24 Jan
2006
24 Jan
'06
6:55 p.m.
All,
way behind on my digests, sorry for the time-warped reply.
At 12:00 -0600 1/5/06, Chuck wrote:
>Why not Shockley diodes? Anyone remember the
Shockley demo of a diode-only
>audio amplifier back in the 60's?
...and my nomination for hobbyist research is: Balanced
trinary! (Possibly using superconductors and SQUID detectors.)
Balanced trinary means place values go up by three each, but instead
of each place containing symbols worth 0, 1, or 2 times the correct
power of 3, the symbols are worth (-1), 0, or 1 times that power.
Using the letter n for the (-1) symbol, a short counting table is:
BT Decimal
...
nn -4
n0 -3
n1 -2
0n -1
00 0
01 1
1n 2
10 3
11 4
1nn 5
1n0 6
1n1 7
10n 8
100 9
101 10
...
No need for a negative sign bit, it's built in. Each memory
cell needs to hold 3 states, which for superconducting loops should
be clockwise, no, or counterclockwise current.
Of course, you could simulate this using 2 binary gates to
carry each trinary digit - thus wasting 25% of the practical power of
your computer (compared to implementing it as base-4). But if Moore's
law holds up, that'll only set you back about 3 months compared to
conventional binary computers....
Hope at least some of you are laughing by now.
Practical applications *do* exist. You can get a long way
with just a few weights (one each power of 3) and a balance scale
using this system, for example. "n" weights go on the platform with
whatever's being weighed, "1" weights go on the other side.
--
- Mark
210-522-6025, temporary cell 240-375-2995
24 Jan
24 Jan
7:13 p.m.
Mark Tapley wrote:
<SNIP>
Of course, you could simulate this using 2 binary
gates to carry
each trinary digit - thus wasting 25% of the practical power of your
<SNIP>
I think you need to call it something other than "trinary digit" because
that contracts to "tit".
Peace... Sridhar
8:54 p.m.
I think you need to call it something other than
"trinary digit" because
that contracts to "tit".
Hey, that might be as close as some computer geeks get to the real
thing...BUT I DIGRESS...
But there is a nit. The information theory people use it. It is basically
a unit of information with e states. e as in 2.818....
William Donzelli
aw288 at osfn.org
7:50 p.m.
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
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
8:02 p.m.
On 1/25/2006 at 12:50 AM ard at p850ug1.demon.co.uk wrote:
Didn't the 8087 use ternary (base 3) for some of its internal logic?
--Chuck
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 
9 p.m.
Chuck Guzis wrote:
On 1/25/2006 at 12:50 AM ard at p850ug1.demon.co.uk
wrote:
Didn't the 8087 use ternary (base 3) for some of its internal logic?
--Chuck
No, my memory was that it used 4-state cells to encode two bits per cell
in the microcode rom. Rather than transistor/no transistor to represent
0/1, it used no transitor = 00, weak transistor=01, normal
transistor=10, strong transistor=11, or something akin to that.
That sounds great, except that the bit cells were a substantial portion
of twice as big as a simple one bit/cell design. There was some area
savings, but not 50%.
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
10:15 p.m.
On 1/24/2006 at 8:00 PM Jim Battle wrote:
No, my memory was that it used 4-state cells to encode
two bits per cell
in the microcode rom. Rather than transistor/no transistor to represent
0/1, it used no transitor = 00, weak transistor=01, normal
transistor=10, strong transistor=11, or something akin to that.
Quite correct! I found a couple of citations in the IEEE online archives.
My muddled mind had it as (zero, one and neither). I understand that some
flash memories also use 4-valued (quaternary) memory cells "under the
hood".
I wonder if eventually multi-valued logic may have its biggest potential
not in speed or conservation of chip space, but rather in decreasing the
number of I/O pins.
Cheers,
Chuck
25 Jan
25 Jan
7:39 a.m.
----- 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
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
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
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
6753
days inactive
6754
days old
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