[Verba] Meeting summary, mind bender

[Stuart D. Gathman]

We mostly discussed arbitrary base numbering systems, focusing on binary
and hexadecimal.  Finally, we saw how to assign values to variables and
use them in calculations.  

The theoretically most "efficient" (in size and energy use) number
representation for both electronic and mechanical computers is trinary (closest
integer base to "e", the natural logarithm base).  The simplest trinary
computers use signed ternary:

http://www.mortati.com/glusker/fowler/ternary.htm

The place values are powers of 3: 1, 3, 9, 27, 81, 243 etc, but each trit
is +1,0,-1 -- *not* 0,1,2.  You can write the trits |,0,- or +,0,-.

So, for instance, |0-||- is
	+1 * 243 	= 243
+	 0 *  81
+	-1 *  27	 - 27
+	+1 *   9	 +  9
+	+1 *   3	 +  3
+	-1 *   1	 -  1
	                -----
			  227

Extra credit:  practice adding signed ternary.  Notice that carries can
be +1 or -1.  Can you see why hardware implementing it is simple
and efficient?  Multiplication is equally simple and efficient.

Question: why doesn't anyone make a signed ternary computer, when everyone
agrees that hardware using it would be smaller and more efficient?

-- 
	      Stuart D. Gathman <stuart at bmsi.com>
Business Management Systems Inc.  Phone: 703 591-0911 Fax: 703 591-6154
"Confutatis maledictis, flamis acribus addictis" - background song for
a Microsoft sponsored "Where do you want to go from here?" commercial.