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From: bson@rice-chex.ai.mit.edu (Jan Brittenson)
Newsgroups: comp.sys.handhelds
Subject: Re: HP 48 Yards.FeetInches
Message-ID: <16478@life.ai.mit.edu>
Date: 13 Jun 91 23:39:24 GMT
References: <2855ad7d:3432comp.sys.handhelds@hpcvbbs.UUCP>
Sender: news@ai.mit.edu
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In a posting of [12 Jun 91 05:40:05 GMT]
   akcs.joehorn@hpcvbbs.UUCP (Joseph K. Horn) writes:

 >              +-----------------------------------------+
 >              | HMS->(x) = x + FP(x)/1.5 + FP(x*100)/90 |
 >              +-----------------------------------------+

 > My question is: If this kind of algorithm works for H.MS, can similar
 > ones be created for any arbitrary fractional systems, like
 > Yards.FeetInches?  If so, how?

How about:

	YFI->(x) = x + FP(x) * 7/3 + FP(x*10) * 22/9

Where YFI is:

	y.fii

I.e. 1 yard, 2 feet, 5 inches = 1.205

---

   So, how does it work? Pretty simple actually. The first term maps
the integer part 1:1 (no conversion necessary). But it also maps the
.f and ..ii parts 1:1, so they need some adjustment. Feet map 1:0.3, so
as far as feet are concerned we fulfill the following equation to get
the feet back in line:

	1 = 0.3 + 0.3 * k ==> k = (1-0.3)/0.3 = 7/3

So we now have:

	YFI->(x) = x + FP(x) * 7/3

   Note that we use FP() since we have already taken care of the
integer part (which mapped 1:1). This also maps the ..ii part, so
again we need to adjust it - we would like it to map 1:0.036 (i.e. 3 *
12in = 1ft):

	1 = 0.036 + 0.036 * k + 0.36 * m

	==> m = (1-0.036-0.036*7/3)/0.36 = 22/9

So now we have our final term.

	YFI->(x) = x + FP(x) * 7/3 + FP(x*10) * 22/9

   We multiply by ten and discard the IP to get rid of what is already
mapped. Apologies if this sounds confusing.


						-- Jan Brittenson
						   bson@ai.mit.edu