Calculator Logic Systems (long) Message #1 Posted by bill platt on 15 July 2003, 6:05 p.m.
Until I discovered this forum, I really was not a calculator Geek. Sure, I used one frequently, but I did not think about them constantly.
Now however, I am a total calculator Geek. I think about them all the time. When asked when this will all blow over, I usually say, "we'll see"!
The point of all this prelude: In my previous life, I was only proficient in RPNmeaning that I have always had an intuitive feel for its use (from frequent use) and when tackling complex manual calcs, I have always been able to use all of the stack, and avoid losing data off the back of the t register etc.
For any non RPN machine, I would work with it in a "crippled" modeusing pencil and paper, or the (usualy solitary) memory register even when not neededalways careful.
But now, whenever I see a machine, I have to see how it worksso I have made some interesting discoveries! I am sure many or most of the present audience has already made them, so please forgive my recent enthusiasm.
So far, I have found at least 5 major different logic systems: (and many subsets!)
RPN/RPL
Adding Machine Logic
"Regular Calculator" Logic
"Algebraic" Logic
"Formula entry"
So, for instance, most of the cheap regular 4 or 6 function machines have a curious stack system: Note that I am indicating chain calculations following on from the original:
1+2=3 4=5 6=7; or also 5/2=2.5 5=1 10=0.5
PLEASE SEE THE FOLLOW ON POST WHICH CORRECTS AND AMENDS THIS PART.
In other words, it is sort of a perfect infix: it remembers the first number and the operator, and if you type anoither number right after, followed by equals, you will get an answer. And therefore if you type equals twice, you will carry on with the answer and the first number. This is actually as good or better than RPN for doing certain chain sums. Of course there is also no precedencebut with a memory register, you can get around this, and in fact I did some big computations and compared them to an HP 20s and they had the same number of keystrokes.
The more curious part is this:
8/=0.125 =0.015625 etc for each equals. In other words, there is an implied leading "1" for some reason. This is sort of a mirror of the other fact: 8x=64 =512 etc.
Interstingly, the builtin Windows calculator does the same thing except that you get the more expected series of:
8/=1 =0.125 =0.015625 etc.
Now, the "algebraics" generally do not seem to have this handy chain behavior, but I am sure some of them do (for instance, the Windows builtin one does). The 20s has no good chain system, other than writing a progam to add or mult a constant, so two keystrokes is still possible.
An interesting thing about the algebraics with precedence, like the 20s, is that you actually do not need to use all the parenthesesand in fact if you use one in every place you see on paper, you will use way more keystrokes. For an RPN guy, this business of whether and when to hit close parentheses, versus =, is quite confusing and a source of error.
Then of course there are the 27s with the stack, and most HP pioneers, with the "input" swap and also last x.......
Finally, a coworker has a casio with "true" algebraicso even sqrt, cos, sin etc are infix rather than postfix. I have not explored it in depth yet, but I am sure there are some interesting nuances.
I must say, I was surprised at the utility of the cheapo regular calculator logic, once I got to trying it out!
Regards to all.
Bill
Edited: 15 July 2003, 11:15 p.m. after one or more responses were posted
