HP Calculators with native C-F temperature conversion

[calc-calcs]

Is the HP-55 the only pre-80s calculator that does C->F/F->C temperature conversions natively?

Could the HP-41 (or any other model) made to have this conversion with an add-on module?

Thanks.

[Namir]

(02-10-2024 11:25 AM)calc-calcs Wrote:  Is the HP-55 the only pre-80s calculator that does C->F/F->C temperature conversions natively?

Could the HP-41 (or any other model) made to have this conversion with an add-on module?

Thanks.

Yes to both questions. In the case of the HP-41C, add-on modules (especially custom ones) can add many many new features, as long as these features can realisticly (speed-wise) run on the 41C.

Namir

[rprosperi]

For the HP-41 family, I'm pretty sure both the Petroleum and Thermal & Transport Science Pac ROMs included these, plus other related conversions.

[DGM]

(02-10-2024 11:25 AM)calc-calcs Wrote:  Is the HP-55 the only pre-80s calculator that does C->F/F->C temperature conversions natively?

Could the HP-41 (or any other model) made to have this conversion with an add-on module?

Thanks.

I used to use statistics for this: enter three known quantities for degrees C and the degrees F equivalents (-40, -40; 0, 32; 100, 212) in the statistics X and Y sum registers, and use the resulting trend line to get the answer given for any input. I did this on the HP-25, my first HP calculator. Sorry I don’t recall the exact steps, but it has been a few years (decades (not quite half a century)).

Not exactly what you were asking for, but it did bring back a happy memory for me.

[C.Ret]

(02-10-2024 11:25 AM)calc-calcs Wrote:  Is the HP-55 the only pre-80s calculator that does C->F/F->C temperature conversions natively?

No. There certainly where a few other calculators that does °C↔°F conversion at the time.
I'm far from knowing them all.

But, for example, the Texas Instruments Ti-59 or Ti-58 were all available with the Main Library solid state module which ML-25 Unit Conversion (2) program allows volume, weight and temperature conversions.

   

(02-10-2024 11:25 AM)calc-calcs Wrote:  Could the HP-41 (or any other model) made to have this conversion with an add-on module?

Yes, most definitely and also without any add-on module as well. Like all programmable calculators of this era.
The high-end calculators of the time were programmable to meet the specific needs of their users. Temperature conversions are a typical example of use. These conversions can simply be programmed directly into these machines.

What's special about the HP-41 is that with a few instructions a program can be composed to offer all conversions between degrees Kelvin, Fahrenheit and Celcius in a user-friendly and intuitive environment:

001 LBL"TCONV" 
002  273.15  STO 00  SF 27  "A:.F B:.K C:.C"  PROMPT
007  LBL A  FC?C 22 XEQ 01  XEQ 00  SF 01  STO 01  FIX 1  "F"  XEQ 10
016  LBL B  FC?C 22 XEQ 02  XEQ 00  SF 02  STO 02  FIX 2  "K"  XEQ 10
025  LBL C  FC?C 22 XEQ 03  XEQ 00  SF 03  STO 03  FIX 1  "C"  XEQ 10  GTO A 

035   LBL 00  CF 01  CF 02  CF 03  RTN
040   LBL 01  FC?C 02 XEQ 02  RCL 00  -  9  *  5  /  32  +  RTN
052   LBL 02  FC?C 03 XEQ 03  RCL 00  +  RTN
058   LBL 03  FC?C 01 XEQ 01  32  –  5  *  9  /  RTN

068   LBL 10  ASTO L  CLA  ARCL X  "~ ."  ARCL L  FIX 4  PROMPT  CF 22
077 END

Usage:
Initialize the program by executing XEQ “TCONV”
Enter a temperature and press A, B or C to indicate respectively whether it is Fahrenheit, Kelvin or Celsius.
To convert the displayed temperature, press A, B or C (without entering a value) to obtain °F, °K or °C respectively.

The displayed temperatures are stored in registers R01, R02 and R03 depending on whether they are °F, °K or °C.
The result of the conversion is in the X register.
The ALPHA register gives the rounded value followed by its unit.
Pressing R/S key cycle through the three units.

Ultimately this is how I like to have the conversions on my HP-41.
Don't hesitate to create your own method. This is the main purpose of the HP-41 which is designed to be customized by the user.

If you don't believe me, just have a look under the display at the message written on the four largest keys this machine has: ON any USER press the PRGM is ALPHA.

[Thomas Klemm]

(02-10-2024 02:34 PM)DGM Wrote:  I used to use statistics for this: enter three known quantities for degrees C and the degrees F equivalents (-40, -40; 0, 32; 100, 212) in the statistics X and Y sum registers, and use the resulting trend line to get the answer given for any input. I did this on the HP-25, my first HP calculator. Sorry I don’t recall the exact steps, but it has been a few years (decades (not quite half a century)).

The HP-25 hasn't linear regression built-in.
You either used a different model or wrote a program similar to this:

Code:

PROG
49
01: 13 31    : GTO 31
02: 13 36    : GTO 36
03: 24 03    : RCL 3
04: 24 06    : RCL 6
05: 61       : *
06: 24 07    : RCL 7
07: 15 02    : g x^2
08: 41       : -
09: 23 00    : STO 0
10: 24 03    : RCL 3
11: 24 05    : RCL 5
12: 61       : *
13: 24 07    : RCL 7
14: 24 04    : RCL 4
15: 61       : *
16: 41       : -
17: 24 00    : RCL 0
18: 71       : /
19: 23 01    : STO 1
20: 24 06    : RCL 6
21: 24 04    : RCL 4
22: 61       : *
23: 24 07    : RCL 7
24: 24 05    : RCL 5
25: 61       : *
26: 41       : -
27: 24 00    : RCL 0
28: 71       : /
29: 23 02    : STO 2
30: 13 00    : GTO 00
31: 24 01    : RCL 1
32: 61       : *
33: 24 02    : RCL 2
34: 51       : +
35: 13 00    : GTO 00
36: 24 02    : RCL 2
37: 41       : -
38: 24 01    : RCL 1
39: 71       : /
40: 13 00    : GTO 00
41: 13 00    : GTO 00
42: 13 00    : GTO 00
43: 13 00    : GTO 00
44: 13 00    : GTO 00
45: 13 00    : GTO 00
46: 13 00    : GTO 00
47: 13 00    : GTO 00
48: 13 00    : GTO 00
49: 13 00    : GTO 00
DATA
8
00: 1600
01: 1.8
02: 32
03: 2
04: -8
05: 1600
06: 1600
07: -40
STATE
3
DEG
FIX
2
HELP
1

END

Example

Insert data:

CLEAR REG

-40 ENTER Σ+
32 ENTER 0 Σ+

Calculate parameters:

GTO 03 R/S

The parameters \(a\) and \(b\) can now be found in registers 1 and 2:

RCL 1
1.80

RCL 2
32.00

Celsius to Fahrenheit:

37
GTO 01 R/S
98.60

Fahrenheit to Celsius:

451
GTO 02 R/S
232.78


How does it work?

For just two points \(P_1 = (x_1, y_1)\) and \(P_2 = (x_2, y_2)\) we want to solve the following linear system of equations:

\(
\begin{bmatrix}
x_1 & 1 \\
x_2 & 1 \\
\end{bmatrix}
\cdot
\begin{bmatrix}
a \\
b \\
\end{bmatrix}
=
\begin{bmatrix}
y_1 \\
y_2 \\
\end{bmatrix}
\)

This leads to:

\(
\begin{align}
a &= \frac{y_1 - y_2}{x_1 - x_2} \\
\\
b &= \frac{x_1 y_2 - x_2 y_1}{x_1 - x_2} \\
\end{align}
\)

However we solve instead the following system of equations:

\(
\begin{bmatrix}
\sum x^2 & \sum x \\
\sum x & n \\
\end{bmatrix}
\cdot
\begin{bmatrix}
a \\
b \\
\end{bmatrix}
=
\begin{bmatrix}
\sum xy \\
\sum y \\
\end{bmatrix}
\)

In case of \(n = 2\) the solutions are:

\(
\begin{align}
a
&= \frac{2(x_1 y_1 + x_2 y_2) - (x_1 + x_2)(y_1 + y_2)}{2 (x_1^2 + x_2^2) - (x_1 + x_2)^2} \\
&= \frac{(x_1 - x_2)(y_1 - y_2)}{(x_1 - x_2)^2} \\
&= \frac{y_1 - y_2}{x_1 - x_2} \\
\\
b
&= \frac{(x_1^2 + x_2^2)(y_1 + y_2) - (x_1 + x_2)(x_1 y_1 + x_2 y_2)}{2 (x_1^2 + x_2^2) - (x_1 + x_2)^2} \\
&= \frac{(x_1 - x_2)(x_1 y_2 - x_2 y_1)}{(x_1 - x_2)^2} \\
&= \frac{x_1 y_2 - x_2 y_1}{x_1 - x_2} \\
\end{align}
\)

Thus, we end up with the same result.

References

• HP-25C Emulator
  

[Dave Britten]

Seems easier to just remember the 9/5 conversion factor and key in a tiny program to carry it out.

[Thomas Klemm]

(02-10-2024 07:07 PM)Dave Britten Wrote:  Seems easier to just remember the 9/5 conversion factor and key in a tiny program to carry it out.

But what if you are an eccentric professor of numerical analysis who wakes up one morning and feels feverish?

(…)

So tossing both thermometers into a sink of lukewarm water, he reads the following pairs of temperatures as the water cools:

\(
\begin{array}{|c|c|c|c|c|c|c|}
\hline
n & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
C & 40.5 & 38.6 & 37.9 & 36.2 & 35.1 & 34.6 \\
\hline
F & 104.5 & 102 & 100 & 97.5 & 95.5 & 94 \\
\hline
\end{array}
\)

Suppose the professor puts the centigrade thermometer in his mouth and finds he has a temperature of 37°C. Should he be worried?

Insert data:

CLEAR REG

104.5 ENTER 40.5 Σ+
102 ENTER 38.6 Σ+
100 ENTER 37.9 Σ+
97.5 ENTER 36.2 Σ+
95.5 ENTER 35.1 Σ+
94 ENTER 34.6 Σ+

Calculate parameters:

GTO 03 R/S

The parameters \(a\) and \(b\) can now be found in registers 1 and 2:

RCL 1
1.76

RCL 2
33.53

Celsius to Fahrenheit:

37
GTO 01 R/S
98.65

It looks like he is safe.

---

This example is from HP-25 Applications Programs:
CHAPTER 6 STATISTICS
CURVE FITTING—LINEAR REGRESSION

I had to chuckle when I read this:

Quote:This thermometer, however, will not fit comfortably into his mouth. Still, with some ingenuity....

I assume that they had a good time writing these manuals.

[AndiGer]

(02-10-2024 07:07 PM)Dave Britten Wrote:  Seems easier to just remember the 9/5 conversion factor and key in a tiny program to carry it out.

Hehehe … practitioner rather than math theorist

[Garth Wilson]

On the 41 I just have a short program and have key assignments for the functions.

[C.Ret]

(02-11-2024 01:25 AM)Garth Wilson Wrote:  On the 41 I just have a short program and have key assignments for the functions.

This is the path of reason and generally speaking a very good practice. Especially if you only need to convert temperatures between the two scales °F and °C.
001 LBL "C2F"  1.8  *  32  +  END  ASN "C2F" -64
001 LBL "F2C"  32  -  1.8  /  END  ASN "F2C" -63

Now in USER mode you have °F←°C conversion on SHIFT-6 key (same key combinaison as the HP-55) instead of rectangular to polar R→P conversion.
And since, there is no 'g' shift key on HP-41, °F→°C conversion is set on SHIFT-5 key instead of polar to rectangular P→R conversion.

As I pointed out in my previous post, the HP-41 is the most versatile programmable calculator of this era. It is easy to configure to the user's exact needs by the user himself, as long as he understands the operating principles or has the excellent instructions booklet on hand.



EDIT: Very proud of my last code, I have just lent my HP-41C to my eldest son (26 years old) who grimaced while using this surprising portable device. He also laughed when he saw the code.
However, he made two relevant remarks which led us to correct my first version together. He was very surprised by the disconcerting ways he has to follow to modify the code while using only the rudimentary one-line display. He is more accustomed of the large colorful touch screens of actual handle devices.
But, the HP-41C is also a handle that you tap on with your fingers, but not on its display, on its keyboard !!

I put below the result of our collaboration so that you can now have the four temperature scale conversions on your machine.

001 LBL"TCONV" 
002  SF 27  "A:F B:K C:C D:R"  PROMPT
005  LBL A  1  "F"  XEQ 10
009  LBL B  2  " K"  XEQ 10
013  LBL C  3  "C"  XEQ 10
017  LBL D  4  "R"  XEQ 10  GTO A

022   LBL 00  CF 01  CF 02  CF 03  CF 04  RTN
028   LBL 01  FC?C 04 XEQ 04  459.67  -  RTN
034   LBL 02  FC?C 03 XEQ 03  273.15  +  RTN
040   LBL 03  FC?C 01 XEQ 01  32  -  1.8  /  RTN
048   LBL 04  FC?C 02 XEQ 02  1.8  *  RTN

054  LBL 10
055    X<>Y  FC?C 22 XEQ IND Y  XEQ 00  SF IND Y  STO IND Y
061    ASTO L  CLA  FIX 2  ARCL X  FC? 02 "~ ."  ARCL L  PROMPT
069 END
But I invite you to do like us and tap your own code on your favorite machine with your own digits.

[DGM]

Thank you, Thomas Klemm, for your in-depth reply. Either I had a program like the one you wrote up, or it could have been another model. The calculators I first bought years after the HP-25 included the HP-19C, HP-55, HP-67, HP-95LX, HP-100LX, HP-200LX, HP-75C, HP-71B, HP-41C and others. Also, and I hesitate to mention, the TI-59 (gasp!). It might have been one of those. I know that doing this on an HP-55 wasn’t necessary, but perhaps I just wanted to show off to myself that I could do it. I will have to scour the PPC Journal to see if I wrote it up, or stole the idea from someone else.

[Paul Dale]

The HP 32E has temperature conversions and was introduced before 1980.

Pauli

[drbarnack]

The HP 32-S II also had native temperature conversion.

[C.Ret]

The rare HP-31E also has keys for temperature conversion.

The powerful HP-67 can also be programmed. But if you're organized enough, you can grab the dedicated program magnetic cards for these specific conversions.
(And if you're really lucky, the magnetic reader might still be able to read it again - No need to retype programs, that would be so much easier!).

Did anyone know the name of this specific magnetic cards pack ?

[AndiGer]

(02-11-2024 03:31 PM)C.Ret Wrote:  Did anyone know the name of this specific magnetic cards pack ?

Standard Pac that came with the HP-67 bought new; card SD12A or SD12B

[calc-calcs]

It seems that the HP32E would be another alternative to get instead of the HP55 with that temperature conversion and LED display. For now I downloaded the Panamatik HP32 simulation and it works just fine, although the blue lettering on the keys is not very clearly visible due to the angle of visualization being a bit too steep. But it works until I can find the real deal.

Too bad the HP34C does not have that temperature function, as I could have converted one of my surplus HP21s to it with the Panamatik keyboard overlay that I already have but so far have never gotten around to use. Some time ago already did convert a HP21 to a HP29C, and also brought back to life one HP25 and a HP27 with Bernhard's ACT.

Thanks everyone for all the information.

[ThomasF]

The mighty HP-67 actually also had temperature conversion ...

Alas not preprogrammed or built in, but on the back label (together with some other conversions):

Quote:FAHRENHEIT = 1.8 CELSIUS + 32
CELSIUS = 5/9 (FAHRENHEIT - 32)

So, easy to remember and easy to program if you would need it ... !

Cheers,
Thomas

[Jake Schwartz]

(02-11-2024 10:03 AM)drbarnack Wrote:  The HP 32-S II also had native temperature conversion.

Hi,
Unfortunately, the 32SII misses the "pre-1980" requirement, as it was introduced in 1991.
Jake

[drbarnack]

(02-13-2024 06:01 PM)Jake Schwartz Wrote:  

(02-11-2024 10:03 AM)drbarnack Wrote:  The HP 32-S II also had native temperature conversion.

Hi,
Unfortunately, the 32SII misses the "pre-1980" requirement, as it was introduced in 1991.
Jake

It's a fair cop