Re: Cohen's paper on byte order

From: Douglas A. Gwyn (DAGwyn_at_null.net)
Date: 05/08/03 

Date: Thu, 08 May 2003 02:09:20 -0400

Mok-Kong Shen wrote:
> "Douglas A. Gwyn" wrote:
>>Mok-Kong Shen wrote:
>>>Now allow me again a detailed argument. Let's
>>>consider the (internal) bit sequence 01001111. At
>>>first, as you also mentioned, it means just 8 bits.
>>You should write it as 0,1,0,0,1,1,1,1,... and also
>>recognize that there are not just 8 bit values but
>>rather a large number of them, of which you have
>>chosen to show just the first 8, presumably because
>>we can agree that whatever I/O processing is done,
>>the FIPS clearly specifies that it be done in groups
>>of 8 successive input bits each.
>>>Excepting its sequential ordering, the whole hasn't
>>>yet a 'meaning' as a binary integer, let alone MSB
>>>or LSB. (It has instead leftmost bit and rightmost
>>>bit).
>>No! A sequence has a "first" or an "earliest" bit,
>>which is also, when indexed by the natural numbers
>>(as is done by the FIPS), a "lowest numbered" bit.
>>If you want to call it a "leftmost" bit you are at
>>that point assuming a big-endian convention (i.e.
>>associating the first bit with the most significant
>>bit in a binary numeration system), which begs the
>>question.

> I don't understand you at all. You wrote 'should
> write it as 0,1,0,0,1,1,1,1'. What does that
> mean exactly?

That's not what I said! The ",..." is important to
remind us that we are not at that point talking about
exactly 8 bits, but introduce an 8-bit grouping for a
specific purpose, as I explained. The reason for the
commas is that that is standard mathematical usage
when indicating a sequence by exhibiting its first
few terms; as you should have understood from the
further discussion, when you elided the ,s and ,...
you changed from a bit sequence to what appears to be
a positive integer expressed in binary notation, and
by so doing you have tacitly adopted a "big endian"
convention. But that is the very step that is under
dispute, so it is not acceptable to assume that.

> ... For convenient reference here
> again is the program (that you snipped) ...

But it isn't relevant, since it has for its input a
bit array, not a multibit array. All along it has
been agreed that there is no problem when the I/O data
is externally organized as a bit sequence.