RPN: HP 32S & DM42: Converting Real Numbers to Hexadecimal Approximations

RPN: HP 32S & DM42: Converting Real Numbers to Hexadecimal Approximations

Introduction

We know calculators that have base conversions easily convert integers to different bases. But what about all real numbers? Not so much. Today’s blog will tackle it.

The procedure given today should work for converting from decimal to octal, binary, and hexadecimal. I chose hexadecimal:

0.A B C D… _16

The digit A is in units of 1/16.

The digit B is in units of 1/16^2 or 1/256.

The digit C is in units of 1/16^3 or 1/4096.

The digit D is in units of 1/16^2 or 1/65536.

and so on.

Note: The procedure considers positive real numbers only.

Example: Convert 7.86 to hexadecimal using 4 places

In hexadecimal, 4 places translates to terms of 1/65536.

Separate 7.86 into its integer and fractional parts.	Integer Part: 7 Fractional Part: 0.86
Convert the fractional part to n parts of 65536. (16^4)*	0.86 * 65536 = 56360.96
Round n to the nearest integer. Use the formula: int(n + 0.5) = int(n + 1/2)	Int(56360.96 + 0.5) = 53361 (round(56360.96, 0) = 53361)
Convert both original integer part and the last result to hexadecimal.	Integer Part: 7_10 → 7_16 Frac in terms of 65536: 53361_10 → DC29_16
**If the fractional part has less than four* digits showing in the calculator, pad the converted part with zeros on the left.
The approximate answer reads as:	7.86_10 → 7.DC29_16
Recall in Hexadecimal: A=10, B=11, C=12, D=13, E=14, F=15.

* precision: number of places.

HP 32S/HP 32SII/DM32 Code

H01 LBL H

H02 ENTER

H03 IP

H04 x<>y

H05 FP

H06 16

H07 4 (** - accuracy level, number of places)

H08 y^x

H09 ×

H10 2

H11 1/x

H12 +

H13 IP

H14 HEX

H15 STOP

H16 DEC

H17 RTN

HP 42S/DM42 Code

01 LBL “→HEX”

02 ENTER

03 IP

04 x<>y

05 FP

06 16

07 4 (** - accuracy level, number of places)

08 Y↑X

09 ×

10 0.5

11 +

12 IP

13 HEXM

14 STOP

15 EXITALL

16 RTN

When the program stops initially, the results are shown as follows:

Y: integer part

X: fractional part – right justified

Remember the number of places (precision) because if the fractional part has less digits, pad zeroes to the left.

Examples

n = precision = 4

Decimal	Y: Hex Integer	X: Hex Fractional (displayed)	Result (base 16)
3.5	3	8000	3.8000
π	3	243F	3.243F
√2	1	6A0A	1.6A0A
0.6732	0	AC57	0.AC57
0.0002	0	D	0.000D
e^4.1	3C	571D	3C.571D
8.2^1.7	23	C460	23.C460

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

All posts are 100% generated by human effort.  The author does not use AI engines and never will.

Spotlight: TI-32 Solar from 1988

Spotlight: TI-32 Solar from 1988

Today’s spotlight is on a standard scientific calculator from Texas Instruments… with a twist. First, let’s start with the quick facts.

Quick Facts

Model: TI-32 Solar

Company: Texas Instruments

Timeline: 1988 (possibly 1989?), this model was very short lived

Type: Scientific

Memory: 1 memory register

Power: Solar

Screen: 10 digits

The TI-32 Solar was a scientific calculator that was sold briefly by Texas Instruments in the last 1980s. The function set is a combination of the TI-30 Solar and the original one line TI-34:

* trigonometry, decimal/dms conversion, rectangular/polar conversions

* logarithms, anti-logarithms (10^x, e^x), powers

* one variable statistics (mean, deviation, sums)

* binary/decimal/hexadecimal conversion (and just conversions, strangely no octal)

* 3-decimal random number generator (RND)

* percent function

The Polar/Rectangular conversions use the [ a ] and [ b ] keys. [ a ] is for x and r, while [ b ] is for y and Θ.

The statistics mode is one-variable only. Though I am not a fan of the STAT mode being the alternative function of the [ C ] key, thankfully, the stat mode works.

What truly sets the TI-32 Solar apart are two things:

(1) The orange trim and keys on a dark gray keyboard. This is a very rare color scheme, especially orange until Texas Instruments started to release the TI-30XIIS and the TI-84 Plus CE in various colors.

(2) The screen tilts. The screen is a set on a hinge that allows the user to tilt the screen to different angles, which allows for more ergonomic operation. To put the calculator away, tilt the screen to be aligned with the keyboard and use the slide case. I think this is a really neat idea. The tilt mechanism seems to hold out well for a nearly 40 year old calculator.

Source

Woerner, Joerg. “Texas Instruments TI-32 SOLAR” Datamath Calculator Museum. September 20, 2002. Accessed July 7, 2025. http://www.datamath.org/Sci/Modern/TI-32Solar.htm

Eddie

 All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

All posts are 100% generated by human effort.  The author does not use AI engines and never will.

Retro Review: TI-36 Solar

Retro Review:  TI-36 Solar 

Just the Facts:

Model:  TI-36 Solar

Company: Texas Instruments

Type: Scientific

Display:  10 digit with 2-digit exponents

Battery:  Solar

Logic: AOS

Memory Registers: 1

Years: 1984-1990

Features:

*  Complex Number Arithmetic

*  Rounding Numbers (to fixed number setting)

*  Base Conversions

*  Normal Distribution

*  Single-Variable Statistics

Examples with Complex Numbers

MODE 5:  CPLX

There are two separate registers to hold parts of complex numbers:

[ a ]:  Real part (rectangular),  Radius (polar)

[ b ]:  Imaginary part (rectangular), Angle (polar)

Example 1:  (4 + 3i) * (11 - 2i)

4 [ a ] 3 [ b ] [ × ] 11 [ a ] 2 [ +/- ] [ b ] [ = ]

Display:  50  

Press [ b ], Display:  25

Result:  50 + 25i

Example 2:  Convert 3 + 2.4i to polar form, degrees

3 [ a ] 2.4 [ b ] [ INV ] (R>P) 

Display:  3.841874542

Press [ b ],  Display:  38.65980826

3 + 2.4i = 3.841874542 ∠ 38.65980826°

Examples with Normal Distribution

MODE 6:  STAT

There are three functions that determine the area under the normal distribution curve:

P(t) from - ∞ to t,  lower tail curve

R(t) from 0 to t

Q(t) from t to ∞, upper tail curve

Note that for any t, P(t) + Q(t) = 1.

Also note that P(t), R(t), and Q(t) will operate on the standard normal curve, where μ = 0 and σ = 1, regardless of the amount of data points entered in Statistics mode through Σ+.

For z = t =2:

2 [ INV ] ( P(t) ) returns 0.97725

2 [ INV ] ( R(t) ) returns 0.47725

2 [ INV ] ( Q(t) ) returns 0.02275

Comparison:  TI-36 Solar vs. TI-35 Plus

The TI-36 Solar and TI-35 Plus have the same set of functions and features.  You can see my retro review from 2017 of the TI-35 Plus here:  http://edspi31415.blogspot.com/2017/09/retro-review-texas-instruments-ti-35.html

There are several keyboard differences:

Shift key is marked [ INV ] (with 2nd above it) for the TI-36 Solar, and the shift key is marked [ 2nd ] for the TI-35 Plus.

The equals key is twice in vertical height, covering the spans of the bottom two rows on the TI-35 Plus.

The top three rows* (all of the shift markings remain intact):

TI-36 Solar:

[CE/C] [ 1/x ] [ a ] [ b ] [ AC ]

[ hyp ] [ sin ] [ cos ] [ tan ] [ DRG ]

[ INV ] [ x^2 ] [ log ] [ ln x ] [ y^x ]

TI-35 Plus:

[ 2nd ] [ x^2 ] [ log ] [ ln x ] [ OFF ]

[ hyp ] [ sin ] [ cos ] [ tan ] [ DRG ]

[ y^x ] [ 1/x ] [ a ] [ b ] [ ÷ ]

The [ hyp ] key has the hyp^-1 label over it on the TI-35 Plus.  

*not counting the [ON/C] key above all the rows on the TI-35 Plus

Comparison:  TI-36 Solar vs. the original TI-36X Solar 

Here is my review from 2018 for the TI-36X Solar:  http://edspi31415.blogspot.com/2018/09/retro-review-texas-instruments-ti-36x.html

The TI-36X Solar:  

*  does not have the complex arithmetic mode of the TI-36 Solar

*  adds the Boolean functions AND, OR, XOR, XNOR, and NOT to the BIN, OCT, and HEX mode

*  adds linear regression

*  adds a second shift key, [ 3rd ]

*  there is no [ MODE ] key, every mode is selected through [ 3rd ] (key) combos

*  adds a fraction/decimal conversions

*  adds 8 scientific constants and 10 metric/US conversions

Verdict

Like the TI-35 Plus, the TI-36 Solar is a step up from the TI-30 series (1980s versions of TI-30).   Again, the TI-34 (1987) has the Boolean functions and fraction functions that the TI-36 Solar doesn't.  You don't have to worry about batteries at all since the TI-36 Solar runs entirely on solar/light power.

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.