HP Prime : Funny Complex Trig in CAS View

(Update: this has been corrected in emulator version 5447 dated 2013-11-25)

OK, so posted some Prime results on the following forum:
For those that have an actual Prime calculator....

This refers to the emulator with firmware rev. 5106. From the link above it is evident that the first release of the actual Prime will give the same result.

Here's the screen capture again:

So what's my problem with this?

OK, apart from the "+-" and "--", quite a bit.

First, let's look at ACOS(2):

The "radian mode" answer is correct:

 (http://mathworld.wolfram.com/InverseTrigonometricFunctions.html equation 14)

This agrees with the symbolic radian mode answer of the Prime.

Numerically:

Now:

So:

But now let's look at the "degrees mode" answer. In the complex domain it is more common to continue with radian angles even when settings are in degrees. However, it is possible to do it in degrees, but it must be done carefully and correctly.

Let's look at the HP Prime approach:

Oh, oh, we are now subtracting a radian angle from degrees!!!

And that's how the Prime gets it's incorrect answer!!

The right way:





Similarly the Prime gets the wrong answer for ACOS(-2) in degrees mode.

Adding a crystal and capacitors the the HP-20b, HP-30b or WP-34s

Here is my experience of mounting the capacitors and crystal in the HP-30b or WP-34s.

The tools I used were simple:

Choosing the crystal and capacitor:
 Pretty much any 32.768 kHz crystal of the right dimensions will do. Usually you will find them under "watch crystals". I used the Abracon AB26T: http://www.abracon.com/Resonators/AB26T.pdf

Choosing the capacitors:
For information on attaching a crystal and capacitors to the AT91SAM7L processor used in the HP-20b/30b see this application note page 9:
http://www.atmel.com/Images/doc6369.pdf

Equivalent circuit:

Total capacitative load on the crystal is the 2 external capacitors in series (as far as the crystal is concerned, the ground connects C1 & C2 in series to itself) + the capacitance of the processor and stray capacitance in parallel:
CL = (C1*C2)/(C1+C2) + Ci  + Cs 

where:
CL = the capacitative load on the crystal
C1 & C2 are the 2 external capacitors we are going to add
Ci = internal capacitance of the processor for the crystal pins
Cs = stray (track & PCB) capacitance

If we keep the 2 external capacitors the same value: C1 = C2 = C
then
CL = C/2 + Ci + Cs

From the Atmel app note above: Ci = 2.5pF
From the crystal data sheet: CL = 12.5 pF
Cs estimated ~1 pF
thus C = (CL - (Ci + Cs))*2 = 18 pF

The Atmel datasheet specifies a maximum of 20pF, so 18pF is in the ball-park.

http://www.atmel.com/Images/Atmel_6257_32-bit-ARM7TDMI-Microcontroller_SAM7L_Datasheet.pdf (section 35.4.3 table 35-15).

For choice of capacitor, I avoided Y5V in this application as they have a wide capacitance variation with temperature which will alter the frequency of the crystal - not what we want for a stable clock.

I would recommend X7R or NP0/C0G. I used Multicomp - MC0603N180J500CT - (MLCC, 18pF, 5%, 50V, C0G / NP0, 0603).

The size of the capacitor is 0603 (1.6 x 0.8 mm).  This is the size of a grain of sand. Order more than two as it is easy to loose them!

(Note 0603 is the imperial size SMT, in metric it would be 1608. Be careful to check when ordering!!)

OK, so now for the mounting. I did the capacitors first and the the crystal.
Here are a video I made mounting the first capacitor:
(Note, I am not a professional solderer, but a home hobbyist)

The final product:

I hope you have fun doing yours :-)

(I ordered my crystal and caps in bulk, so have about 100 spare sets. Anyone want some for postage only, see eml below. Each set  will have 1 crystal and 4 caps).

Entering a complex number in vector on the HP-50G

Entering complex numbers can be done as folows:

Rectangular:
standard form: x + yi
or
vector form: (x,y)

Polar:
can only be entered as vector form: (r,<ø)

The HP-50G can only accept real numbers in Vector Form:
E.g.

is not allowed.


 It has to be entered as:




Here is one method to convert and enter the number (other suggestions welcome):

(note: change to "complex" mode at 00:12 is Press-and-Hold LeftShift & press i  (on TOOL button)

Curve fitting program for the HP-35s (combines the manual's programs into one label)

Chapter 16 of the HP-35s manual has programs for 4 different curve fittings. They are spread accross several labels and so take up valuable labels that could be used for other programs.

I have combined them into one label.

Here are instructions:

and here is the program listing:

Comments, suggestions & corrections welcome.

(Edit: updated as C065, C114 & C118 are e^x and C128 & C135 are y^x and were showing incorrectly)

Corrections in calculations on a modern "textbook" display calclator

Modern calculators that have a real textbook like display can offer advantages not only to inputting formulas, but when realising a mistake several steps down the line. Here is one such calculator that, when an error is corrected a few steps back, the updated results are automatically flowed down.

Here is the problem statement:

The respondent has come to the second part and written down some equations and decided to calculate it on the calculator. When the last answer seems a bit strange, an error is found in the earlier entry, corrected and the correct answer is immediately visible at the last calculation.

Installing AAAA batteries on the HP-30b

As I am of the opinion that coin cells are not a good idea for programmable calculators, particularly those powered by processors with high speed capability, I decided to look into modifying my HP-30b to take AAAA-style batteries.

For non-programmable calculators, coin cells are fine as the routines for all functions are optimised and will complete usually within microseconds (some really complex functions may take a few tenths of a second at most).

However, programmable calculators allow the user to write their own functions and routines that may have many iterative loops that could take several seconds or even hours to complete. This often puts the processor in a mode that a higher current usage. The current drawn during this time is usually at levels that coin cells struggle to maintain – they have significant internal resistance to start with which gets worse as they discharge.

I have read that the ATMEL based range of calculators can use upwards of 20mA during program execution. There has been mention that the processor speed is reduced if a program continues for an extended period. However, someone regularly running a program that takes a few seconds, would put some strain on the CR2032.

Some comparisons of data between CR2032 (used in the 30b) and AAAA cells:

Parameter	CR2032	AAAA
Internal Resistance	10 000 – 40 000 mΩ	150 to 300 mΩ
Voltage	3V	1.5V
Capacity	230mAh @ 0.2mA to 2.0V	600mAh @10mA to 1.0V

The 30b uses 2 CR2032 in parallel, that is ~460mAh. To get the same operating voltage, two AAAA would need to be in series, still giving 600mAh capacity. Also with an internal resistance of two orders lower than the CR2032’s, voltage drop for the AAAA at 20mA is max. 0.006V whereas the CR2032 is min. 0.2V. Thus the AAAA should give a lot more "head room" and be less likely to cause the calculator to die or behave erroneously during "heavy" use during program or formula execution.

Also, I have repurposed this unit to a WP-34s.

Opening the 30b

First remove the back cover and undo the 5 screws, 2 are under the bottom rubber:

Just lift up the corners to get the last 2:

Now carefully pull the back off the front, bending the sides outwards to undo the clips:

 DO be careful so as not to damage the screen.

Finding space for the 2 AAAA cells

The cells were taken from a 9V battery. They are already conveniently tab welded together, so they can be split into pairs. (for more info to dismantle a 9V, google something like "AAAA from 9V").

NOTE: the cells that I obtained from a 9V battery, were of OPPOSITE polarity than expected (flat side was +ve) - so check first before connecting!!

After some measurements, I decided that directly behind the screen was the only place that had a reasonable chance of success such that when the back sliding cover was in place, it would look like an ordinary 30b.

BUT this would mean removing some of the padding that normally protects the screen.

First, cut a rectangle in the back:

I measured the approximate size for the 2 AAAA and marked it, drilled small holes around the inner perimeter of the marking, cut it out and smoothed the edges as best I could.

Back with original screen backing plate in place:

Screen backing plate removed and hole cut in its place: (note the metal plate - is it really necessary for the screen or just to give the calculator some heft?)

The rubber spacer in front of the screen also had to be removed:

Removing all this padding probably makes the HP calculator engineers cringe. But then I may have lost the guarantee when I opened it and started cutting... ;-)

However, I did think the screen needed a bit of protection. A piece of thin foam packing material was just right:

Some of this came with the WP-34s programming cable.

After seating the LCD properly and bending the wires in approximately the right route (to fit through the openings in the backing ribs - see dashed lines):

The two halves are clipped back together:

And now to see how much they protrude:

This should be fine when the slide on battery cover is replaced:

And it sill works:

The most frustrating bit for me was getting the inside of the LCD window clean, possibly because it's winter and the dry heated air in the house is making the plastic more static. Hopefully now it is closed there won't be too much dust getting in even though the gasket is removed. Only time will tell how susceptible the screen will be to damage without it's normal padding and batteries right behind it.

Other observations

The quality control of HP calculators has come to light again. When I first opened it up, I noticed a small chip on the top of the screen. Now note that I never brought a sharp object anywhere near the calculator and I am always careful to ensure the screen in not bent.

So now it's a race as to what will cause the screen to fail first, the batteries directly behind it or this chip cracking through on a cold winters night?

Opening the HP-12C Platinum (original silver faceplate)

A while ago I got a HP-12C platinum (aka HP-12CP) off eBay. It had a depressed decimal point key. Today I decided to investigate, so opened it was. To open, first remove the battery and the rubber feet and then undo the 5 screws. With a plastic pry tool, lift off the back. the PCB is now visible. To go further, the tops of the heat stakes have to be removed. I cut them off carefully using the blade of a Stanley knife (Note - these will have to be replaced by screws. As the plastic stakes are hollow they take small screws quite easily but these may be difficult to find. I salvaged some from a 50G that fell into dis-repair due to screen problems. Look out for my next blog). Carefully taking the PCB off (to which the screen is attached) reveals a rubber mat under which is the keyboard.

Back removed showing PCB with heat stakes cut off and showing some of the replacement screws

All keys apart from the two shift keys are hinged plastic type. I have seen this (dis)proven technology before, in a cheap '70s four-banger (see the picture of the Satek 8M - suffering the same problem). This is not what I would expect in a top-of-the-range calculator that this is supposed to be! The shift keys are on separate rotating hinges - much better, but what do HP think? that the shift keys are used most often? is a calculator not used for numbers? wouldn't it seem  reasonable that the number keys would need to have the better design?

The loose 12CP key

Cheap '70s Satek 8M with broken hinged key

In this case the decimal key has become totally detached from its hinges and the 9-key has one leg detached and the 5-key is showing signs of weakness at the hinges - as I would expect the number keys are first to go as they are likely used more often.

To get the key more-or-less back to normal, it needs a spring to keep it lifted up and a "hinge" to rotate on. The hinge was fashioned from aluminium tape and a sponge added as I did not have a spring of the right size handy. (Other keys were taped as well in the hope that it will prevent breaking, note the white piece of sponge under the decimal key in the last picture).

The repaired unit put back together:

The decimal key feels a bit squidgy, so I guess an actual spring would be the better solution.

PLEASE NOTE: the newer black faceplate model apparently has a better keyboard (it certainly feels better).