Actually, this is more monkey business than real business
A fun series of e-mails :-))
You guys may enjoy this (recently-updated) note on IBM's website about DECIMAL ARITHMETIC Turns out, it's making a big comeback (indeed, if it can ever be said that it left! It's fascinating to see how a large number of problems don't work quite so well in Binary as they do in Decimal. Perhaps the 1401 had it figured out long ago? http://www2.hursley.ibm.com/decimal/decifaq1.html for the General FAQ page and http://www2.hursley.ibm.com/decimal/decifaq.html for the rest of the sections. -Mike Mike@1401.Org |
which I forwarded to some friends outside of the 1401 group, asking for opinions
and the following came back
HI: Of course, I'm opinionated. This is more noise from Mike Cowlishaw who thinks the world just has to be decimal. I am among the few who feel that from a pure "simple arithmetic" point of view God messed up when he did not give us 6 fingers on each hand. Then we would have been using base 12 which DOES have advantages. Otherwise, except for tradition, binary is better than base 10. Mike is British, and it is funny he is not proposing making a computer based on Roman Numerals. LaFarr |
All right guys, You are both wrong. God (if he/she/it exists) should have removed one finger from each hand, giving us base 8 (or base 4). In any case, it seems that this guys argument is that computers must change, and not the various stupid rules in the decimal world. I hate backward compatibility. Bob |
From LaFarr Stuart - 5/7/2007
Yea, Bob: I agree about backward compatibility. God/nature, created the "Three toed Sloth". but unfortunately computer designers seem to have ignored him. I guess we have missed our only chance for using base 12. Cheers, LaFarr PS. Bob may point out God (??) should have removed one toe from the Sloth? Two seems to work quite well for such things as pliers, and tongs. Then we would have had divine support for binary. |
I see the entire discussion as silly. Numeric representations are just tools that we use to stand-in for the actual numbers. Picking the wrong numeric representation for a problem is like picking a hammer instead of a screwdriver when you want to put in screws... you will have difficulty and things can break. There are many issues in numeric representations far beyond base and fixed vs. floating point. For example if the problem requires EXACT representation of rational numbers, floating point is useless (regardless of base used to represent it). You must use rational number representation! I don't know of any computers designed for rational numbers, although I do know that the Ada programming language uses rational number representation at compile time for what it calls "Named Numbers". Writing a numeric function library for rational number representation is not difficult. In other words study the requirements of the problem to be solved and then pick the right tools for the problem. Numeric representation is one of those tools. -- R. Tim Coslet rtcoslet@rockwellcollins.com (408)-532-4505 Rockwell Collins Display Systems |
... When Mike Cowlishaw was proposing a mutilated 16-bit format for decimal floating point, I suggested floating point base 60060 which is fairly close to 65,536 and hence would make fairly efficient use of a 16-bit word. The advantage is: 60060=12*5*7*11*13 (the *'s mean multiplication) so almost all fractions with reasonably small denominators, including 10, could be represented without truncation errors. At the time Mike Cowlishaw was obsessed in trying to get IBM to implement HIS form of decimal floating point in hardware, and didn't want to hear of anything else. Apparently that effort failed, and he went to IEEE, who in my opinion will adopt almost anything if it adds enough confusion to that which should be simple. Example: RS-232 with 25 wires, and two opposite polarity voltages, when the Teletype Corp. and DEC were doing very well with a 20ma current loop that had much greater distance capabilities; and everybody understood it. Quite frankly, I think computers should stick with plain old floating binary, and agree with Van Snyder when he said: "I suspect the financial applications supposed to be of decimal floating point arithmetic really ought to be using decimal fixed point arithmetic" For people who want to propose something new, I have a couple web pages that might give you a chuckle: http://www.zyvra.org/math/wn.htm about how we write numbers. http://www.zyvra.org/math/zen.htm about how we pronounce in English larger numbers http://www.zyvra.org/math/bmerit.htm where I try to give a measure of different number system bases. http://www.zyvra.org/math/dozenal.htm an older page about Dozenal, where near the bottom are suggestions for Time and Angle measures. Cheers, LaFarr |