SPUG: Cool power-of-2 trick

Johnston, Mark mark.johnston at pnl.gov
Thu Jan 20 14:39:09 PST 2005

```SQL uses a sort of three-valued logic -- False, True and Null (in the
table below, F, T and N):

&| F T N
-+------
F| F F N
T| F T N
N| N N N

Of course there is lots of argument over whether Null ought to be
considered a "value".

--Mark

-----Original Message-----
From: spug-list-bounces at pm.org [mailto:spug-list-bounces at pm.org] On
Behalf Of Michael R. Wolf
Sent: Thursday, January 20, 2005 2:08 PM
To: Brian Hatch
Cc: spug-list at mail.pm.org
Subject: Re: SPUG: Cool power-of-2 trick

At 01:30 PM 1/20/2005, Michael R. Wolf wrote:
>At 12:29 PM 1/20/2005, Brian Hatch wrote:
>
>
>> > While reading through the perl-quiz-of-the-week, I noticed this
>> > neat test to find if a number is a power of 2.  Originally, I
>> > didn't even
>> believe it
>> > worked so I wrote a little program to test it.  The program helped
>> > me figure out that it does, in deed, work, and *how* it works.  If
>> > a
>> number is
>> > a pure powere of 2, it only has one bit set.
>>...
>>
>>
>>This only works on systems where data is stored in binary.  If you're
>>on a machine that uses ternary storage units (-1 0 +1) then it does
>>not work for powers of two, but it does work for powers of three.

What does a trinary trit-wise &-operator act like?  What's the
boolean(?)
value of each of the trit states?  What's the semantic meaning of the
lowest-level '&' operator in that context?

Here's a binary table for the results of the &-operator:

& | 0  1
--+-----
0 | 0  0
1 | 0  1

Analagous to this boolean truth table

& | F  T
--+-----
F | F  F
T | F  T

What's the trinary logic table?

& | -1  0  1
--+---------
-1 |  x  x  x
0 |  x  x  x
1 |  x  x  x

What's Boole have to say about its analog?

& | -1  0  1
--+---------
-1 |  x  x  x
0 |  x  x  x
1 |  x  x  x

Michael R. Wolf
All mammals learn by playing!
MichaelRWolf at att.net

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