Re: Did Commodore cheat with the quad density floppies?

On Freitag, 4. Januar 2019 20:56:49 CET smf wrote:
> On 04/01/2019 19:13, afachat@gmx.de wrote:
> > You are mixing up FM and MFM.
> > See https://extrapages.de/archives/20190102-Floppy-notes.html
> 
> FM and MFM both require two transitions per bit.
> 
> https://en.wikipedia.org/wiki/Modified_Frequency_Modulation#MFM_coding
> 
> Both FM and MFM encodings can also be thought of as having data bits
> separated by clock bits, but with different rules for encoding the bits.
> Still, both formats encode each data bit as two bits on disk (because of
> delimiters that are required at the beginning and end of a sequence, the
> actual density is slightly lower).

Both formats encode each data bit as two "cells" on disk, but while the rule 
for FM says that first cell always has a 1 clock bit (i.e. a flux transition), 
the rules for MFM dictate to leave out many of the clock bit transitions, 
there are two cells for each data bit in MFM, but at most one transition per 
data bit in MFM.

> 
> The basic encoding rule for FM is that all clock bits are 1: zeros are
> encoded as 10, ones are encoded as 11. The number of magnetic
> transitions per bit is on average 1.5 (50%*1 + 50%*2).
> 
> The basic encoding rule for MFM is that (x, y, z, ...) encodes to (x,
> xNOR <https://en.wikipedia.org/wiki/Logical_NOR>y, y, y NOR z, z, z
> NOR...). A zero is encoded as 10 if preceded by a zero, and 00 if
> preceded by a one (each of these cases occurs 25% of the time); a one is
> always encoded as 01 (which happens 50% of the time); thus the number of
> magnetic transitions is on average 0.75 (25%*1 + 25%*0 + 50%*1).

As I said, there are only 0.75 transitions per bit in MFM, distributed on 2 
cells per bit. 

> > The misunderstanding here is probably due to the fact that "data bit cell"
> > and "encoded bit cell" are all different between FM, MFM, and GCR.
> 
> In practice they usually are, but not all systems used those exact sizes
> and there is nothing to say you have to use those particular sizes with
> GCR or MFM as they are just encoding schemes.
> 
> People often squeezed in as much as they thought they could. Chuck
> peddle did an even more insane GCR floppy at Sirrius.
> 
> > Data bit cells in FM are 8us, and 4us in MFM, while there are no real data
> > bit cells in GCR.
> 
> Right, because GCR is coded in groups. Each FM and MFM bit requires
> double the space, while GCR is more efficient.

If MFM were recorded at the same frequency, if would also require double the 
space. But it is recorded at the double frequency. So in total, encoding, plus 
double frequency, it is more efficient than MFM.

André