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Frequency Modulation (FM)

The first common encoding system for recording digital data on magnetic media was frequency modulation, of course abbreviated FM. This is a simple scheme, where a one is recorded as two consecutive flux reversals, and a zero is recorded as a flux reversal followed by no flux reversal. This can also be thought of as follows: a flux reversal is made at the start of each bit to represent the clock, and then an additional reversal is added in the middle of each bit for a one, while the additional reversal is omitted for a zero.

This table shows the encoding pattern for FM (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 1.5. The best case (all zeroes) would be 1, the worst case (all ones) would be 2:

 Bit Pattern Encoding Pattern Flux Reversals Per Bit Bit Pattern Commonality In Random Bit Stream 0 RN 1 50% 1 RR 2 50% Weighted Average 1.5 100%

The name "frequency modulation" comes from the fact that the number of reversals is doubled for ones compared to that for zeros. This can be seen in the patterns that are created if you look at the encoding pattern of a stream of ones or zeros. A byte of zeroes would be encoded as "RNRNRNRNRNRNRNRN", while a byte of all ones would be "RRRRRRRRRRRRRRRR". As you can see, the ones have double the frequency of reversals compared to the zeros; hence frequency modulation (meaning, changing frequency based on data value).

 FM encoding write waveform for the byte "10001111". Each bit cell is depicted as a blue rectangle with a pink line representing the position where a reversal is placed, if necessary, in the middle of the cell.

The problem with FM is that it is very wasteful: each bit requires two flux reversal positions, with a flux reversal being added for clocking every bit. Compared to more advanced encoding methods that try to reduce the number of clocking reversals, FM requires double (or more) the number of reversals for the same amount of data. This method was used on the earliest floppy disk drives, the immediate ancestors of those used in PCs. If you remember using "single density" floppy disks in the late 1970s or early 1980s, that designation commonly refers to magnetic storage using FM encoding. FM was actually made obsolete by MFM before the IBM PC was introduced, but it provides the basis for understanding MFM.

Note: This has nothing whatever to do with FM radio, of course, except for a similarity in the concept of how the data is encoded.

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