Path: utzoo!attcan!uunet!know!zaphod.mps.ohio-state.edu!rpi!uupsi!rodan.acs.syr.edu!isr
From: isr@rodan.acs.syr.edu (Michael S. Schechter - ISR group account)
Newsgroups: comp.sys.mac.programmer
Subject: Re: Why can't the Mac add?
Message-ID: <1990Oct3.190234.16818@rodan.acs.syr.edu>
Date: 3 Oct 90 19:57:06 GMT
References: <45060@apple.Apple.COM> <1990Sep24.010249.16647@agate.berkeley.edu> <8614@jarthur.Claremont.EDU>
Organization: Institute for Sensory Research
Lines: 62

In article <8614@jarthur.Claremont.EDU> wilkins@jarthur.Claremont.EDU (Mark Wilkins) writes:
>  For any message relating to the countability of infinitely-extended
>fractional rational numbers the number of copies of the message needed to
>get the point across has the cardinality of Aleph-null.
>  See the last message on the subject for a practical example.
>:-)
>-- M. W.

Not neccesarily.
After explaining this point to the "unwashed hordes" perhaps  3,4, or
even 5 hundred times previously, I've gotten pretty good at it.
Here Goes:
  Computers, since they store 0's and 1's (you know that much that right?)
  can't keep track of numbers like we do. We say 0-9 hundreds and then
  0-9 tens and then 0-9 ones etc etc. The poor stupid computers could
  only say 0 or 1 hundred and then 0 or 1 ten and then 0 or 1 one.
  This means there's lotsa missing numbers. And since my paycheck doesn't
  have any 0's or 1's, I really want there to be a way for a computer to
  keep track of all these numbers!
   So what computers do is say "i have 0 or 1 ones,
  then 0 or 1 twos
   then 0 or 1 fours
    then 0 or 1 eights
 etc etc etc
   It just happens that by doubling the size of the numbers it
    keep tracks of each time you get to "say" each number.
 so for example we say: 56
  That's five ten's and six ones.
The computer says (for 56):101110
That's one 32, no 16's, one 8, one 4, one 2, no ones.

See? isn't it easy?
Now the way the computer does fractions is just the same.
We use 0.1 0.01 0.001 etc for tenths, hundreds, thousands.

The computer uses
   0.1  0.01 0.001 for halves, quarters, eighths!!!
But don't forget, 3/8's isn't  0.003 No! it's 0.011
(which is 1 quarter and 1 eighth=3/8's)

it's like you can't really put 1/3 in as a decimal number nicely
it's 0.3333333333 for as long as you wanna go.
some numbers we can write nicely, like 0.1 in decimal
the computer has to write very mesily as 0.000110011001+
This is no halves, no quarters, no eights
one sixteenth, one thirty-second, no sixty-fourths, no-128's
one 256th, one 512th etc etc
Luckily, computers only figure numbers in this internally because
they only have 0's and 1's inside 'em. On screens and printers
they have 2's 4's 0's, everything from 0-9......
But now you see why there's problems. it's like adding
1/3 to 1/3 to 1/3 with a calculator.. you either 0.99999 or1.00001
depending on your calculator.






--
Mike Schechter, Computer Engineer,Institute Sensory Research, Syracuse Univ.
InterNet: Mike_Schechter@isr.syr.edu isr@rodan.syr.edu Bitnet: SENSORY@SUNRISE