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From: turk@apple.UUCP (Ken "Turk" Turkowski)
Newsgroups: comp.arch
Subject: Re: byte order and positional number systems
Message-ID: <396@apple.UUCP>
Date: Wed, 21-Jan-87 20:47:25 EST
Article-I.D.: apple.396
Posted: Wed Jan 21 20:47:25 1987
Date-Received: Thu, 22-Jan-87 04:07:13 EST
References: <760@orcisi.UUCP> <2@ipmoea.UUCP>
Reply-To: turk@apple.UUCP (Ken "Turk" Turkowski)
Organization: Apple Computer Inc., Cupertino, USA
Lines: 32

Big or little-endian ordering makes more sense if you think of the numbers
being fractions or integers, respectively.  On a big-endian system, the most
natural way to a number in terms of its digits is as:

	d  d  d  d  d  ...
	 -1 -2 -3 -4 -5

The indices are associated with powers of the radix, so here the
numbers are considered to be fractions, having a value less than 1.
For brevity, we may eliminate the minus signs, or start the digit
indexing at 0, so that the following variants exist:

	d d d d d ...	d d d d d ...	d  d  d  d  d  ...
	 1 2 3 4 5	 0 1 2 3 4	 -0 -1 -2 -3 -4

Whereas on a little-endian system it is most natural to have the digits
indexed in the following [more familiar] way:

	...d d d d d
	    4 3 2 1 0

as is suitable for an integer.

For communication purposes, the digit with index closest to 0 is the
one that is transmitted first.  If the base of the digit is 2, then we
have big- or little- endian BIT ordering, whereas if the base of the
digit is 256, we have big- or little-endian BYTE ordering.
-- 
Ken Turkowski @ Apple Computer, Inc., Cupertino, CA
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