Re: OT: Need help with numeric bases

On Mon, Feb 24, 2003 at 10:12:14PM +0000, Tim May wrote:
[snip]
> How exactly does your system work without zero?  Most systems without
> zero are tally systems rather than place-value systems.  I think some
> early systems (Babylonian? Egyptian) were place value and simply
> ommitted zero, leading to ambiguity.  But this doesn't seem to be
> either.  List the numbers from 1 to 16.
I've already pointed this out in a private reply, but I'll repeat it here
for the sake of others who might be interested in this:

Peter's system is basically identical to "normal" or "traditional" octal,
except that where there is a 0, it is substituted with 8 and the digit in
the next place is decremented. For example:
        105 normal octal = 85 Peter-octal ;-) (the leading 1 is gone after
                the decrement)
        1302 normal octal = 1282 Peter-octal
        2005 normal octal = 1785 Peter-octal
        1005 normal octal = 785 Peter-octal

Obviously, if the result of the decrement is less than 0, the next digit
after it will be decremented ("borrowed" from), as is shown above. If it
becomes 0, then the process is repeated: substitute 8 and decrement next
digit, etc.. (Oh BTW Peter, I made a mistake in the private reply, where I
said a sequence of 0's turns into 8's -- only the first digit becomes 8,
the rest becomes 7's.)

This scheme even works for fractional numbers, as I've demonstrated to
Peter in a private reply:
        11.05 normal octal = 8.85 Peter-octal
        20.001 normal octal = 17.781 Peter-octal


T

--
Not all rumours are as misleading as this one.

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