<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
group	B-Device
coded	I-Device
recording	I-Device
or	O
group	B-Device
code	I-Device
recording	I-Device
(	O
GCR	B-Device
)	O
refers	O
to	O
several	O
distinct	O
but	O
related	O
encoding	O
methods	O
for	O
representing	O
data	O
on	O
magnetic	B-Architecture
media	I-Architecture
.	O
</s>
<s>
The	O
first	O
,	O
used	O
in	O
bpi	O
magnetic	O
tape	O
since	O
1973	O
,	O
is	O
an	O
error-correcting	B-Error_Name
code	I-Error_Name
combined	O
with	O
a	O
run	B-Protocol
length	I-Protocol
limited	I-Protocol
(	O
RLL	B-Protocol
)	O
encoding	O
scheme	O
,	O
belonging	O
into	O
the	O
group	O
of	O
modulation	O
codes	O
.	O
</s>
<s>
The	O
others	O
are	O
different	O
mainframe	B-Architecture
hard	B-Device
disk	I-Device
as	O
well	O
as	O
floppy	B-Device
disk	I-Device
encoding	O
methods	O
used	O
in	O
some	O
microcomputers	B-Architecture
until	O
the	O
late	O
1980s	O
.	O
</s>
<s>
GCR	B-Device
is	O
a	O
modified	O
form	O
of	O
a	O
NRZI	O
code	O
,	O
but	O
necessarily	O
with	O
a	O
higher	O
transition	O
density	O
.	O
</s>
<s>
Group	B-Device
coded	I-Device
recording	I-Device
was	O
first	O
used	O
for	O
magnetic	B-Architecture
tape	I-Architecture
data	I-Architecture
storage	I-Architecture
on	O
9-track	B-Device
reel-to-reel	O
tape	O
.	O
</s>
<s>
The	O
term	O
was	O
coined	O
during	O
the	O
development	O
of	O
the	O
IBM	B-Device
3420	I-Device
Model	O
4/6/8	O
Magnetic	O
Tape	O
Unit	O
and	O
the	O
corresponding	O
3803	O
Model2	O
Tape	O
Control	O
Unit	O
,	O
both	O
introduced	O
in	O
1973	O
.	O
</s>
<s>
IBM	O
referred	O
to	O
the	O
error	B-Error_Name
correcting	I-Error_Name
code	I-Error_Name
itself	O
as	O
"	O
group	B-Device
coded	I-Device
recording	I-Device
"	O
.	O
</s>
<s>
However	O
,	O
GCR	B-Device
has	O
come	O
to	O
refer	O
to	O
the	O
recording	O
format	O
of	O
bpi	O
(	O
250bits/mm	O
)	O
tape	O
as	O
a	O
whole	O
,	O
and	O
later	O
to	O
formats	O
which	O
use	O
similar	O
RLL	B-Protocol
codes	I-Protocol
without	O
the	O
error	B-Error_Name
correction	I-Error_Name
code	I-Error_Name
.	O
</s>
<s>
Prior	O
to	O
bpi	O
tapes	O
,	O
bpi	O
tapes	O
satisfied	O
these	O
constraints	O
using	O
a	O
technique	O
called	O
phase	B-Protocol
encoding	I-Protocol
(	O
PE	B-Protocol
)	O
,	O
which	O
was	O
only	O
50%	O
efficient	O
.	O
</s>
<s>
For	O
bpi	O
GCR	B-Device
tapes	O
,	O
a	O
(	O
0	O
,	O
2	O
)	O
RLL	B-Protocol
code	I-Protocol
is	O
used	O
,	O
or	O
more	O
specifically	O
a	O
(	O
0	O
,	O
2	O
)	O
block	O
code	O
sometimes	O
also	O
referred	O
to	O
as	O
GCR	B-Device
(	O
4B-5B	B-Protocol
)	O
encoding	O
.	O
</s>
<s>
This	O
RLL	B-Protocol
code	I-Protocol
is	O
applied	O
independently	O
to	O
the	O
data	O
going	O
to	O
each	O
of	O
the	O
nine	O
tracks	O
.	O
</s>
<s>
The	O
bpi	O
GCR	B-Device
RLL	B-Protocol
code	I-Protocol
:	O
</s>
<s>
Because	O
of	O
the	O
back	O
then	O
extremely	O
high	O
density	O
of	O
bpi	O
tape	O
,	O
the	O
RLL	B-Protocol
code	I-Protocol
is	O
not	O
sufficient	O
to	O
ensure	O
reliable	O
data	O
storage	O
.	O
</s>
<s>
On	O
top	O
of	O
the	O
RLL	B-Protocol
code	I-Protocol
,	O
an	O
error-correcting	B-Error_Name
code	I-Error_Name
called	O
the	O
Optimal	O
Rectangular	O
Code	O
(	O
ORC	O
)	O
is	O
applied	O
.	O
</s>
<s>
This	O
code	O
is	O
a	O
combination	O
of	O
a	O
parity	B-Error_Name
track	O
and	O
polynomial	O
code	O
similar	O
to	O
a	O
CRC	O
,	O
but	O
structured	O
for	O
error	O
correction	O
rather	O
than	O
error	O
detection	O
.	O
</s>
<s>
For	O
every	O
seven	O
bytes	B-Application
written	O
to	O
the	O
tape	O
(	O
before	O
RLL	B-Protocol
encoding	I-Protocol
)	O
,	O
an	O
eighth	O
check	O
byte	B-Application
is	O
calculated	O
and	O
written	O
to	O
the	O
tape	O
.	O
</s>
<s>
When	O
reading	O
,	O
the	O
parity	B-Error_Name
is	O
calculated	O
on	O
each	O
byte	B-Application
and	O
exclusive-ORed	O
with	O
the	O
contents	O
of	O
the	O
parity	B-Error_Name
track	O
,	O
and	O
the	O
polynomial	O
check	O
code	O
calculated	O
and	O
exclusive-ORed	O
with	O
the	O
received	O
check	O
code	O
,	O
resulting	O
in	O
two	O
8-bit	O
syndrome	O
words	O
.	O
</s>
<s>
The	O
error	B-Error_Name
correcting	I-Error_Name
code	I-Error_Name
is	O
able	O
to	O
correct	O
any	O
number	O
of	O
errors	O
in	O
any	O
single	O
track	O
,	O
or	O
in	O
any	O
two	O
tracks	O
if	O
the	O
erroneous	O
tracks	O
can	O
be	O
identified	O
by	O
other	O
means	O
.	O
</s>
<s>
In	O
newer	O
IBM	O
half-inch	O
18-track	O
tape	O
drives	O
recording	O
at	O
bpi	O
,	O
(	O
0	O
,	O
2	O
)	O
GCR	B-Device
was	O
replaced	O
by	O
a	O
more	O
efficient	O
(	O
0	O
,	O
3	O
)	O
modulation	O
code	O
,	O
mapping	O
eight	O
bits	O
to	O
nine	O
bits	O
.	O
</s>
<s>
In	O
the	O
mid	O
1970s	O
,	O
Sperry	O
Univac	O
,	O
ISS	O
Division	O
was	O
working	O
on	O
large	O
hard	B-Device
drives	I-Device
for	O
the	O
mainframe	B-Architecture
business	O
using	O
group	O
coding	O
.	O
</s>
<s>
Like	O
magnetic	B-Architecture
tape	I-Architecture
drives	I-Architecture
,	O
floppy	B-Device
disk	I-Device
drives	I-Device
have	O
physical	O
limits	O
on	O
the	O
spacing	O
of	O
flux	O
reversals	O
(	O
also	O
called	O
transitions	O
,	O
represented	O
by	O
one-bits	O
)	O
.	O
</s>
<s>
Offering	O
GCR-compatible	O
diskette	B-Device
drives	O
and	O
floppy	B-Device
disk	I-Device
controllers	I-Device
(	O
like	O
the	O
100163-51-8	O
and	O
100163-52-6	O
)	O
,	O
Micropolis	O
endorsed	O
data	O
encoding	O
with	O
group	B-Device
coded	I-Device
recording	I-Device
on	O
5¼-inch	O
100	O
tpi	O
77-track	O
diskette	B-Device
drives	O
to	O
store	O
twelve	O
512-byte	O
sectors	O
per	O
track	O
since	O
1977	O
or	O
1978	O
.	O
</s>
<s>
Micro	O
Peripherals	O
,	O
Inc	O
.	O
(	O
MPI	O
)	O
marketed	O
double-density	O
5¼-inch	B-Device
disk	I-Device
drives	O
(	O
like	O
the	O
single-sided	O
B51	O
and	O
double-sided	O
B52	O
drives	O
)	O
and	O
a	O
controller	O
solution	O
implementing	O
GCR	B-Device
since	O
early	O
1978	O
.	O
</s>
<s>
The	O
Durango	B-Device
Systems	I-Device
F-85	I-Device
(	O
introduced	O
in	O
September	O
1978	O
)	O
used	O
single-sided	O
5¼-inch	O
100tpi	O
diskette	B-Device
drives	O
providing	O
480KB	O
utilizing	O
a	O
proprietary	O
high-density	O
4/5	B-Device
group	I-Device
coded	I-Device
encoding	I-Device
.	O
</s>
<s>
The	O
machine	O
was	O
using	O
a	O
Western	O
Digital	O
FD1781	O
floppy	B-Device
disk	I-Device
controller	I-Device
,	O
designed	O
by	O
a	O
former	O
Sperry	O
ISS	O
engineer	O
,	O
with	O
77-track	O
Micropolis	O
drives	O
.	O
</s>
<s>
In	O
later	O
models	O
such	O
as	O
the	O
Durango	O
800	O
series	O
this	O
was	O
expanded	O
to	O
a	O
double-sided	O
option	O
for	O
960KB	O
(	O
946KB	O
formatted	O
)	O
per	O
diskette	B-Device
.	O
</s>
<s>
For	O
the	O
Apple	B-Device
II	I-Device
floppy	B-Device
drive	I-Device
,	O
Steve	O
Wozniak	O
invented	O
a	O
floppy	B-Device
controller	I-Device
which	O
(	O
along	O
with	O
the	O
Disk	B-Device
II	I-Device
drive	O
itself	O
)	O
imposed	O
two	O
constraints	O
:	O
</s>
<s>
Each	O
8-bit	O
byte	B-Application
must	O
start	O
with	O
a	O
one	O
bit	O
.	O
</s>
<s>
The	O
simplest	O
scheme	O
to	O
ensure	O
compliance	O
with	O
these	O
limits	O
is	O
to	O
record	O
an	O
extra	O
"	O
clock	O
"	O
transition	O
before	O
each	O
data	O
bit	O
according	O
to	O
differential	B-Protocol
Manchester	I-Protocol
encoding	I-Protocol
or	O
(	O
digital	O
)	O
FM	B-Protocol
(	O
Frequency	O
Modulation	O
)	O
.	O
</s>
<s>
Known	O
as	O
4-and-4	O
encoding	O
,	O
the	O
resulting	O
Apple	O
implementation	O
allowed	O
only	O
ten	O
256-byte	O
sectors	O
per	O
track	O
to	O
be	O
recorded	O
on	O
a	O
single-density	O
5¼-inch	O
floppy	B-Device
.	O
</s>
<s>
It	O
uses	O
two	O
bytes	B-Application
for	O
each	O
byte	B-Application
.	O
</s>
<s>
Close	O
to	O
a	O
month	O
prior	O
to	O
the	O
shipment	O
of	O
the	O
disk	O
drive	O
in	O
spring	O
1978	O
,	O
Wozniak	O
realized	O
that	O
a	O
more	O
complex	O
encoding	O
scheme	O
would	O
allow	O
each	O
eight-bit	O
byte	B-Application
on	O
disk	O
to	O
hold	O
five	O
bits	O
of	O
useful	O
data	O
rather	O
than	O
four	O
bits	O
.	O
</s>
<s>
This	O
is	O
because	O
there	O
are	O
34	O
bytes	B-Application
which	O
have	O
the	O
top	O
bit	O
set	O
and	O
no	O
two	O
zero	O
bits	O
in	O
a	O
row	O
.	O
</s>
<s>
Reserved	O
GCR-codes	O
:	O
0xAA	O
and	O
0xD5	O
.	O
</s>
<s>
Later	O
,	O
the	O
design	O
of	O
the	O
floppy	B-Device
drive	I-Device
controller	O
was	O
modified	O
to	O
allow	O
a	O
byte	B-Application
on	O
disk	O
to	O
contain	O
up	O
to	O
one	O
pair	O
of	O
zero	O
bits	O
in	O
a	O
row	O
.	O
</s>
<s>
This	O
allowed	O
each	O
eight-bit	O
byte	B-Application
to	O
hold	O
six	O
bits	O
of	O
useful	O
data	O
,	O
and	O
allowed	O
16	O
sectors	O
per	O
track	O
.	O
</s>
<s>
This	O
scheme	O
is	O
known	O
as	O
6-and-2	O
encoding	O
,	O
and	O
was	O
used	O
on	O
Apple	B-Operating_System
Pascal	I-Operating_System
,	O
Apple	O
DOS	O
3.3	O
and	O
ProDOS	B-Operating_System
,	O
and	O
later	O
with	O
Apple	B-Device
FileWare	I-Device
drives	O
in	O
the	O
Apple	B-Device
Lisa	I-Device
and	O
the	O
400K	O
and	O
800K	O
3½-inch	O
disks	O
on	O
the	O
Macintosh	B-Device
and	O
Apple	B-Device
II	I-Device
.	O
</s>
<s>
Apple	O
did	O
not	O
originally	O
call	O
this	O
scheme	O
"	O
GCR	B-Device
"	O
,	O
but	O
the	O
term	O
was	O
later	O
applied	O
to	O
it	O
to	O
distinguish	O
it	O
from	O
IBM	B-Device
PC	I-Device
floppies	B-Device
which	O
used	O
the	O
MFM	B-Protocol
encoding	I-Protocol
scheme	O
.	O
</s>
<s>
Reserved	O
GCR-codes	O
:	O
0xAA	O
and	O
0xD5	O
.	O
</s>
<s>
Independently	O
,	O
Commodore	O
Business	O
Machines	O
(	O
CBM	O
)	O
created	O
a	O
group	B-Device
coded	I-Device
recording	I-Device
scheme	O
for	O
their	O
Commodore	B-Device
2040	I-Device
floppy	B-Device
disk	I-Device
drive	I-Device
(	O
launched	O
in	O
the	O
spring	O
of	O
1979	O
)	O
.	O
</s>
<s>
The	O
relevant	O
constraints	O
on	O
the	O
2040	O
drive	O
were	O
that	O
no	O
more	O
than	O
two	O
zero	O
bits	O
could	O
occur	O
in	O
a	O
row	O
;	O
the	O
drive	O
imposed	O
no	O
special	O
constraint	O
on	O
the	O
first	O
bit	O
in	O
a	O
byte	B-Application
.	O
</s>
<s>
This	O
more	O
efficient	O
GCR	B-Device
scheme	O
,	O
combined	O
with	O
an	O
approach	O
at	O
constant	B-Device
bit-density	I-Device
recording	O
by	O
gradually	O
increasing	O
the	O
clock	O
rate	O
(	O
zone	B-Architecture
constant	I-Architecture
angular	I-Architecture
velocity	I-Architecture
,	O
ZCAV	B-Architecture
)	O
and	O
storing	O
more	O
physical	O
sectors	O
on	O
the	O
outer	O
tracks	O
than	O
on	O
the	O
inner	O
ones	O
(	O
zone	B-Architecture
bit	I-Architecture
recording	I-Architecture
,	O
ZBR	O
)	O
,	O
enabled	O
Commodore	O
to	O
fit	O
170kB	O
on	O
a	O
standard	O
single-sided	O
single-density	O
5.25-inch	O
floppy	B-Device
,	O
where	O
Apple	O
fit	O
140kB	O
(	O
with	O
6-and-2	O
encoding	O
)	O
or	O
114kB	O
(	O
with	O
5-and-3	O
encoding	O
)	O
and	O
an	O
FM-encoded	O
floppy	B-Device
held	O
only	O
88kB	O
.	O
</s>
<s>
Similar	O
,	O
the	O
5.25-inch	O
floppy	B-Device
drives	I-Device
of	O
the	O
Victor	O
9000	O
aka	O
Sirius	O
1	O
,	O
designed	O
by	O
Chuck	O
Peddle	O
in	O
1981/1982	O
,	O
used	O
a	O
combination	O
of	O
ten-bit	O
GCR	B-Device
and	O
constant	B-Device
bit-density	I-Device
recording	O
by	O
gradually	O
decreasing	O
a	O
drive	O
's	O
rotational	O
speed	O
for	O
the	O
outer	O
tracks	O
in	O
nine	O
zones	O
(	O
a	O
form	O
of	O
zoned	O
constant	O
linear	O
velocity	O
(	O
ZCLV	O
)	O
)	O
while	O
increasing	O
the	O
number	O
of	O
sectors	O
per	O
track	O
(	O
a	O
variant	O
of	O
zone	B-Architecture
bit	I-Architecture
recording	I-Architecture
(	O
ZBR	O
)	O
)	O
to	O
achieve	O
formatted	O
capacities	O
of	O
606kB	O
(	O
single	O
sided	O
)	O
/	O
kB	O
(	O
double-sided	O
)	O
on	O
96	O
tpi	O
media	O
.	O
</s>
<s>
Starting	O
around	O
1985	O
,	O
Brother	O
introduced	O
a	O
family	O
of	O
dedicated	O
word	O
processor	O
typewriters	O
with	O
integrated	O
3.5-inch	O
38-track	O
diskette	B-Device
drive	O
.	O
</s>
<s>
Early	O
models	O
of	O
the	O
WP	O
and	O
used	O
a	O
Brother-specific	O
group-coded	B-Device
recording	I-Device
scheme	O
with	O
twelve	O
256-byte	O
sectors	O
to	O
store	O
up	O
to	O
120KB	O
on	O
single-sided	O
and	O
up	O
to	O
240KB	O
on	O
double-sided	O
double-density	O
(	O
DD	O
)	O
diskettes	B-Device
.	O
</s>
<s>
In	O
1986	O
,	O
Sharp	O
introduced	O
a	O
turnable	O
2.5-inch	O
pocket	O
disk	O
drive	O
solution	O
(	O
drives	O
:	O
CE-1600F	B-Device
,	O
CE-140F	O
;	O
internally	O
based	O
on	O
the	O
FDU-250	O
chassis	O
;	O
media	O
:	O
CE-1650F	B-Device
)	O
for	O
their	O
series	O
of	O
pocket	B-Device
computers	I-Device
with	O
a	O
formatted	O
capacity	O
of	O
bytes	B-Application
per	O
side	O
(	O
2×	O
64kB	O
nominal	O
,	O
16	O
tracks	O
,	O
8	O
sectors/track	O
,	O
512bytes	O
per	O
sector	O
,	O
48	O
tpi	O
,	O
250kbit/s	O
,	O
270rpm	O
)	O
with	O
GCR	B-Device
(	O
4/5	O
)	O
recording	O
.	O
</s>
<s>
GCR	B-Device
was	O
also	O
evaluated	O
for	O
a	O
possible	O
use	O
in	O
bar	O
code	O
encoding	O
schemes	O
(	O
packing	O
efficiency	O
,	O
timing	O
tolerances	O
,	O
amount	O
of	O
storage	O
bytes	B-Application
for	O
timing	O
information	O
,	O
and	O
DC	O
output	O
level	O
)	O
.	O
</s>
