Group Code Recording - GCR For Floppy Disks

GCR For Floppy Disks

Like magnetic tape drives, floppy disk drives have physical limits on the spacing of flux reversals (also called transitions, represented by 1 bits).

For the Apple II floppy drive, Steve Wozniak invented a floppy controller which (along with the drive itself) imposed two constraints

• Between any two one bits, there may be a maximum of one zero bit.
• Each 8-bit byte must start with a one bit.

The simplest scheme to ensure compliance with these limits is to record an extra "clock" transition between each data bit. This scheme is called FM (Frequency Modulation) or "4 and 4", and allows only 10 256-byte sectors per track to be recorded on a single-density 5¼ floppy.

Wozniak realized that a more complex encoding scheme would allow each 8-bit byte on disk to hold 5 bits of useful data rather than 4 bits. This is because there are 34 bytes which have the top bit set and no two zero bits in a row. This encoding scheme became known as "5 and 3" encoding, and allowed 13 sectors per track; it was used for Apple DOS 3.1, 3.2, and 3.2.1, as well as for the earliest version of Apple CP/M. Later, the design of the floppy drive controller was modified to allow a byte on disk to contain up to one pair of zero bits in a row. This allowed each 8-bit byte to hold 6 bits of useful data, and allowed 16 sectors per track. This scheme is known as "6 and 2", and was used on Apple Pascal, Apple DOS 3.3 and ProDOS, and later on the 400K and 800K 3½ disks on the Macintosh and Apple II. Apple did not originally call this scheme "GCR", but the term was later applied to it to distinguish it from IBM PC floppies which used the MFM encoding scheme.

Independently, Commodore Business Machines created a Group Code 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, nor more than eight one bits 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 6250 tape drives. Every 4 bits of data are translated into 5 bits on disk, according to the following table:

Note no code starts with two zero bits, nor ends with two zero bits. This ensures that regardless of the input data, the encoded data will never contain more than two zero bits in a row. Also note that with this encoding not more than eight one bits in a row are possible. Therefore Commodore used sequences of ten or more one bits in a row as synchronization mark.

Partially because of this more efficient scheme, Commodore was able to fit 170KB on a standard single-density floppy, where Apple fit 140K (6 and 2) or 114K (5 and 3) and an FM-encoded floppy held only 88K.