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Modified Frequency Modulation (MFM)
A refinement of the FM encoding method is modified frequency modulation, or MFM. MFM improves on FM by reducing the number of flux reversals inserted just for the clock. Instead of inserting a clock reversal at the start of every bit, one is inserted only between consecutive zeros. When a 1 is involved there is already a reversal (in the middle of the bit) so additional clocking reversals are not needed. When a zero is preceded by a 1, we similarly know there was recently a reversal and another is not needed. Only long strings of zeros have to be "broken up" by adding clocking reversals.
This table shows the encoding pattern for MFM (where I have designated "R" to represent a flux reversal and "N" to represent no flux reversal). The average number of flux reversals per bit on a random bit stream pattern is 0.75. The best case (a repeating pattern of ones and zeros, "101010...") would be 0.25, the worst case (all ones or all zeros) would be 1:
Since the average number of reversals per bit is half that of FM, the clock frequency of the encoding pattern can be doubled, allowing for approximately double the storage capacity of FM for the same areal density. The only cost is somewhat increased complexity in the encoding and decoding circuits, since the algorithm is a bit more complicated. However, this isn't a big deal for controller designers, and is a small price to pay for doubling capacity.
MFM encoding was used on the earliest hard disks, and also on floppy disks. Since the MFM method about doubles the capacity of floppy disks compared to earlier FM ones, these disks were called "double density". In fact, MFM is still the standard that is used for floppy disks today. For hard disks it was replaced by the more efficient RLL methods. This did not happen for floppy disks, presumably because the need for more efficiency was not nearly so great, compared to the need for backward compatibility with existing media.
Next: Run Length Limited (RLL)