In another thread the question of unnecessary functions & redundant keys is raised:

http://www.hpmuseum.org/forum/thread-3345.html
What could be the least number of keys needed to reproduce all the functions of, say, the HP 35S keyboard?

If you were happy with a purely binary calculator, only two number keys would be required - but probably you would want to keep decimal input, so let's say you stay decimal.

(03-13-2015 08:17 AM)Gerald H Wrote: [ -> ]In another thread the question of unnecessary functions & redundant keys is raised:

http://www.hpmuseum.org/forum/thread-3345.html

What could be the least number of keys needed to reproduce all the functions of, say, the HP 35S keyboard?

If you were happy with a purely binary calculator, only two number keys would be required - but probably you would want to keep decimal input, so let's say you stay decimal.

With 16 keys you can have the complete HP 41CX function set:

Is chording permitted? This greatly multiplies the number of keyboard positions. For a two chord keyboard with n keys, you get n+

^{n}C

_{2} = ½(n²+n). A three chord keyboard gives n+

^{n}C

_{2}+

^{n}C

_{3} = ⅙(n³+5n). And so forth. The effect is multiplied again if the order the chord keys is considered.

As for minimal, one key is clearly sufficient -- input using

Morse code or similar.

- Pauli

(03-13-2015 08:17 AM)Gerald H Wrote: [ -> ]What could be the least number of keys needed to reproduce all the functions of, say, the HP 35S keyboard?

The ENTER key.

If you press ENTER repeatedly with special timing gaps you can enter 2^6 different codes with a maximum of 4 key presses each. This is more than sufficient for the HP35S 43 keys. The first ENTER is the start bit followed by 6 bits key code. With 2 baud, that is a maximum one keystroke per second, you can enter 100 program steps in approximately 400 seconds.

Even less keys needed by speech entry.

Bernhard

Edit: Clearly I don't have imagination enough & now rescind my decision below to one in favour of PANAMATIK with zero keys. I should have added the proviso of entry only by key.

(03-13-2015 08:51 AM)Paul Dale Wrote: [ -> ]Is chording permitted? This greatly multiplies the number of keyboard positions. For a two chord keyboard with n keys, you get n+^{n}C_{2} = ½(n²+n). A three chord keyboard gives n+^{n}C_{2}+^{n}C_{3} = ⅙(n³+5n). And so forth. The effect is multiplied again if the order the chord keys is considered.

As for minimal, one key is clearly sufficient -- input using Morse code or similar.

- Pauli

OK, definitely winner of the competition.

My specifications were vague (not deliberately, as I guess most people are mind-readers & have the same background thoughts as me) & I should have added the proviso of not inducing repetitive strain injury after 60 mins usage.

(03-13-2015 08:17 AM)Gerald H Wrote: [ -> ]In another thread the question of unnecessary functions & redundant keys is raised:

http://www.hpmuseum.org/forum/thread-3345.html

What could be the least number of keys needed to reproduce all the functions of, say, the HP 35S keyboard?

If you were happy with a purely binary calculator, only two number keys would be required - but probably you would want to keep decimal input, so let's say you stay decimal.

Not the least number of keys, but what I'd be comfortable using without too many shifts & menu's. Small form factor with 23 keys:

http://pickyb.blogspot.co.uk/2014/05/pro...kcalc.html
Best regards.

(03-13-2015 08:32 AM)Didier Lachieze Wrote: [ -> ]With 16 keys you can have the complete HP 41CX function set:

And operators are on the left, of course... ;)

A calculator without any key: MyScript Calculator (available for IOS & Android).

The way the question is posed

"least number of keys" would imply a minimum of two keys and disallow none or one. In this case two keys are clearly enough -- the morse code key and a power button

- Pauli

(03-13-2015 11:14 AM)Paul Dale Wrote: [ -> ]The way the question is posed "least number of keys" would imply a minimum of two keys and disallow none or one. In this case two keys are clearly enough -- the morse code key and a power button

- Pauli

Don't be overhasty. Perhaps some mathematician will show a solution with a negative number of key

s. Might be useful for entering imaginary numbers. Is minus infinity keys less than zero keys?

Bernhard

(03-13-2015 11:26 AM)PANAMATIK Wrote: [ -> ] (03-13-2015 11:14 AM)Paul Dale Wrote: [ -> ]The way the question is posed "least number of keys" would imply a minimum of two keys and disallow none or one. In this case two keys are clearly enough -- the morse code key and a power button

- Pauli

Don't be overhasty. Perhaps some mathematician will show a solution with a negative number of keys. Might be useful for entering imaginary numbers. Is minus infinity keys less than zero keys?

Bernhard

No, no, this is stretching things too far.

As clarification, in this & any other issues I may raise, answers must be limited to real rationals, or if you like Diophantine.

(03-13-2015 11:26 AM)PANAMATIK Wrote: [ -> ] (03-13-2015 11:14 AM)Paul Dale Wrote: [ -> ]The way the question is posed "least number of keys" would imply a minimum of two keys and disallow none or one. In this case two keys are clearly enough -- the morse code key and a power button

- Pauli

Don't be overhasty. Perhaps some mathematician will show a solution with a negative number of keys. Might be useful for entering imaginary numbers. Is minus infinity keys less than zero keys?

Bernhard

Hoist with my own petard, the underlined "s"!

It's an unfortunate idiosyncracy of colloquial English that grammatical number has to be specified.

Fortunately Japanese does not have this obsession with number - I'll try to nipponize my English in this respect in future.

(03-13-2015 11:14 AM)Paul Dale Wrote: [ -> ]The way the question is posed "least number of keys" would imply a minimum of two keys and disallow none or one. In this case two keys are clearly enough -- the morse code key and a power button

- Pauli

No, Paul, I must criticize your use of English.

While one is clearly disallowed, the expression is correctly "zero keys" or "no keys"!

(03-13-2015 12:13 PM)Gerald H Wrote: [ -> ]While one is clearly disallowed, the expression is correctly "zero keys" or "no keys"!

But Paul wrote 'none', which is correctly

none (not one) key .

(03-13-2015 05:59 PM)Thomas Radtke Wrote: [ -> ] (03-13-2015 12:13 PM)Gerald H Wrote: [ -> ]While one is clearly disallowed, the expression is correctly "zero keys" or "no keys"!

But Paul wrote 'none', which is correctly none (not one) key .

Except "none key" is wrong & "the least number of keys" would not exclude zero.

Please don't confuse the many language learners reading this thread.

(03-13-2015 08:32 AM)Didier Lachieze Wrote: [ -> ] (03-13-2015 08:17 AM)Gerald H Wrote: [ -> ]In another thread the question of unnecessary functions & redundant keys is raised:

http://www.hpmuseum.org/forum/thread-3345.html

What could be the least number of keys needed to reproduce all the functions of, say, the HP 35S keyboard?

If you were happy with a purely binary calculator, only two number keys would be required - but probably you would want to keep decimal input, so let's say you stay decimal.

With 16 keys you can have the complete HP 41CX function set:

Didier - could you please post a larger, hi-res scan of that, or point out where it may be found if already online somewhere. It looks mightly interesting, even if all it does is answer the topic of this thread, however I'd guess it does more than that. Thanks.

There was one overlay for sale on

ebay.de some weeks ago.

Here is a picture from this auction:

Laitram XQ2.

You can also find the Laitram manual on TAS.

LOL, how finely could a knob be turned connected to a rheostat, and an appropriate digital VOM circuit attached, and each unique resistance reading would correspond to a digit or function ??