Nixie tubes are neat. They're nostalgic, and not too hard to get working. Russia still has bazillions of them.

Here's an actual calculator that was sold, for money, made with Nixie tubes:

Everyone's making clocks with them.

Some are rethinking calculators with them.

So I thought it would be fun to go bigger, and interactive, but not too crazy. So that's where the Reverse Polish Notation Nixie calculator comes in. Like the venerable HP-48, it should have four visible stack levels. I would use IN-12B tubes, since they are top-read and have a decimal separator: a comma, which makes it compatible with most of South America, Europe and Asia.

## Reverse Polish Notation

Polish Notation was invented by the Polish logician Jan Łukasiewicz in 1924. He was stuck in Poland under German occupation during World War II, and after the war he emigrated to Ireland. It wasn't until 1954 that Reverse Polish Notation came into being, but it wasn't used in calculators and computers until the early 1960s. RPN was certainly inspired by Łukasiewicz's work.

## Alternate History

In my alternate history, Łukasiewicz did not leave Poland after the war. He was deported from Poland to the USSR as part of Operation Osoaviakhim to work on mathematics and help other captured scientists. However, the Soviets quickly realized the utility of Polish Notation, except reversed, in calculations, and by the 1950s were building large RPN desk-calculators with Nixie tube displays.

## Features

Here are the features I want to support:

- 4-level stack display
- scientific notation
- IEEE 754 double-precision floating point (binary64, which is 15-17 decimals of precision)
- Functions 10
^{x}, e^{x}, log_{10}, ln - Functions x
^{2}, x^{y}, √x,^{y}√x - Trigonometric functions (arc) sin, cos, tan (h)
- π, e
- Stack operations drop, dup, swap, rot3
- Auxilliary memory store and recall

## Display

I want to have enough digits on each stack level to display a double-precision number to 17 digits with 3 digits of exponent. To represent scientific notation, instead of the usual practice of using "E" or a space to separate the mantissa from the exponent, I'd use a light shining through a panel overlay between the 3rd and 4th digits, showing either "
`+`

"or "
`-`

". So
`O.778`

would be
^{+}O43`0.778x10`

. Negative numbers would also be represented by having a "
^{43}`-`

" panel light on the far left side.

The interesting thing about this representation is that numbers not needing an exponent, which are those having an exponent of 0, could either be displayed with that exponent (

) or, probably better, by leaving off the exponent and leaving the last three digits blank. That would make exponentiated and non-exponentiated numbers line up.^{+}OOO

Infinity could be represented by
`OO`

and NaN by lighting all the commas.

## Insides

As for electronics, as I said above, I'd use IN-12B tubes. These require a supply of 170VDC. Russia also has bazillions of K155ID1 chips, which drive these tubes, except for the decimal separator, for which I'd just use a simple transistor driver. This driver chip is pin-for-pin compatible with (and sadly much more available than) the 74141. One could use any 4-to-16 decoder and couple it with some high-voltage tolerant circuitry, but then you'd have essentially built a K155ID1.

I'd run the whole thing off of (of course) an Arduino. Now, each stack level has 20 digits times 5 bits each (4 for the BCD digit, and 1 for the separator), plus at least three indicators (sign, exponent signs). That's 103 bits per level, times 4 levels is 412 bits.

Conveniently, there are chips which take I^{2}C and can latch many outputs (or read many inputs). There are two nice ones:

- NXP PCA9698, with 40 I/O.
- Cypress CY8C9560, with 60 I/O.

Each can be programmed with a 7-bit address, so there is no cramped address space to deal with.

If I want to be modular, each stack level can be powered using three of the NXP chips, or two of the Cypress chips. The NXP chips seem more approachable to me.

## Keyboard

I figure the keyboard will be a 4x8 matrix, which should be able to handle all the functions plus digits as long as I have a shift key.

Keys without shift functions (18):

- 0-9
- .
- SH (shift)
- +, -, x, ÷
- CHS (change sign)
- EE (enter exponent)
- HYP (hyperbolic, for trigonometric functions)

Keys with shift functions (12):

- sin / asin
- cos / acos
- tan / atan
- log / 10
^{x} - ln / e
^{x} - x
^{2}/ √x - x
^{y}/^{y}√x - 1/x / x!
- π / e
- DROP / DUP
- ROT2 / ROT3
- STO / RCL

These 30 keys would be placed in a 4x8 matrix, not necessarily physically but electrically. Each row of eight keys would be read via I^{2}C, with a full keyboard scan happening many times per second.