Editing Modified frequency modulation (section)

== MFM coding ==
[[File:FM-MFM-Codierung-int.svg|thumb|right|A byte encoded using FM (above) and MFM (below). Dashed blue line denotes clock pulse (the signal level change in it is ignored), and dashed red line, data pulse (signal level change encodes 1, and absence thereof, 0).]]

Modified frequency modulation encodes the clock signal and the data in a single "clock window". Unlike FM, a clock bit is only written when needed to achieve synchronization when both current and preceding data bits are not set. On average, MFM achieves double the information density of FM.<ref>{{cite book |last1=Sammes |first1=Anthony |last2=Jenkinson |first2=Brian |title=Forensic Computing |date=18 August 2007 |publisher=Springer Science & Business Media |isbn=978-1-84628-732-9 |page=109 |url=https://books.google.com/books?id=Ee9PF6Zv_tMC&dq=mfm+encoding&pg=PA109 |language=en}}</ref>

The basic encoding rule for MFM is that (x, y, z, ...) encodes to (x, x [[Logical NOR|NOR]] y, y, y NOR z, z, z NOR...). A zero bit is encoded as {{mono|10}} if preceded by a zero bit in the input stream, and {{mono|00}} if preceded by a one; a one bit is always encoded as {{mono|01}}. The number of magnetic transitions per one bit of encoded data is on average 0.75 to 1.<ref>{{cite web |last1=Prosise |first1=Jeff |title=Choosing a Hard Disk |url=https://books.google.com/books?id=l3Z0ZgEexGEC&dq=mfm+encoding&pg=PT445 |website=PC Magazine |page=427 |date=30 October 1990}}</ref>

{| class=wikitable
! Data
| {{mono|... '''0''' '''0''' ...}} || {{mono|... '''0''' '''1''' ...}} || {{mono|... '''1''' '''0''' ...}} || {{mono|... '''1''' '''1''' ...}}
|-
! MFM clock bits
| {{mono|...? 1 ?...}} || {{mono|...? 0 0...}} || {{mono|...0 0 ?...}} || {{mono|...0 0 0...}}
|-
! MFM encoding
| {{mono|...?'''0'''1'''0'''?...}} || {{mono|...?'''0'''0'''1'''0...}} || {{mono|...0'''1'''0'''0'''?...}} || {{mono|...0'''1'''0'''1'''0...}}
|}

Note that the surrounding clock bits are sometimes known, but sometimes require knowledge of the adjacent data bits.{{Citation needed|date=March 2023|reason=Unusual way to describe clock recovery. Confuses bits of information with magnetic pulses.}} A longer example:
 Data:          '''0 0 0 1 1 0 1 1''' ...
 FM encoded:   1'''0'''1'''0'''1'''0'''1'''1'''1'''1'''1'''0'''1'''1'''1'''1'''1...
 MFM clock:    ? 1 1 0 0 0 0 0 0...
 MFM encoded:  ?'''0'''1'''0'''1'''0'''0'''1'''0'''1'''0'''0'''0'''1'''0'''1'''0...
(The bold bits are the data bits, the others are the clock bits.)

In FM encoding, the number of 0-bits that may appear between consecutive 1-bits is either 0 or 1. In MFM encoding there is a minimum of 1 zero bit between adjacent ones (there are never two adjacent one bits), and the maximum number of zeros in a row is 3.{{Citation needed|date=March 2023|reason=Appears to confuse bits of information with magnetic pulses.}} Thus, FM is a (0,1) RLL code, while MFM is a (1,3) code.