## Introduction

A recent thread here asks, "What is the most useless

function on a scientific calculator?" Many people have answered and a

spirited discussion has ensued. One argument against functions such

as x^2 and % is that it's easy to calculate the function without

needing a special key.

That got me to wondering: how *few* functions can we

use to build a scientific calculator. Right now I'm looking at my

11C: a beautiful machine, to be sure, but loaded with keys and

functions. The engineer in me asks, "How can I reduce its complexity?

What can I get rid of?" The 10C was a step in the right direction

but in my opinion was a failure because it did not go far enough.

Let's see how much of the extra functionality we can remove. True, we

will have to learn some new key sequences but HP users are used to

doing things a little diffenently, what with RPN and all.

Let's call this new machine the HP-11C-. (Although some other names,

like HP-11D- or HP-11F may come to mind too.) Readers of the other

thread will be happy to learn that the 11C- does not include %, x^2,

Grads, n!, or hyperbolics; thus, it should make everyone happy.

## Hello, Numbers, Goodbye -, /, Trig and Logs

First, let's mention a few things we'll keep. All of the number entry

and stack manipulation keys: [0]-[9], [.], [CHS], [EEX], [ENTER],

[<-], [x<>y], [R Down], [R Up], [LST x]. Display Mode keys: [FIX],

[SCI], [ENG]. Shift keys: [f], [g]. Not to mention [ON].

Now let's get rid of some stuff. We still need to add, so [+] stays.

But with [CHS] to negate numbers we don't [-] any more; use the

sequence [CHS] [+] to subtract.

Similarly, we may eliminate [/] if we keep [1/x], which is useful in

contexts other than just straight division, in forming negative

exponents, for example.

All trig functions will be done in

radians so [DEG], [RAD], [GRD] go away. We don't need the trig

functions either: **angle** [ENTER] 1 [->R] gives us the

cosine in x and the sine in y. They can be divided to get the tangent.

[->P] gives the arctangent; the other inverse trig functions can be

calculated from the arctangent with the appropriate formulas. [0]

[1] [CHS] [->P] [x<>y] gives us pi, so there goes another key. With

pi still available, we don't need [->DEG] or [->RAD].

Let's hold onto [LN] and [e^x]. We can then calculate common logs and

antilogs, and arbitrary powers and roots, so we don't need [LOG],

[10^x], [y^x], [x^2] or [sqrt x]. Hyperbolic functions and their

inverses are defined in terms of exponentials and natural logs, so

they go out the window, too.

## Other Functions

Memory ([STO], [RCL]): Keep.

[%], [Delta %]: Not necessary, compute using formula on back panel of

calculator.

[ABS]: Trivial to do by hand or in a program.

[CLEAR Sum], [CLEAR PRGM], [CLEAR REG]: Don't need. Get rid of them.

[CLEAR PREFIX]: Useful for correcting incorrect prefix key press.

Keep.

[CLx]: Not sure about this one. Let's get rid of it and put it back

later if it proves necessary.

[RAN #]: Too hard to duplicate. Keep.

[Py,x], [Cy,x]: Can be computed with factorials. Get rid of them.

[x!]: Get rid of it unless you need the gamma function.

[->H.MS], [->H]: Drop; easy to implement.

[FRAC], [INT]: We don't them both. Keep [INT] and compute fractional

part with Frac(x) = x - INT(x).

[USER]: Just a conveinence function. Don't need it.

[MEM]: Why bother? Get rid of it.

Statistics: [Sum+], [Sum-], [x bar], [s], [y hat, r], [L.R.]: Can all

be computed by hand. Get rid of them.

## Programming Functions

We will keep all of the programming stuff with the following exceptions:

[BST]: We can just go back to the start of memory and [SST]. Drop.

[DSE], [ISG]: Can rewrite with other sequences of instructions. Get

rid of them.

Flags: We can duplicate their effect using regular memory registers.

Out they go!

Conditionals: We certainly don't need eight of them! First, get rid

of the four "compare x to 0" tests. We can just put the zero in

ourselves and use the "compare x to y" tests. Next, [x=y] and [x!=y]

are exact opposites; we only need one. Let's keep [x=y]. Finally,

[x<=y] and [x>y] are also opposites; let's keep [x>y]. This eliminates

six of the eight conditionals and leaves just two nonredundant ones.

## Examples

Now let's put it all together. First some simple examples (all to 4

decimal places):

Square root of 625: 625 [LN] .5 [X] [e^x] (Answer: 25.0000)

Common log of 2: 2 [LN] 10 [LN] [1/x] [X] (Answer: 0.3010)

Common antilog of 2.775: 2.775 [ENTER] 10 [LN] [X] [e^x] (Answer: 595.6621)

2^5: 2 [LN] 5 [X] [e^x] (Answer: 32.0000)

cos 0.75: .75 [ENTER] 1 [->R] (Answer: 0.7317. [x<>y] gives sin 0.75 (0.6816))

And finally, a larger example:

Arc sin 0.6, in degrees: [LN] [LST x] [x<>y] 2 [X] [e^x] [CHS] 1 [+]

[LN] .5 [X] [e^x] [->P] [X] 180 [X] 0 [ENTER] 1 [CHS] [->P]

[X] [1/x] [X] (Answer: 36.8699)

Isn't this more satisfying than hitting just two keys, like on other

calculators? Here you have a real sense of ownership of your answer,

having worked hard for it. The HP-11C- will give you many

opportunities for this kind of satisfaction.

## Conclusion

The appeal of the proposed HP-11C- is clear. Fewer built-in functions

mean less ROM and fewer keys. This translates to lower manufacturing

costs and higher reliability. Fewer keys also means that the

calculator can be made smaller without sacrificing key size or spacing,

preserving the excellent Voyager series ergonomics. And as can be

seen from the description above, the calculator provides a built-in

never-ending refresher course in math, as opposed to other calculators

which only act as a mental crutch the more you use them. This aspect

alone could make the 11C- a hit in the educational market.

Comments and suggestions are always welcome.