----- Original Message -----
From: ard at p850ug1.demon.co.uk (Tony Duell)
Date: Wednesday, January 25, 2006 0:50 am
Subject: Re: Homebuilt TTL and transistor CPUs - wierd logic
Balanced
trinary means place values go up by three each, but
instead
Personally, I prefer negabinary (base -2). It uses 2-state
signals, but
the column values are powers of -2 : . . .16, -8, 4, -2, 1
So thats what its
called! I've been playing around with it for years
but never tried to track down other work. While were at it other
variations could be imaginary negabinary to (base -2i), imagibinary
(base 2i)
all the best
Laurence Cuffe
Every postive and negative integer has a unique representation.
The
adder works (obvuiously) with +ve and -ve numbers. Shift-and-and
multiplication works, as does shift-and-subtract division (using
negabinary adders/subtractors). To negate a number, shift it left
one bit
and add it to the origiginal number (this is multiplying by 11,
which is
-1 of course)
negabinary decimal
1100 -4
1101 -3
0010 -2
0011 -1
0000 0
0001 1
0110 2
0111 3
0100 4
Note that numbers of a odd-number of bits length (ingoring leading
zeros)
are +ve, those of an even number of bits are -ve
Years ago I built a 4-bit negabinary adder. The full adder stage
has 3
outputs (sum, carry, carry+1) since you have to be able to add 1+1
giveing 110 and therefore has 4 inputs (2 bits to sum, carry in
from last
stage, carry in to last-but-one stage).
-tony