## CHAPTER 3 - DISK II HARDWARE AND TRACK FORMATTING

Apple Computer's excellent manual on the Disk Operating System (DOS) provides
only very basic information about how diskettes are formatted.  This chapter
will explain in detail how information is structured on a diskette.  The first
section will contain a brief introduction to the hardware, and may be skipped by
those already familiar with the DOS manual.

For system housekeeping, DOS divides diskettes into tracks and sectors.  This is
done during the initialization process.  A track is a physically defined
circular path which is concentric with the hole in the center of the diskette.
Each track is identified by its distance from the center of the disk.  Similar
to a phonograph stylus, the read/write head of the disk drive may be positioned
over any given track.  The tracks are similar to the grooves in a record, but
they are not connected in a spiral.  Much like playing a record, the diskette is
spun at a constant speed while the data is read from or written to its surface
with the read/write head.  Apple formats its diskettes into 35 tracks.  They are
numbered from 0 to 34, track 0 being the outermost track and track 34 the
innermost.  Figure 3.1 illustrates the concept of tracks, although they are
invisible to the eye on a real diskette.

*** INSERT FIGURE 3.1 HERE ***

It should be pointed out, for the sake of accuracy, that the disk arm can
position itself over 70 "phases".  To move the arm past one track to the next,
two phases of the stepper motor, which moves the arm, must be cycled.  This
implies that data might be stored on 70 tracks, rather than 35.  Unfortunately,
the resolution of the read/write head and the accuracy of the stepper motor are
such, that attempts to use these phantom "half" tracks create so much cross-talk
that data is lost or overwritten.  Although the standard DOS uses only even
phases, some protected disks use odd phases or combinations of the two, provided
that no two tracks are closer than two phases from one another.  See APPENDIX B
for more information on protection schemes.

A sector is a subdivision of a track.  It is the smallest unit of "updatable"
data on the diskette.  DOS generally reads or writes data a sector at a time.
This is to avoid using a large chunk of memory as a buffer to read or write an
entire track.  Apple has used two different track formats to date.  One divides
the track into 13 sectors, the other, 16 sectors.  The sectoring does not use
the index hole, provided on most diskettes, to locate the first sector of the
track.  The implication is that the software must be able to locate any given
track and sector with no help from the hardware.  This scheme, known as "soft
sectoring", takes a little more space for storage but allows flexibility, as
evidenced by the recent change from 13 sectors to 16 sectors per track.  The
following table catagorizes the amount of data stored on a diskette under both
13 and 16 sector formats.

         DISK ORGANIZATION

TRACKS
  All DOS versions................35

SECTORS PER TRACK
  DOS 3.2.1 and earlier...........13
  DOS 3.3.........................16

SECTORS PER DISKETTE
  DOS 3.2.1 and earlier..........455
  DOS 3.3........................560

BYTES PER SECTOR
  All DOS versions...............256

BYTES PER DISKETTE
  DOS 3.2.1 and earlier.......116480
  DOS 3.3.....................143360

USABLE* SECTORS FOR DATA STORAGE
  DOS 3.2.1 and earlier..........403
  DOS 3.3........................496

USABLE* BYTES PER DISKETTE
  DOS 3.2.1 and earlier.......103168
  DOS 3.3.....................126976

* Excludes DOS, VTOC, and CATALOG

TRACK FORMATTING

Up to this point we have broken down the structure of data to the track and
sector level.  To better understand how data is stored and retrieved, we will
start at the bottom and work up.

As this manual is primarily concerned with software, no attempt will be made to
deal with the specifics of the hardware.  For example, while in fact data is
stored as a continuous stream of analog signals, we will deal with discrete
digital data, i.e.  a 0 or a 1.  We recognize that the hardware converts analog
data to digital data but how this is accomplished is beyond the scope of this
manual.

Data is recorded on the diskette using frequency modulation as the recording
mode.  Each data bit recorded on the diskette has an associated clock bit
recorded with it.  Data written on and read back from the diskette takes the
form shown in Figure 3.2.  The data pattern shown represents a binary value of
101.

*** INSERT FIGURE 3.2 HERE ***

As can be seen in Figure 3.3, the clock bits and data bits (if present) are
interleaved.  The presence of a data bit between two clock bits represents a
binary 1, the absence of a data bit between two clock bits represents a binary
0.  We will define a "bit cell" as the period between the leading edge of one
clock bit and the leading edge of the next clock bit.

*** INSERT FIGURE 3.3 HERE ***

A byte would consist of eight (8) consecutive bit cells.  The most significant
bit cell is usually referred to as bit cell 7 and the least significant bit cell
would be bit cell 0.  When reference is made to a specific data bit (i.e. data
bit 5), it is with respect to the corresponding bit cell (bit cell 5).  Data is
written and read serially, one bit at a time.  Thus, during a write operation,
bit cell 7 of each byte would be written first, with bit cell 0 being written
last.  Correspondingly, when data is being read back from the diskette, bit cell
7 is read first and bit cell 0 is read last.  The diagram below illustrates the
relationship of the bits within a byte.

*** INSERT FIGURE 3.4 HERE ***

To graphically show how bits are stored and retrieved, we must take certain
liberties.  The diagrams are a representation of what functionally occurs within
the disk drive.  For the purposes of our presentation, the hardware interface to
the diskette will be represented as an eight bit "data latch".  While the
hardware involves considerably more complication, from a software standpoint it
is reasonable to use the data latch, as it accurately embodies the function of
data flow to and from the diskette.

*** INSERT FIGURE 3.5 HERE ***

Figure 3.5 shows the three bits, 101, being read from the diskette data stream
into the data latch.  Of course another five bits would be read to fill the
latch.  As can be seen, the data is separated from the clock bits.  This task is
done by the hardware and is shown more for accuracy than for its importance to
our discussion.

Writing data can be depicted in much the same way (see Figure 3.6).  The clock
bits which were separated from the data must now be interleaved with the data as
it is written.  It should be noted that, while in write mode, zeros are being
brought into the data latch to replace the data being written.  It is the task
of the software to make sure that the latch is loaded and instructed to write in
32 cycle intervals.  If not, zero bits will continue to be written every four
cycles, which is, in fact, exactly how self-sync bytes are created.  Self-sync
bytes will be covered in detail shortly.

*** INSERT FIGURE 3.6 HERE ***

A "field" is made up of a group of consecutive bytes.  The number of bytes
varies, depending upon the nature of the field.  The two types of fields present
on a diskette are the Address Field and the Data Field.  They are similar in
that they both contain a prologue, a data area, a checksum, and an epilogue.
Each field on a track is separated from adjacent fields by a number of bytes.
These areas of separation are called "gaps" and are provided for two reasons.
One, they allow the updating of one field without affecting adjacent fields (on
the Apple, only data fields are updated).  Secondly, they allow the computer
time to decode the address field before the corresponding data field can pass
beneath the read/write head.

All gaps are primarily alike in content, consisting of self-sync hexadecimal
FF's, and vary only in the number of bytes they contain.  Figure 3.7 is a
diagram of a portion of a typical track, broken into its major components.

*** INSERT FIGURE 3.7 HERE ***

Self-sync or auto-sync bytes are special bytes that make up the three different
types of gaps on a track.  They are so named because of their ability to
automatically bring the hardware into synchronization with data bytes on the
disk.  The difficulty in doing this lies in the fact that the hardware reads
bits and the data must be stored as eight bit bytes.  It has been mentioned that
a track is literally a continuous stream of data bits.  In fact, at the bit
level, there is no way to determine where a byte starts or ends, because each
bit cell is exactly the same, written in precise intervals with its neighbors.
When the drive is instructed to read data, it will start wherever it happens to
be on a particular track.  That could be anywhere among the 50,000 or so bits on
a track.  Distinguishing clock bits from data bits, the hardware finds the first
bit cell with data in it and proceeds to read the following seven data bits into
the eight bit latch.  In effect, it assumes that it had started at the beginning
of a data byte.  Of course, in reality, the odds of its having started at the
beginning of a byte are only one in eight.  Pictured in Figure 3.8 is a small
portion of a track.  The clock bits have been stripped out and 0's and 1's have
been used for clarity.

*** INSERT FIGURE 3.8 HERE ***

There is no way from looking at the data to tell what bytes are represented,
because we don't know where to start.  This is exactly the problem that
self-sync bytes overcome.

A self-sync byte is defined to be a hexadecimal FF with a special difference.
It is, in fact, a 10 bit byte rather than an eight bit byte.  Its two extra bits
are zeros.  Figure 3.9 shows the difference between a normal data hex FF that
might be found elsewhere on the disk and a self-sync hex FF byte.

*** INSERT FIGURE 3.9 HERE ***

A self-sync is generated by using a 40 cycle (micro-second) loop while writing
an FF.  A bit is written every four cycles, so two of the zero bits brought into
the data latch while the FF was being written are also written to the disk,
making the 10 bit byte. (DOS 3.2.1 and earlier versions use a nine bit byte due
to the hardware's inability to always detect two consecutive zero bits.)  It can
be shown, using Figure 3.10, that five self-sync bytes are sufficient to
guarantee that the hardware is reading valid data.  The reason for this is that
the hardware requires the first bit of a byte to be a 1.  Pictured at the top of
the figure is a stream of five auto-sync bytes.  Each row below that demonstates
what the hardware will read should it start reading at any given bit in the
first byte.  In each case, by the time the five sync bytes have passed beneath
the read/write head, the hardware will be "synched" to read the data bytes that
follow.  As long as the disk is left in read mode, it will continue to correctly
interpret the data unless there is an error on the track.

*** INSERT FIGURE 3.10 ***

We can now discuss the particular portions of a track in detail.  The three gaps
will be covered first.  Unlike some other disk formats, the size of the three
gap types will vary from drive to drive and even from track to track.  During
the initialization process, DOS will start with large gaps and keep making them
smaller until an entire track can be written without overlapping itself.  A
minimum of five self-sync bytes must be maintained for each gap type (as
discussed earlier).  The result is fairly uniform gap sizes within each
particular track.

Gap 1 is the first data written to a track during initialization.  Its purpose
is twofold.  The gap originally consists of 128 bytes of self-sync, a large
enough area to insure that all portions of a track will contain data.  Since the
speed of a particular drive may vary, the total length of the track in bytes is
uncertain, and the percentage occupied by data is unknown.  The initialization
process is set up, however, so that even on drives of differing speeds, the last
data field written will overlap Gap 1, providing continuity over the entire
physical track.  Care is taken to make sure the remaining portion of Gap 1 is at
as long as a typical Gap 3 (in practice its length is usually more than 40),
enabling it to serve as a Gap 3 type for Address Field number 0 (See Figure 3.7
for clarity).

Gap 2 appears after each Address Field and before each Data Field.  Its length
varies from five to ten bytes on a normal drive.  The primary purpose of Gap 2
is to provide time for the information in an Address Field to be decoded by the
computer before a read or write takes place.  If the gap were too short, the
beginning of the Data Field might spin past while DOS was still determining if
this was the sector to be read.  The 240 odd cycles that six self-sync bytes
provide seems ample time to decode an address field.  When a Data Field is
written there is no guarantee that the write will occur in exactly the same spot
each time.  This is due to the fact that the drive which is rewriting the Data
Field may not be the one which originally INITed or wrote it.  Since the speed
of the drives can vary, it is possible that the write could start in mid-byte.
(See Figure 3.11)  This is not a problem as long as the difference in
positioning is not great.  To insure the integrity of Gap 2, when writing a data
field, five self-sync bytes are written prior to writing the Data Field itself.
This serves two purposes.  Since relatively little time is spent decoding an
address field, the five bytes help place the Data Field near its original
position.  Secondly, and more importantly, the five self-sync bytes are the
minimum number required to guarantee read-synchronization.  It is probable that,
in writing a Data Field, at least one sync byte will be destroyed.  This is
because, just as in reading bits on the track, the write may not begin on a byte
boundary, thus altering an existing byte.  Figure 3.12 illustrates this.

*** INSERT FIGURE 3.11 HERE ***

*** INSERT FIGURE 3.12 HERE ***

Gap 3 appears after each Data Field and before each Address Field.  It is longer
than Gap 2 and generally ranges from 14 to 24 bytes in length.  It is quite
similar in purpose to Gap 2.  Gap 3 allows the additional time needed to
manipulate the data that has been read before the next sector is to be read.
The length of Gap 3 is not as critical as that of Gap 2.  If the following
Address Field is missed, DOS can always wait for the next time it spins around
under the read/write head, at most one revolution of the disk.  Since Address
Fields are never rewritten, there is no problem with this gap providing
synchronization, since only the first part of the gap can be overwritten or
damaged. (See Figure 3.11 for clarity)

An examination of the contents of the two types of fields is in order.  The
Address Field contains the "address" or identifying information about the Data
Field which follows it.  The volume, track, and sector number of any given
sector can be thought of as its "address", much like a country, city, and street
number might identify a house.  As shown previously in Figure 3.7, there are a
number of components which make up the Address Field.  A more detailed
illustration is given in Figure 3.13.

*** INSERT FIGURE 3.13 HERE ***

The prologue consists of three bytes which form a unique sequence, found in no
other component of the track.  This fact enables DOS to locate an Address Field
with almost no possibility of error.  The three bytes are $D5, $AA, and $96.
The $D5 and $AA are reserved (never written as data) thus insuring the
uniqueness of the prologue.  The $96, following this unique string, indicates
that the data following constitutes an Address Field (as opposed to a Data
Field).  The address information follows next, consisting of the volume, track,
and sector number and a checksum.  This information is absolutely essential for
DOS to know where it is positioned on a particular diskette.  The checksum is
computed by exclusive-ORing the first three pieces of information, and is used
to verify its integrity.  Lastly follows the epilogue, which contains the three
bytes $DE, $AA and $EB.  Oddly, the $EB is always written during initialization
but is never verified when an Address Field is read.  The epilogue bytes are
sometimes referred to as "bit-slip marks", which provide added assurance that
the drive is still in sync with the bytes on the disk.  These bytes are probably
unnecessary, but do provide a means of double checking.

The other field type is the Data Field.  Much like the Address Field, it
consists of a prologue, data, checksum, and an epilogue. (Refer to Figure 3.14)
The prologue is different only in the third byte.  The bytes are $D5, $AA, and
$AD, which again form a unique sequence, enabling DOS to locate the beginning of
the sector data.  The data consists of 342 bytes of encoded data.  The encoding
scheme used will be discussed in the next section.  The data is followed by a
checksum byte, used to verify the integrity of the data just read.  The epilogue
portion of the Data Field is absolutely identical to the epilogue in the Address
Field and it serves the same function.

DATA FIELD ENCODING

Due to Apple's hardware, it is not possible to read all 256 possible byte values
from a diskette.  This is not a great problem, but it does require that the data
written to the disk be encoded.  Three different techniques have been used.  The
first one, which is currently used in Address Fields, involves writing a data
byte as two disk bytes, one containing the odd bits, and the other containing
the even bits.  It would thus require 512 "disk" bytes for each 256 byte sector
of data.  Had this technique been used for sector data, no more than 10 sectors
would have fit on a track.  This amounts to about 88K of data per diskette, or
roughly 72K of space available to the user; typical for 5 1/4 single density
drives.

Fortunately, a second technique for writing data to diskette was devised that
allows 13 sectors per track.  This new method involved a "5 and 3" split of the
data bits, versus the "4 and 4" mentioned earlier.  Each byte written to the
disk contains five valid bits rather than four.  This requires 410 "disk" bytes
to store a 256 byte sector.  This latter density allows the now well known 13
sectors per track format used by DOS 3 through DOS 3.2.1.  The "5 and 3" scheme
represented a hefty 33% increase over comparable drives of the day.

Currently, of course, DOS 3.3 features 16 sectors per track and provides a 23%
increase in disk storage over the 13 sector format.  This was made possible by a
hardware modification (the P6 PROM on the disk controller card) which allowed a
"6 and 2" split of the data.  The change was to the logic of the "state machine"
in the P6 PROM, now allowing two consecutive zero bits in data bytes.

These three different encoding techniques will now be covered in some detail.
The hardware for DOS 3.2.1 (and earlier versions of DOS) imposed a number of
restrictions upon how data could be stored and retrieved.  It required that a
disk byte have the high bit set and, in addition, no two consecutive bits could
be zero.  The odd-even "4 and 4" technique meets these requirements.  Each data
byte is represented as two bytes, one containing the even data bits and the
other the odd data bits.  Figure 3.15 illustrates this transformation.  It
should be noted that the unused bits are all set to one to guarantee meeting the
two requirements.

*** INSERT FIGURE 3.15 HERE ***

No matter what value the original data data byte has, this technique insures
that the high bit is set and that there can not be two consecutive zero bits.
The "4 and 4" technique is used to store the information (volume, track, sector,
checksum) contained in the Address Field.  It is quite easy to decode the data,
since the byte with the odd bits is simply shifted left and logically ANDed with
the byte containing the even bits.  This is illustrated in Figure 3.16.

*** INSERT FIGURE 3.16 HERE ***

It is important that the least significant bit contain a 1 when the odd-bits
byte is left shifted.  The entire operation is carried out in the RDADR
subroutine at $B944 in DOS (48K).

The major difficulty with the above technique is that it takes up a lot of room
on the track.  To overcome this deficiency the "5 and 3" encoding technique was
developed.  It is so named because, instead of splitting the bytes in half, as
in the odd-even technique, they are split five and three.  A byte would have the
form 000XXXXX, where X is a valid data bit.  The above byte could range in value
from $00 to $1F, a total of 32 different values.  It so happens that there are
34 valid "disk" bytes, ranging from $AA up to $FF, which meet the two
requirements (high bit set, no consecutive zero bits).  Two bytes, $D5 and $AA,
were chosen as reserved bytes, thus leaving an exact mapping between five bit
data bytes and eight bit "disk" bytes.  The process of converting eight bit data
bytes to eight bit "disk" bytes, then, is twofold.  An overview is diagrammed in
Figure 3.17.

*** INSERT FIGURE 3.17 HERE ***

First, the 256 bytes that will make up a sector must be translated to five bit
bytes.  This is done by the "prenibble" routine at $B800.  It is a fairly
involved process, involving a good deal of bit rearrangement.  Figure 3.18 shows
the before and after of prenibbilizing.  On the left is a buffer of eight bit
data bytes, as passed to the RWTS subroutine package by DOS.  Each byte in this
buffer is represented by a letter (A, B, C, etc.) and each bit by a number (7
through 0).  On the right side are the results of the transformation.  The
primary buffer contains five distinct areas of five bit bytes (the top three
bits of the eight bit bytes zero-filled) and the secondary buffer contains three
areas, graphically illustrating the name "5 and 3".

*** INSERT FIGURE 3.18 HERE ***

A total of 410 bytes are needed to store the original 256.  This can be
calculated by finding the total bits of data (256 x 8 = 2048) and dividing that
by the number of bits per byte (2048 / 5 = 409.6). (two bits are not used)  Once
this process is completed, the data is further transformed to make it valid
"disk" bytes, meeting the disk's requirements.  This is much easier, involving a
one to one look-up in the table given in Figure 3.19.

*** INSERT FIGURE 3.19 HERE ***

The Data Field has a checksum much like the one in the Address Field, used to
verify the integrity of the data.  It also involves exclusive-ORing the
information, but, due to time constraints during reading bytes, it is
implemented differently.  The data is exclusive-ORed in pairs before being
transformed by the look-up table in Figure 3.19.  This can best be illustrated
by Figure 3.20 on the following page.

*** INSERT FIGURE 3.20 HERE ***

The reason for this transformation can be better understood by examining how the
information is retrieved from the disk.  The read routine must read a byte,
transform it, and store it -- all in under 32 cycles (the time taken to write a
byte) or the information will be lost.  By using the checksum computation to
decode data, the transformation shown in Figure 3.20 greatly facilitates the
time constraint.  As the data is being read from a sector the accumulator
contains the cumulative result of all previous bytes, exclusive-ORed together.
The value of the accumulator after any exclusive-OR operation is the actual data
byte for that point in the series.  This process is diagrammed in Figure 3.21.

*** INSERT FIGURE 3.21 HERE ***

The third encoding technique, currently used by DOS 3.3, is similar to the "5
and 3".  It was made possible by a change in the hardware which eased the
requirements for valid data somewhat.  The high bit must still be set, but now
the byte may contain one (and only one) pair of consecutive zero bits.  This
allows a greater number of valid bytes and permits the use of a "6 and 2"
encoding technique.  A six bit byte would have the form 00XXXXXX and has values
from $00 to $3F for a total of 64 different values.  With the new, relaxed
requirements for valid "disk" bytes there are 69 different bytes ranging in
value from $96 up to $FF.  After removing the two reserved bytes, $AA and $D5,
there are still 67 "disk" bytes with only 64 needed.  An additional requirement
was introduced to force the mapping to be one to one, namely, that there must be
at least two adjacent bits set, excluding bit 7.  This produces exactly 64 valid
"disk" values.  The initial transformation is done by the prenibble routine
(still located at $B800) and its results are shown in Figure 3.22.

*** INSERT FIGURE 3.22 (20) HERE ***

A total of 342 bytes are needed, shown by finding the total number of bits (256
x 8 = 2048) and dividing by the number of bits per byte (2048 / 6 = 341.33).
The transformation from the six bit bytes to valid data bytes is again performed
by a one to one mapping shown in Figure 3.23.  Once again, the stream of data
bytes written to the diskette are a product of exclusive-ORs, exactly as with
the "5 and 3" technique discussed earlier.

*** INSERT FIGURE 3.23 (21) HERE ***

SECTOR INTERLEAVING

Sector interleaving is the staggering of sectors on a track to maximize access
speed.  There is usually a delay between the time DOS reads or writes a sector
and the time it is ready to read or write another.  This delay depends upon the
application program using the disk and can vary greatly.  If sectors were stored
on the track sequentially, in ascending numerical order, unless the application
was very quick indeed, it would usually be necessary to wait an entire
revolution of the diskette before the next sector could be accessed.
Rearranging the sectors into a different order or "interleaving" them can
provide different access speeds.

On DOS 3.2.1 and earlier versions, the 13 sectors are physically interleaved on
the disk.  Since DOS resides on the diskette in ascending sequential order and
files generally are stored in descending sequential order, no single
interleaving scheme works well for both booting and sequentially accessing a
file.

A different approach has been used in DOS 3.3 in an attempt to maximize
performance.  The interleaving is now done in software.  The 16 sectors are
stored in numerically ascending order on the diskette (0, 1, 2, ... , 15) and
are not physically interleaved at all.  A look-up table is used to translate the
physical sector number into a "pseudo" or soft sector number used by DOS.  For
example, if the sector number found on the disk were a 2, this is used as an
offset into a table where the number $0B is found.  Thus, DOS treats the
physical sector 2 as sector 11 ($0B) for all intents and purposes.  This
presents no problem if RWTS is used for disk access, but would become a
consideration if access were made without RWTS.

To eliminate the access differences between booting and reading files, another
change has been made.  During the boot process, DOS is loaded backwards in
descending sequential order into memory, just as files are accessed.  This means
one interleaving scheme can minimize disk access time.

It is interesting to point out that Pascal, Fortran, and CP/M diskettes all use
software interleaving also.  However, each uses a different sector order.  A
comparison of these differences is presented in Figure 3.24.

*** INSERT FIGURE 3.24 (22) HERE ***

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