I have found a calculator  which has only 15 keys, though it calculates all four arithmetic functions.

Keys are: [C], [0]..[9], [.], [+ =], [- =], [x -:-]

This is the Elektronika C3-07.

Hi Sergei,

I have 2 pocket calculators with (only) 15 keys, Sharp EL-8 and Santron 12S.

Regards,

This keyboard arrangement was used by Sharp on the EL-8 (also the Facit 1111 which was a clone of the EL-8). It was also used on the earlier and larger Sharp QT-8 (with Burroughs C3146 as a clone). Vintage of these Sharp/Facit/Burroughs machines is the 1970 timeframe.

To multiply, you enter first number, press |X -:-|, enter 2nd number, then press "+=" To divide, you enter first number, press |X -:-|, enter 2nd number, then press "-="

I'm sure that the C3-07 is likely a Soviet 'copy' of the QT-8 or EL-8.

You can see these machines (except the QT-8, which I'm still looking for) at my Web site at http://www.geocities.com/SiliconValley/Lab/7510

Remarkable! That must be the minimum, really. How do you make it divide rather than multiply, when the commands for both are on the same key? do you push the key twice? Sometimes I think of building my own RPN four-function machine. While 15 or 16 keys might be too few for RPN, at least it does show that the rather-common 16-key keypads available here in the USA could be used for four functions.

Don't underestimate Russian ingenuity! Although Russian claims, some time back, to have invented all sorts of things were a bit embarrassing, nevertheless there's oodles of true creativity and capability in Russia. (I was very impressed by the huge ground-effect cargo aircraft, btw; also by the reliability of large Russian rockets.)

My regards to all,

The section "The first Soviet calculators" of "Soviet Calculators History" written by Sergei Frolov explains how it was done. The procedure is very interesting.

Regards,

At 02:40 PM 11/7/98 -0500, you wrote:

>Sometimes I think of building my own RPN four-function machine. Why do that? Just pick up an old Novus RPN calc. They're only worth a few bucks. I had several that I gave away. >

>Don't underestimate Russian ingenuity!  >(I was very impressed by the huge ground-effect cargo aircraft,

You're one of the few that I know of that's ever heard of them! It's an amazing aircraft, I don't know why we have bought some of them or developed our own.

>Remarkable! That must be the minimum, really.

How about removing the [C] key? That function is performed by powering the machine off then on again, anyway. Then you'd only need 14 keys, using the overloaded [*/], [-=] and [+=].

Hello, Andrew and All!

Andrew Davie wrote:

> How about removing the [C] key?

[C] key should be required for correction entering number or operation as minimum.

Good luck!

The Elektronika C3-07 calculator that Sergei mentions performs its operation by overloading the [-=] and [+=] key. To perform division, say 9 divide 3, you press [9] [* /] 3 [-=]. To perform 9 times 3 you press [9] [*/] [3] [+=].

Another early precedent in key reduction is the first pocket Sinclair calculator, an RPN machine which had no ENTER key! To input the very first number, you assumed you'd just powered on your calculator - the display was 0, and you simply added it to the existing 0 (ie: 23 + ).

Cheers

Hello, Nicholas and all!

Nicholas Bodley wrote:

> Remarkable! That must be the minimum, really. How do you make it divide   rather than multiply, when the commands for both are on the same key? do > you push the key twice?

Elektronika C3-07 is a pseudo-RPN calculator.

For addition and substraction:
[C] [first number] [+] [second number] [operation] [3-rd number] [operation] etc.
(first [+] used for addition initial zero and first number)

For multiplication:
[first number or previous result] [X -:-] [second number] [+ =]

For division:
[first number or previous result] [X -:-] [second number] [- =]

Example:
(1 + 2) * 3 / 4 - 5 = -2.75
[C] [1] [+=] [2] [+=] [X -:-] 3 [+=] [X -:-] [4] [- =] [5] [- =]

Good luck!

Talking about key reduction, the 15 keys example provided by Sergei is very interesting although it is rather clear why it was soon replaced by an expanded keyboard. The key reduction was obviously done in a effort to reduce the cost of the calculator rather than increase its functionality or easiness of use.

This case, however, reminded me of another example of key reduction used by Aristo in one if its earliest calculators, the M-36. Although it had 20 keys and was a plain four function calculator (with only a % function key), it had a very powerful set of memory functions handled only by 2 keys: [x<->y] and [M]. The "Swap" key and the "Memory" key. By combining these keys with the arithmetic operators and the clear key it was possible to do the following:

1. Add the displayed value to the memory. [M][+]
2. Subtract the displayed value from the memory. [M][-]
3. Clear the contents of the memory. [M][C]
4. Replace the displayed value with the memory value. [M][=]
5. Swap the displayed value with the memory value. [M][Swap]
6. Multiply the memory value by the displayed value. [M][x]
7. Divide the memory value by the displayed value. [M][/]
8. Recall the last numbered enter in a previous entry. [Swap][Swap]
9. Get the inverse value of a number. [number][/][Swap]

The system was so flexible that it was even possible to calculate the square root of a number even though it didn't have a SQRT function key -This was done by using the Newton-Raphson method of successive approximations - I recall that the value was usually obtained in 3 to 4 iterations (although I don't recall now the sequence of keystrokes used after entering the number - It was explained in the user manual). To increase the key reduction without sacrificing functionality, it had also a real implicit CONSTANT mode, where the last operand entered was always considered the constant (for example, [25][+][+][+] would yield 75. It was very useful for financial calculations. I used mine for five years until it was stolen 20 years ago. I never found it again, the next Aristo model I got, has a SQRT key and the two memory keys had already been replaced by the four memory keys used nowadays in every calculator.

I still resent the fact that modern simple calculators (not talking about the advanced scientific models), have four memory keys [M+], [M-], [MC] and [MR], which only perform the following set of functions:

1. Add the display value to the memory.
2. Subtract the displayed value from the memory.
3. Clear the contents of the memory.
4. Replace the displayed value with the memory value.

The swap key was never implemented and so the single memory key. One step back in the evolution of calculators that was never recovered. I think that was part of the price to pay for standardization.

Regards,