GCR and constant bit-density recording by gradually decreasing a drive's rotational speed for the outer tracks in nine zones (a form of zoned constant linear velocity (ZCLV)) while increasing the number of sectors per track (a variant of [[Engineering:Zone bit recording|zone bit recording]] (ZBR)) to achieve formatted capacities of 606&nbsp;kB<!-- 1024-based --> (single sided) / {{val|1188}}&nbsp;kB<!-- 1024-based --> (double-sided) on 96&nbsp;tpi media<!-- (physical geometry: 80&nbsp;tracks&nbsp;× 1/2&nbsp;heads&nbsp;× (11-19) variable sectors&nbsp;× 512&nbsp;bytes, [[FAT12]] file system, unknown logical geometry and FAT ID) -->.<ref name="Sirius1_Specs"/><ref name="Victor_1983_Technical_Reference"/><ref name="Victor_1982_Technical_Reference"/><ref name="Sargent_1988"/>

=== Brother ===<!-- used in redirects -->
Starting around 1985, [[Company:Brother Industries|Brother]] introduced a family of dedicated word processor typewriters with integrated 3.5-inch 38-track<ref group="nb" name="NB_Brother_capacity"/> diskette drive. Early models of the WP and {{ill|Brother LW series{{!}}LW series|de|Brother LW-Reihe}} used a Brother-specific group-coded recording scheme with twelve 256-byte sectors to store up to 120&nbsp;KB<ref group="nb" name="NB_Brother_formats"/> on single-sided and up to 240&nbsp;KB<ref group="nb" name="NB_Brother_formats"/> on double-sided double-density (DD) diskettes.<ref name="Guzis_2015_Multi"/><ref name="Gieseke_2003_Brother"/><ref name="Mick_2002_Brother_WP-6"/><ref name="Cotgrove_2009_Brother"/> Reportedly, prototypes were already shown at the Internationale Funkausstellung 1979 (IFA) in Berlin.

=== {{anchor|4-5}}Sharp ===<!-- used in redirects -->
In 1986, [[Company:Sharp Corporation|Sharp]] introduced a turnable 2.5-inch pocket disk drive solution (drives: CE-1600F, CE-140F; internally based on the FDU-250 chassis; media: CE-1650F) for their series of pocket computers with a formatted capacity of {{val|62464}} bytes per side (2× 64&nbsp;kB nominal, 16 tracks, 8 sectors/track, 512&nbsp;bytes per sector, 48&nbsp;tpi, 250&nbsp;kbit/s, 270&nbsp;rpm) with GCR (4/5) recording.<ref name="Sharp_1986_CE1600F"/><ref name="Sharp_1986_CE140F"/>

== Other uses ==
GCR was also evaluated for a possible use in bar code encoding schemes (packing efficiency, timing tolerances, amount of storage bytes for timing information, and [[Physics:Direct current|DC]] output level).<ref name="Moseley_1979_Byte"/>

== See also ==
*[[Modified Frequency Modulation]] (MFM)
*Run Length Limited (RLL)
*Eight-to-Fourteen Modulation (EFM)
*Error-correcting code
*8b/10b encoding
*[[Group code]]
*4B5B
*Integrated Woz Machine (IWM, a GCR disk controller in Apple computers)
*Paula (MOS Technology 8364, a GCR-capable disk controller in Commodore Amiga computers)
*[[Biology:Individual Computers Catweasel|Individual Computers Catweasel]] (a special diskette controller able to read some GCR formats)
*[[Engineering:KryoFlux|KryoFlux]] (a special diskette controller able to read some GCR formats)
<!-- *Disk2FDI (a special program able to read some GCR formats) -->

== Notes ==
{{reflist|group="nb"|refs=
<ref group="nb" name="NB_On-line_capacity">The product flyer for the Durango 800 series documents a formatted "on-line capacity" of 1.892&nbsp;MB for the diskette drives. The system, however, was equipped with two 5¼-inch [[Company:Micropolis|Micropolis]] 100&nbsp;tpi 77-track floppy drives by default, and 1.892&nbsp;MB is about twice as large as the physical drive capacity documented in various other sources (480&nbsp;KB per side), therefore, by "on-line capacity" they must have meant the available storage capacity available to users for the combination of two drives.</ref>
<ref group="nb" name="NB_Brother_capacity">The sources give slightly contradicting parameters regarding the [[Company:Brother Industries|Brother]] diskette formats. 12 sectors á 256 bytes would give 120&nbsp;KB per side on a 40-track drive, but one source claims the drives were 38-track only.</ref>
<ref group="nb" name="NB_Brother_formats">The following [[Company:Brother Industries|Brother]] models are known to support a 120&nbsp;KB diskette format (incomplete list): WP-1 (1985/1987), WP-5 (1987/1989), WP-6 (1989), WP-55 (1987/1989), WP-500 (1987/1989). The following models are known to support a 240&nbsp;KB format (incomplete list): WP-70, WP-75 (1989), WP-80 (1985/1989), WP-3400, WP-3410, WP-3550, WP-3650D, WP-760D, WP-760D+, LW-1 (1989), LW-20, LW-30, LW-100, LW-400.</ref>
}}

== References ==
{{Reflist|refs=
<ref name="Savard_2006">{{cite web |title=Digital Magnetic Tape Recording |author-first=John J. G. |author-last=Savard |date=2018 |orig-year=2006 |work=quadibloc |url=http://www.quadibloc.com/comp/tapeint.htm |access-date=2018-07-16 |url-status=live |archive-url=https://web.archive.org/web/20180702234956/http://www.quadibloc.com/comp/tapeint.htm |archive-date=2018-07-02}}</ref>
<ref name="Patel_1988_MR">{{cite book |title=Magnetic Recording |chapter=5. Signal and Error-Control Coding |author-last=Patel |author-first=Arvind Motibhai |editor-last1=Mee |editor-first1=C. Denis |editor-last2=Daniel |editor-first2=Eric D. |publisher=McGraw-Hill Book Company |date=1988 |volume=II: Computer Data Storage |edition=1st |isbn=0-07-041272-3 }}</ref>
<ref name="Harris_1981_IBM">{{cite journal |title=Innovations in the Design of Magnetic Tape Subsystems |author-first1=John P. |author-last1=Harris |author-first2=William B. |author-last2=Phillips |author-first3=Jack F. |author-last3=Wells |author-first4=Wayne D. |author-last4=Winger |journal=IBM Journal of Research and Development |volume=25 |number=5 |date=September 1981 |publisher=International Business Machines Corporation |pages=691–700 |doi=10.1147/rd.255.0691 |citeseerx=10.1.1.83.2700}}</ref>
<ref name="CW_1973_IBM">{{cite journal |author=CW staff |title=6,250 Byte/In. Density - IBM 3420 Storage More Than Tripled |journal=Computerworld |location=White Plains, New York, USA |pages=1–2 |date=1973-03-14 |volume=VII |issue=11 |url=https://books.google.com/books?id=11t5CuO-UfUC&pg=PP1 |access-date=2017-03-23  |quote=[[Company:IBM|IBM]] added three new models to the 3420 magnetic tape system than can record data at the "densest recording capability yet offered", according to the company. Using a new method called Group Coded Recording (GCR), the IBM drives can handle tapes containing a data density of 6,250 byte/in. compared with 1,600 byte/in. on earlier models of the 3420. […] An upgraded control unit was also announced - the 3803 Model 2 - which operates with both the earlier and latest 3420 tape units. The Model 2 includes the capability of correcting errors in one or two tracks "simultaneously while the tape is in motion", IBM said. […] The GCR method segments data written on tape into groups of characters to which a special coding character is added. And the higher density is based on a combination of a modified coding scheme, a smaller interrecord gap (called an interblock gap) and modified electronics and electromechanical components, IBM said. Installed 3803/3420 tape systems can be converted to the higher densities in the field. […]}}</ref>
<ref name="OldIron_2004_IBM3803">{{cite web |title=The Gallery of Old Iron |date=2004 |url=http://www.thegalleryofoldiron.com/3803.HTM |url-status=dead |archive-url=https://web.archive.org/web/20081225092106/http://www.thegalleryofoldiron.com/3803.HTM |archive-date=2008-12-25 |quote=[…]<!-- I was the Lead Designer and Architect of the 3803. I started with IBM in 1956 as a CE trainee on the 705 Model II; we installed 2 705s in Nashville, TN in 1957, one at National Life and Accident and one at General Shoe. --> I moved to the lab at Poughkeepsie in 1958 […]<!-- and worked on the 705 Model III and the Tractor and Swift tape drive projects. Swift became Hypertape and I was Lead designer of the Hypertape control unit. --> I later was Lead designer and architect for the 2802 Tape Control Unit and a few years after that, Lead Designer and Architect of the 3803 which was a very large modification based on the 2802. Three of us shared a Corporate Award for the 3803 and I, along with Planner Charlie Von Reyn, came up with the name "Group Coded Recording (GCR)" as the name of the recording method. […]<!-- The 3803 was so much in demand even after production ceased that we put competitors tape systems in our own data center so that we could recondition the 3803s and 3420s and ship them to customers. I retired in 1991 as a Senior Engineer with 30 filed patents, at least 29 of which issued. -->}} (NB. An anonymous comment by one of the developers on the origin of the name "Group Coded Recording".)</ref>
<ref name="Patel_1974_ORC">{{cite journal |author-last1=Patel |author-first1=Arvind Motibhai |author-last2=Hong |author-first2=Se June |title=Optimal Rectangular Code for High Density Magnetic Tapes |journal=IBM Journal of Research and Development |volume=18 |issue=6 |pages=579–588 |date=1974 |doi=10.1147/rd.186.0579 |url=https://domino.research.ibm.com/tchjr/journalindex.nsf/a3807c5b4823c53f85256561006324be/f27484e80210353385256bfa0067f987!OpenDocument |access-date=2017-03-21  |archive-date=2017-11-04  |archive-url=https://web.archive.org/web/20171104194300/https://domino.research.ibm.com/tchjr/journalindex.nsf/a3807c5b4823c53f85256561006324be/f27484e80210353385256bfa0067f987!OpenDocument |url-status=dead }}</ref>
<ref name="Allen_1978_Byte">{{cite journal |title=A Minifloppy Interface |author-first=David |author-last=Allen |location=Kansas City, USA |journal=BYTE |date=February 1978 |volume=3 |number=2 |pages=114, 116–118, 120, 122, 134–125 |url=http://www.rsp-italy.it/IT/Magazines/Byte/_contents/BYTE%20Vol%2003-02%201978-Feb%20-%20Hardware%20Projects.pdf |access-date=2017-06-14 |archive-url=https://web.archive.org/web/20170614002927/http://www.rsp-italy.it/IT/Magazines/Byte/_contents/BYTE%20Vol%2003-02%201978-Feb%20-%20Hardware%20Projects.pdf |archive-date=2017-06-14 |quote=[…] Of the alternative codes used to achieve double density, GCR (Group Coded Recording) looks quite attractive. Micro Peripherals Inc has implemented double density using GCR in a full size floppy disk and controller system currently being marketed. […] GCR is nothing more than the old standby NRZ with its attendant advantages, but, since ordinary NRZ has no clocking information and a potentially high DC content during long strings of ones or zeros, the data is reformatted to eliminate the long strings. The reformatting converts each four bit group of original data into five bits of group coded data; the five bits in the encoded version will always have a mix of ones and zeros, even if the real data is all in one state. Reformatting in GCR can be accomplished in software, as opposed to MFM, etc, which almost unavoidably must be encoded and decoded in hardware. Thus, GCR has good possibilities as a low cost, high reliability scheme for achieving double density. […]}}[http://www.americanradiohistory.com/Archive-Byte/70s/Byte-1978-02.pdf]</ref>
<ref name="Schultz_1978_Durango">{{cite journal |url=https://books.google.com/books?id=QmEH10OiXZkC&pg=PA4 |title=Business Mini Weighs 65 Pound - What is Durango? |author-first=Brad |author-last=Schultz |pages=1, 4 |journal=Computerworld |publisher=CW Communications, Inc. |volume=XII |number=40 |date=1978-10-02 |access-date=2017-06-13}}</ref>
<ref name="CW_1979_MPI">{{cite journal |title=Floppies Claim Improved Performance |journal=Computerworld |publisher=CW Communications, Inc. |date=1979-02-12 |volume=XIII |number=7 |page=90 |url=https://books.google.com/books?id=sglMaWvdPEUC&pg=RA1-PA90 |access-date=2017-06-14}}</ref>
<ref name="Watkinson_1990">{{cite book |title=Coding for Digital Recording |chapter=3.4. Group codes |author-first=John |author-last=Watkinson |publisher=Focal Press |location=Stoneham, MA, USA |date=1990 |isbn=0-240-51293-6 |pages=51–61}}</ref>
<ref name="Feichtinger_1987">{{cite book |author-first=Herwig |author-last=Feichtinger |title=Arbeitsbuch Mikrocomputer |language=de |location=Munich, Germany |publisher=Franzis-Verlag GmbH |isbn=3-7723-8022-0 |date=1987 |edition=2 |pages=223–224}}</ref>
<ref name="Sirius1_Specs">{{cite web |title=Victor 9000/Sirius 1 Specification |url=http://www.commodore.ca/history/people/chuck_peddle/Sirius_1_Victor_9000_Specification.pdf |publisher=commodore.ca |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323230447/http://www.commodore.ca/history/people/chuck_peddle/Sirius_1_Victor_9000_Specification.pdf |archive-date=2017-03-23}}</ref>
<ref name="Victor_1983_Technical_Reference">{{cite web |title=Supplemental Technical Reference Material |id=Application Note: 002 |publisher=Victor Publications |location=Scotts Valley, CA, USA |date=1983-03-23 |edition=1st printing |version=Revision 0 |url=https://archive.org/stream/bitsavers_victorvict83_1876736/appNote002_Mar83#page/n0/mode/1up |quote=[…] Single-sided floppy drive offers 80&nbsp;tracks at 96 TPI […] Double-sided floppy drive offers 160 tracks at 96&nbsp;TPI […] Floppy drives have 512&nbsp;byte sectors; utilising a GCR, 10-bit recording technique. […] Although the [[Engineering:Victor 9000|Victor 9000]] uses 5&nbsp;1/4-inch minifloppies of a similar type to those used in other computers, the floppy disks themselves are not readable on other machines, nor can the Victor 9000 read a disk from another manufacturers machine. The Victor 9000 uses a unique recording method to allow the data to be packed as densely as 600&nbsp;kbytes on a single-sided single-density minifloppy; this recording method involves the regulation of the speed at which the floppy rotates, explaining the fact that the noise from the drive sometimes changes frequency.}}</ref>
<ref name="Victor_1982_Technical_Reference">{{cite book |title=Victor 9000 Technical Reference Manual |chapter=Chapter 7. Disk Drive Assembly |date=June 1982 |publisher=Victor Business Products, Inc. |id=710620 |pages=7–1..7–9 |url=https://www.mirrorservice.org/sites/www.bitsavers.org/pdf/victor/victor9000/Victor9000TechRef_Jun82.pdf |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323232847/https://www.mirrorservice.org/sites/www.bitsavers.org/pdf/victor/victor9000/Victor9000TechRef_Jun82.pdf |archive-date=2017-03-23 |quote=[…] Track density is 96 tracks per inch, and recording density is maintained at approximately 8000 bits per inch on all tracks. […] The [[Engineering:Victor 9000|VICTOR 9000]] uses an encoding technique called group code recording (GCR) to convert the data from internal representation to an acceptable form. GCR converts each (4-bit) nibble into a 5-bit code that guarantees a recording pattern that never has more than two zeros together. Then data is recorded on the disk by causing a flux reversal for each "one" bit and no flux reversal for each "zero" bit. […]}}</ref>
<ref name="Sharp_1986_CE1600F">{{cite book |title=Sharp PC-1600 Service Manual |chapter=Model CE-1600F |pages=98–104 |date=July 1986 |publisher=[[Company:Sharp Corporation|Sharp Corporation]], Information Systems Group, Quality & Reliability Control Center |location=Yamatokoriyama, Japan |url=http://sharppocketcomputers.com/4HK7JnFJDuVm/Service/ce1600f_service_manual.pdf |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170507223047/http://sharppocketcomputers.com/4HK7JnFJDuVm/Service/ce1600f_service_manual.pdf |archive-date=2017-05-07 |quote=GCR is an abbreviation of Group Coded Recording. A single byte, 8 bits, data are divided into two 4-bit data which is also converted onto a 5-bit data. Thus, a single byte (8 bits) is recorded on the media as a 10-bit data.}}</ref>
<ref name="Sharp_1986_CE140F">{{cite book |title=Sharp Service Manual Model CE-140F Pocket Disk Drive |publisher=[[Company:Sharp Corporation|Sharp Corporation]] |id=00ZCE140F/SME |url=http://pockemul.free.fr/Documents/ce-140f_Service_manual.pdf |access-date=2017-03-11 |url-status=live |archive-url=https://web.archive.org/web/20170311145818/http://pockemul.free.fr/Documents/ce-140f_Service_manual.pdf |archive-date=2017-03-11}}</ref>
<ref name="Lechner_1982_Beneath_Apple_DOS">{{cite book |author-last2=Lechner |author-first2=Pieter M. |author-last1=Worth |author-first1=Don D. |title=Beneath Apple DOS |date=May 1982 |orig-year=1981 |edition=4th printing |publisher=Quality Software |location=Reseda, CA, USA |url=https://archive.org/stream/Beneath_Apple_DOS_OCR#page/n24/mode/1up |access-date=2017-03-21 }} [http://asciiexpress.net/files/docs/Beneath%20Apple%20DOS%20OCR.pdf<!-- https://web.archive.org/web/20170320233805/http://asciiexpress.net/files/docs/Beneath%20Apple%20DOS%20OCR.pdf -->] [https://mirrors.apple2.org.za/Apple%20II%20Documentation%20Project/Books/Beneath%20Apple%20DOS.pdf] [http://fd.fabiensanglard.net/prince_of_persia/Beneath%20Apple%20DOS.pdf] {{Webarchive|url=https://web.archive.org/web/20160309202219/http://fd.fabiensanglard.net/prince_of_persia/Beneath%20Apple%20DOS.pdf |date=9 March 2016 }}</ref>
<ref name="Lechner_1985_Beneath_Apple_ProDOS">{{cite book |author-last2=Lechner |author-first2=Pieter M. |author-last1=Worth |author-first1=Don D. |title=Beneath Apple ProDOS - For Users of Apple II Plus, Apple IIe and Apple IIc Computers |date=March 1985 |orig-year=1984 |edition=2nd printing |publisher=Quality Software |location=Chatsworth, CA, USA |isbn=0-912985-05-4 |lccn=84-61383 |url=http://www.apple-iigs.info/doc/fichiers/beneathprodos.pdf |access-date=2017-03-21 |url-status=live |archive-url=https://web.archive.org/web/20170321014045/http://www.apple-iigs.info/doc/fichiers/beneathprodos.pdf |archive-date=2017-03-21}} [https://archive.org/details/A2_BENEATH_APPLE_PRODOS_1_1984]</ref>
<ref name="Sather_1983_Understanding_Apple_II">{{cite book |author-last=Sather |author-first=James<!-- Jim --> Fielding |title=Understanding the Apple II - A Learning Guide and Hardware Manual for the Apple II Computer |date=1983 |edition=1st |publisher=Quality Software |location=Chatsworth, CA, USA |isbn=0-912985-01-1 |pages=[https://archive.org/details/Understanding_the_Apple_II_1983_Quality_Software/page/9 9–26, 9–27] |url=https://archive.org/details/Understanding_the_Apple_II_1983_Quality_Software/page/9 |access-date=2017-03-21 }}</ref>
<ref name="CP_1989_CopyII">{{cite book |title=Copy II Plus Version 9 - ProDOS/DOS Utilities - Data Recovery, File Management, Protected Software Backup |publisher=Central Point Software, Inc. |version=9.0 |date=1989-10-31 |orig-year=1982 |url=http://cps.applearchives.com/copy_ii_plus_9x_manual.pdf |access-date=2017-03-21 |archive-url=https://archive.today/20170507224326/http://cps.applearchives.com/copy_ii_plus_9x_manual.pdf |archive-date=7 May 2017 |url-status=dead }}</ref>
<ref name="Williams_1985_Byte">{{cite journal |title=The Apple Story / Part 2: More History and the Apple III |journal=BYTE |date=January 1985 |author-last1=Williams |author-first1=Gregg |author-last2=Moore |author-first2=Rob |page=166 |type=interview |url=http://apple2history.org/museum/articles/byte8501/ |access-date=2013-10-26 |url-status=dead |archive-url=https://web.archive.org/web/20120212185115/http://apple2history.org/museum/articles/byte8501/ |archive-date=2012-02-12}} [https://archive.org/stream/byte-magazine-1985-01/1985_01_BYTE_10-01_Through_the_Hourglass#page/n167/mode/2up] (NB. Interview with [[Biography:Steve Wozniak|Steve Wozniak]], where he describes creating the Apple version of GCR.)</ref>
<ref name="Hendrie_2003_Comstock">{{cite web |title=Oral History of George Comstock |location=Mountain View, California, USA |author-first=George E. |author-last=Comstock |interviewer-first=Gardner |interviewer-last=Hendrie |date=2003-08-13 |id=CHM X2727.2004 |publisher=Computer History Museum |url=http://archive.computerhistory.org/resources/text/Oral_History/Comstock_George/Comstock_George_1.oral_history.102658008.pdf |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323110042/http://archive.computerhistory.org/resources/text/Oral_History/Comstock_George/Comstock_George_1.oral_history.102658008.pdf |archive-date=2017-03-23}}</ref>
<ref name="Guzis_2015_Multi">{{cite web |title=Multi-platform distribution format |author-first=Charles "Chuck" P. |author-last=Guzis |date=2015-09-20 |publisher=Sydex |url=https://www.mail-archive.com/search?l=cctalk@classiccmp.org&q=subject:%22Re%5C%3A+Multi%5C-platform+distribution+format+%5C(Was%5C%3A+Backups+%5C%5Bwas%22&o=newest&f=1 |access-date=2017-06-14 |url-status=live |archive-url=https://web.archive.org/web/20170614234505/https://www.mail-archive.com/search?l=cctalk@classiccmp.org&q=subject:%22Re%5C%3A+Multi%5C-platform+distribution+format+%5C(Was%5C%3A+Backups+%5C%5Bwas%22&o=newest&f=1 |archive-date=2017-06-14 |quote=[…] At the same time Micropolis was working a 5.25" drive that could hold about as much as an 8", using some tricks. The Micropolis drive was 100 tpi, 77 track and, by using GCR, could hold 12 512-byte sectors per track. That's 462 KiB. This was about 1977-78. […] The […] drive and controller implementation (ours was done by a guy we'd recruited from Sperry ISS) was […] complex and expensive […] Brother WP disks […] are 38 track, single-sided, Brother-encoded GCR that hold […] 120K on 2D floppies. […]}}</ref>
<ref name="Guzis_2006_F85">{{cite web |title=The Durango F-85 Computer |author-first=Charles "Chuck" P. |author-last=Guzis |date=October 2006 |publisher=Sydex |url=http://www.sydex.com/durango/durango.html |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323113240/http://www.sydex.com/durango/durango.html |archive-date=2017-03-23}}</ref>
<ref name="Durango_800">{{cite web |title=800 Technical Summary - 800 Series Business Computer System |publisher=Durango Systems, Inc. |location=San Jose, CA, USA |url=http://www.sydex.com/durango/durango.pdf |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323112022/http://www.sydex.com/durango/durango.pdf |archive-date=2017-03-23}}</ref>
<ref name="Micropolis_1978">{{cite journal |title=NCC Preview: OEMs at NCC - Micropolis Corp. |journal=Computerworld |publisher=CW Communications, Inc. |volume=XII |number=22 |date=1978-05-28 |page=P/50 |url=https://books.google.com/books?id=Qrjca3MN6nIC&pg=PT66 |access-date=2017-06-12 |quote=[…] [[Company:Micropolis Corporation|Micropolis]] has extended the capacity of 5.25-in. floppy disk subsystems via double-sided models with formatted file storage of up to nearly 2 million bytes […] The Megafloppy series also features an intelligent controller that facilitates interconnection of four subsystems to a common host interface for a total on-line storage capacity of more than 15M bytes […] Double-sided versions of the product line will be implemented first in two [[Finance:Original equipment manufacturer|OEM]] series - Model 1015 and Model 1055 […] The Model 1015 is an unpackaged drive designed for the manufacturer who integrates floppy disk storage into his own system enclosure. A range of storage capacities from 143,000 to 630,000 bytes per drive is available […] Model 1015 customers have the option of using the Micropolis intelligent controller and Group Code Recording (GCR) method to further expand file space up to 946,000 bytes […] Offering GCR and a microprocessor-based controller as standard features, the Model 1055 5.25-in. floppy has four soft-sectored formats for each of its 77 tracks, yielding a maximum capacity of 1,892,000 bytes of file space on its double-sided version […] An add-on module available for the 1055 is {{sic|comprised |hide=y|of}} two read/write heads and two drives, sharing a common controller. The subsystem capacity (formatted) with the module is 3,784,000 bytes […] Up to four 1055s, each with an add-on module, can be [[Daisy chain (electrical engineering)|daisy-chained]] to a common host for a maximum on-line storage capacity of more than 15M bytes […]}}</ref>
<ref name="Jacoby_1977_3PM">{{cite journal |author-first=George V. |author-last=Jacoby |location=Sperry Univac, ISS Division, Cupertino, CA, USA |title=A new look-ahead code for increased data density |journal=[[Physics:IEEE Transactions on Magnetics|IEEE Transactions on Magnetics]] |volume=13 |issue=5 |date=2003-01-06 |orig-year=September 1977 |pages=1202–1204 |doi=10.1109/TMAG.1977.1059670 |publisher=IEEE}} (NB. This article about the 3PM code was also presented at the Intermag 1977 in June 1977.)</ref>
<ref name="McClelland_1979_GCR">{{cite patent |title=Compatible Digital Magnetic Recording System |country=US |number=4261019 |pubdate=1981-04-07 |fdate=1979-11-29 |pridate=1979-11-29 |inventor-first=S. Barry |inventor-last=McClelland |assign1=[[Company:Micropolis Corporation|Micropolis Corporation]]}} (NB. Application Number: US 06/098381)</ref>
<ref name="Hildon_1985_Anthology">{{cite book |author-last=Hildon |author-first=Karl J. H. |title=The Complete Commodore Inner Space Anthology |chapter=GCR codes |date=March 1985 |publisher=Transactor Publishing Incorporated |location=Milton, Ontario, Canada |isbn=0-9692086-0-X |page=49 |url=http://www.classiccmp.org/cini/pdf/Commodore/The%20Complete%20Commodore%20Inner%20Space%20Anthology.pdf |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323143602/http://www.classiccmp.org/cini/pdf/Commodore/The%20Complete%20Commodore%20Inner%20Space%20Anthology.pdf |archive-date=2017-03-23}} [http://www.zimmers.net/anonftp/pub/cbm/manuals/anthology/p049.jpg<!-- https://web.archive.org/web/20170323115314/http://www.zimmers.net/anonftp/pub/cbm/manuals/anthology/p049.jpg -->] (NB. Commodore GCR codes—but this reference erroneously claims that a 1-bit indicates a lack of a transition.)</ref>
<ref name="Keong_GCR">{{citation |title=Computer Peripherals |at=Chapter 7. Magnetic Recording Fundamentals |author-first=Kwoh Chee |author-last=Keong |publisher=School of Computer Engineering, Nanyang Technological University, Singapore |url=http://www.lintech.org/comp-per/07MAGREC.pdf |access-date=2017-03-23 |url-status=live |archive-url=https://web.archive.org/web/20170323134401/http://www.lintech.org/comp-per/07MAGREC.pdf |archive-date=2017-03-23}}</ref>
<ref name="Guzis_2009_Micropolis">{{cite web |title=Durango GCR |author-first=Charles "Chuck" P. |author-last=Guzis |publisher=Sydex |date=2009-09-13 |url=http://www.vcfed.org/forum/archive/index.php/t-17262.html<!-- http://www.vcfed.org/forum/showthread.php?17262-5-25-quot-floppy-disks-with-bad-sectors-any-solutions/page4 --> |access-date=2017-03-25 |url-status=live |archive-url=https://web.archive.org/web/20171104185445/http://www.vcfed.org/forum/archive/index.php/t-17262.html |archive-date=2017-11-04}}</ref>
<ref name="IWM_1982">{{cite book |title=Integrated Woz Machine (IWM) Specification |edition=19 |publisher=DigiBarn Computer Museum |author=Apple Computer, Inc. |date=February 1982 |orig-year=1978 |url=http://www.brutaldeluxe.fr/documentation/iwm/apple2_IWM_Spec_Rev19_1982.pdf |access-date=2016-08-06 |url-status=live |archive-url=https://web.archive.org/web/20160806095036/http://www.brutaldeluxe.fr/documentation/iwm/apple2_IWM_Spec_Rev19_1982.pdf |archive-date=2016-08-06}}</ref>
<ref name="Micropolis_1979_DiskMaint">{{cite book |title=Micropolis Maintenance Manual Floppy Disk Subsystem |publisher=[[Company:Micropolis Corporation|Micropolis Corporation]] |id=1082-04 |edition=revision 1, 1st |date=February 1979 |url=http://bitsavers.trailing-edge.com/pdf/micropolis/metafloppy/1084-02_Micropolis_Floppy_Disk_Subsystem_Maintenance_Manual_Feb79.pdf |access-date=2017-06-12 |url-status=live |archive-url=https://web.archive.org/web/20170612210907/http://bitsavers.trailing-edge.com/pdf/micropolis/metafloppy/1084-02_Micropolis_Floppy_Disk_Subsystem_Maintenance_Manual_Feb79.pdf |archive-date=2017-06-12}} (NB. Micropolis 100163-51-8 and 100163-52-6 are GCR-based.)</ref>
<ref name="IW_1980_Micropolis">{{cite journal |title=InfoNews/Hardware: Hardware/Briefs |journal=InfoWorld |volume=2 |number=2 |date=1980-03-03 |page=19 |url=https://books.google.com/books?id=aj4EAAAAMBAJ&pg=PT42 |access-date=2017-06-12 |quote=[…] Four new 96 tracks-per-inch products have been added to [[Company:Micropolis Corporation|Micropolis]]' current line of 100 tpi single-sided and double-sided floppy disks. The 96 tpi drives offer 70 tracks-per-side, as opposed to the 77 offered by the MegaFloppy line. The four models are: 1) The 1015-V: 436 KB, unformatted, FM/MFM recording […] 2) The 1016-V: 532 KB unformatted, Group Coded Recording (GCR) […] 3) The 1015-VI: a two-head version of the MFM drive, 872 KB […] 4) The 1016-VI: also a two-head drive, 1.064 MB GCR encoding […]}}</ref>
<ref name="Moseley_1979_Byte">{{cite journal |title=Technical Forum: A Comparison of Bar Code Encoding Schemes |author-first=Robin C. |author-last=Moseley |location=Andover, MA, USA |journal=BYTE |date=April 1979 |volume=4 |number=4 |pages=50, 52 |url=http://www.americanradiohistory.com/Archive-Byte/70s/Byte-1979-04.pdf |access-date=2017-06-14}}</ref>
<ref name="Gieseke_2003_Brother">{{cite web |title=Brother WP-1 |author-first=Hans-Werner |author-last=Gieseke |date=2003-08-27 |language=de |url=http://de.alt.folklore.computer.narkive.com/8FzmdtOA/brother-wp-1 |access-date=2017-06-14 |url-status=live |archive-url=https://web.archive.org/web/20170614234300/http://de.alt.folklore.computer.narkive.com/8FzmdtOA/brother-wp-1 |archive-date=2017-06-14}} (NB. Reportedly, the Brother WP-1 technical data was derived from page 109 of the user manual.)</ref>
<ref name="Mick_2002_Brother_WP-6">{{cite web |author-first=Mick |author-last=French |title=Brother WP-6 |date=2002-09-13 |url=http://myweb.tiscali.co.uk/mickfrench/brotherwp6.htm |access-date=2017-06-14 |quote=[…] The 3.5" 240Kb disk drive is a single head Brother part no.13194989 and is connected with a 15 pin ribbon. […] it initializes (formats) the disk to a capacity of 236.5Kb. […] |archive-date=2017-11-22  |archive-url=https://web.archive.org/web/20171122120112/http://myweb.tiscali.co.uk/mickfrench/brotherwp6.htm |url-status=dead }}</ref>
<ref name="Cotgrove_2009_Brother">{{cite web |title=archaic floppy disc format |author-first=Michael S. |author-last=Cotgrove |date=2009-02-26 |url=https://groups.google.com/forum/#!msg/comp.sys.ibm.pc.hardware.storage/MajJ_2qJBk0/jZnlyCTZkgYJ |access-date=2017-06-14 |quote=[…] There were several 3.5" Brother disks that are completely nonstandard. […] One had 1296 byte sectors and another had 12 x 256 byte GCR sectors […]}}</ref>
<ref name="Sargent_1988">{{cite book |title=Assemblersprache und Hardware des IBM PC/XT/AT |language=de  |author-first1=Murray |author-last1=Sargent III. |author-first2=Richard L. |author-last2=Shoemaker |author-first3=Ernst H. K. |author-last3=Stelzer |publisher=Addison-Wesley Verlag (Deutschland) GmbH / Addison-Wesley Publishing Company |edition=1 |date=1988 |isbn=3-89319-110-0 |id=. VVA-Nr. 563-00110-4}}</ref>
<ref name="Geoffroy_2002">{{cite book |title=Design of Dependable Computing Systems |chapter=15.12 Exercise GCR (4B - 5B) code |author-first1=Jean-Claude |author-last1=Geffroy |author-first2=Gilles |author-last2=Motet |translator-first=Irene |translator-last=Aleksanova original title: "Linear Programming" by F.P. Vasilyev and A. Yu. Ivanitskiy, published in the Russian language by Factorial, Moscow, 1998 ??? --> |publisher=Springer Science+Business Media, B.V. / Kluwer Academic Publishers |location=Toulouse, France |isbn=978-1-4020-0437-7 |lccn=2002-284974 |id={{ISBN|94-015-9884-3}} |date=2013-03-09 |orig-date=2002 |pages=426, 591 |url=https://books.google.com/books?id=9uaoCAAAQBAJ&pg=PA426 |access-date=2021-11-18}} (672 pages)</ref>
}}

== Further reading ==
* ANSI INCITS 40-1993 (R2003) Unrecorded Magnetic Tape for Information Interchange (9-track, 800&nbsp;bpi, NRZI; {{val|1600}}&nbsp;bpi, PE; and {{val|6250}}&nbsp;bpi, GCR)
* ANSI INCITS 54-1986 (R2002) Recorded Magnetic Tape for Information Interchange ({{val|6250}}&nbsp;bpi, GCR)
* {{cite journal |journal=IEEE Spectrum |title=Magnetic tape: A high performer: Magnetic tape has evolved into a highly effective medium for high-density and low-cost-per-bit data recording |author-first=Herbert W. |author-last=Sallet |volume=14 |issue=7 |date=July 1977 |pages=26–31 |doi=10.1109/MSPEC.1977.6501525}}
* {{cite journal |journal=Computer Design |title=Group-Coded Recording Reliably Doubles Diskette Capacity |author-first=Pawitter S. |author-last=Sidhu |date=December 1976 |pages=84–88}}
* {{cite journal |title=(unknown) |publisher=Perkin-Elmer Data Systems |journal=Perkin-Elmer Data Systems News |date=1977-06-14}}<!-- info on GCR -->
* {{cite journal |author-first1=(Ben) M. Y. |author-last1=Hsiao |author-first2=William C. |author-last2=Carter |author-first3=James W. |author-last3=Thomas |author-first4=William R. |author-last4=Stringfellow |title=Reliability, Availability, and Serviceability of IBM Computer Systems |journal=IBM Journal of Research and Development |volume=25 |issue=5 |doi=10.1147/rd.255.0453 |pages=462 |date=September 1981}} (NB. Mentions the 5/4 RLL code used on {{val|6250}}&nbsp;bpi tape drives.)
* {{cite book|title=Qualstar 34XX Technical Service Manual |publisher=Qualstar Corporation |location=Canoga Park, CA, USA |id=500450 |edition=Revision J |pages=3-4..3-7 |url=http://www.qualstar.com/500450.pdf |access-date=2017-03-23 |url-status=dead |archive-url=https://web.archive.org/web/20110930233939/http://www.qualstar.com/500450.pdf |archive-date=2011-09-30}} (NB. Additional detail on the GCR tape format.)
* {{cite patent |title=Block encoding for magnetic recording systems |country=US |number=3685033 |pubdate=1972-08-15 |fdate=1970-08-24 |pridate=1970-08-24 |inventor1-first=Ashok K. |inventor1-last=Agrawala |inventor2-first=Keshava |inventor2-last=Srivastava |assign1=Honeywell Inc.}} (NB. Application No: US {{val|66199}}. See also: CA993998A, CA993998A1, DE2142428A1)
* {{cite patent |title=Controller for magnetic disc, recorder, or the like |country=US |number=4210959 |pubdate=1980-07-01 |fdate=1978-05-10 |pridate=1978-05-10 |inventor-first=Stephen G. |inventor-last=Wozniak |inventor-link=Stephen G. Wozniak |assign1=Apple Computer, Inc.}} (NB. Application Number: US 5/904420)
* {{cite patent |title=Error detection system |country=US |number=4564941 |pubdate=1986-01-14 |fdate=1983-12-08 |pridate=1983-12-08 |inventor1-first=Richard N. |inventor1-last=Woolley |inventor2-first=Neal |inventor2-last=Glover |inventor3-first=Richard |inventor3-last=Williams |assign1=Apple Computer, Inc.}} (NB. Application Number: US 06/559210. See also: CA1208794A, CA1208794A1, DE3443272A1, DE3443272C2)
* {{cite web |author-first=Sean Brendan |author-last=Dockery |title=Apple II disk encoding |url=ftp://ftp.apple.asimov.net/pub/apple_II/documentation/misc/disk_encoding.doc.txt}}
* {{cite book |title=NEC µPD72070 - Floppy Disk Controller Specification Version 2.0 |version=2.0 preliminary |publisher=NEC Corporation |date=October 1991 |url=http://dec8.info/Apple/uPD72070.pdf |access-date=2017-03-20 |url-status=dead |archive-url=https://web.archive.org/web/20170320235834/http://dec8.info/Apple/uPD72070.pdf |archive-date=20 March 2017 }}
* {{cite web |title=GCR decoding on the fly |author-first=Linus |author-last=Åkesson |date=2013-03-31 |url=https://www.linusakesson.net/programming/gcr-decoding/index.php |access-date=2017-03-21 |url-status=live |archive-url=https://web.archive.org/web/20170321014657/https://www.linusakesson.net/programming/gcr-decoding/index.php |archive-date=2017-03-21}}
* {{cite web |title=Commodore GCR "mysteries" |author-first=Spiro |author-last=Trikaliotis |date=2010-03-05 |url=http://blog.trikaliotis.net/2010/03/05/Commodore-GCR-mysteries |url-status=dead |archive-url=https://web.archive.org/web/20140805202755/http://blog.trikaliotis.net/2010/03/05/Commodore-GCR-mysteries |archive-date=2014-08-05}}
* {{cite web |title=GCR ROM en-/decoder in Commodore 8050 and 8250 disk drives |work=Forum 64 |url=http://www.forum64.de/wbb3/board13-sonstige-commodore/board16-cbm-rechner/34423-backup-einer-8250-diskette-funzt-nicht/index4.html#post408597 |url-status=live |archive-url=https://web.archive.org/web/20100312090430/http://www.forum64.de/wbb3/board13-sonstige-commodore/board16-cbm-rechner/34423-backup-einer-8250-diskette-funzt-nicht/index4.html#post408597 |archive-date=2010-03-12}}
* {{cite journal |title=The IBM 3803/3420 Magnetic Tape Subsystem |author-first1=John W. |author-last1=Irwin |author-first2=John V. |author-last2=Cassie |author-first3=Harlyn C. |author-last3=Oppeboen |date=September 1971 |orig-year=1970-12-11 |journal=IBM Journal of Research and Development |publisher=[[Company:IBM|IBM]] |pages=391–400 |citeseerx=10.1.1.89.7834}}
* {{cite web |title=Milestone-Proposal:Introduction of the Apple Macintosh Computer, 1984 |author-last=Docket |date=June 2014 |url=http://ieeemilestones.ethw.org/Milestone-Proposal:Introduction_of_the_Apple_Macintosh_Computer,_1984 |access-date=2018-07-09 |url-status=live |archive-url=https://web.archive.org/web/20180709092346/http://ieeemilestones.ethw.org/Milestone-Proposal:Introduction_of_the_Apple_Macintosh_Computer,_1984 |archive-date=2018-07-09}}
* {{cite web |title=Crazy Disk Encoding Schemes |work=Big Mess O' Wires (BMOW) - Plus Too |date=2011-10-02 |url=http://www.bigmessowires.com/2011/10/02/crazy-disk-encoding-schemes/ |access-date=2018-07-09 |url-status=live |archive-url=https://web.archive.org/web/20180709092935/https://www.bigmessowires.com/2011/10/02/crazy-disk-encoding-schemes/ |archive-date=2018-07-09}}
* {{cite book |title=Handbuch der Tonstudiotechnik |language=de 
|author-first1=Michael |author-last1=Dickreiter |author-first2=Volker |author-last2=Dittel |author-first3=Wolfgang |author-last3=Hoeg |author-first4=Martin |author-last4=Wöhr |publisher=Walter de Gruyter GmbH & Co KG |date=2014 |isbn=978-3-11031650-6 |id={{ISBN|3-11031650-1}} |url=https://books.google.com/books?id=DqLoBQAAQBAJ&pg=PA835 |access-date=2018-07-09 }}
* {{cite book |title=Digital Baseband Transmission and Recording  |chapter=Chapter 4.8.3 Group-Coded Recording (GCR) Code |author-first=Jan W. M. |author-last=Bergmans |date=2013-03-09 |orig-year=1996 |publisher=Kluwer Academic Publishers / Springer Science & Business Media |location=Philips Research, Eindhoven, Netherlands |edition=reprint |isbn=978-1-4419-5164-9 |doi=10.1007/978-1-4757-2471-4  |url=https://books.google.com/books?id=PB_aBwAAQBAJ&pg=PA179 |access-date=2018-07-09 }}
* {{cite book |title=Magnetic Recording Handbook |author-first=Marvin |author-last=Camras |date=2012 |orig-year=1988 |edition=reprint |lccn=86-24762 |doi=10.1007/978-94-010-9468-9 |isbn=978-9-40109468-9 |id={{ISBN|9-40109468-3}} |publisher=Van Nostrand Reinhold Company / Springer Science & Business |url=https://books.google.com/books?id=PdruCAAAQBAJ&pg=PA602 |access-date=2018-07-09 }}
* {{cite journal |title=In Single-Drive Setup - Tape System Has Three Densities |date=1979-05-07 |journal=Computerworld |volume=XIII |number=19 |publisher=CW Communications/Inc. |location=Louisville, Colorado, USA |page=59 |url=https://books.google.com/books?id=f8kLXVsJ3J8C&pg=RA1-PA59 |access-date=2018-07-09 }}

== External links ==
* {{cite web |title=Les Disquettes Et Le Drive Disk II |language=fr |url=http://www.hackzapple.com/DISKII/DISKIITECH.HTM |access-date=2018-07-09 |url-status=live |archive-url=https://web.archive.org/web/20180709100551/http://www.hackzapple.com/DISKII/DISKIITECH.HTM |archive-date=2018-07-09}}, {{cite web |title=Les Nibbles |language=fr |url=http://www.hackzapple.com/DISKII/DISKIITECH02A.HTM |access-date=2018-07-09 |url-status=live |archive-url=https://web.archive.org/web/20170322014922/http://www.hackzapple.com/DISKII/DISKIITECH02A.HTM |archive-date=2017-03-22}}, {{cite web |title=La Methode PRODOS: Rapide Et Efficace |language=fr |url=http://www.hackzapple.com/DISKII/DISKIITECH06E.HTM |access-date=2018-07-09 |url-status=live |archive-url=https://web.archive.org/web/20180709100607/http://www.hackzapple.com/DISKII/DISKIITECH06E.HTM |archive-date=2018-07-09}}

[[Category:Computer storage tape media]]
[[Category:Rotating disc computer storage media]]
[[Category:Error detection and correction]]

{{Sourceattribution|Group coded recording}}