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# Calculator blog

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## Calculate digits of e

Several years ago Valentín Albillo posted a document, "Long Live to the HP15c", where he lauded the HP15c, describing how wonderfully put together it was. Also, to demo the calculator possibilities, he created a program that calculated digits of e, using the expansion e = 1 + 1/1! + 1/2! + 1/3! + 1/4! + ..., and using matrices.

The method he used was able to get up to 208 digits of e in the available memory of the HP15c. He himself said the program was not optimized for performance - indeed, he introduced a Pause displaying the digit being calculated, so you can imagine how slow it could be.

The program gets 8 decimals of e per register used; the input to the program is the number of registers to be used. The time to get 208 decimals is 62'43'' with the original HP15c. The program as such could not be run on the HP15c LE, since it had the Pause bug, and this program uses PSE once per iteration!

I have run the program and found that for the HP15c CE the biggest time consumer was the pause step. (it did work well - the PSE bug has been erradicated in this firmware!). I removed it and the previous RCL I, and got 21 seconds for the 208 decimals - quite an improvement from the original.

The maximum digits in the original HP15c were 208. The program uses 2 matrices with the same size, in this case 26x1. Therefore it is 52 registers used. The program occupies 10 registers, and we have left 3: we have occupied 65 registers.

Valentín told me that to go further we need to get just 7 digits per register. So far we have lived with 8 since there were 2 max digits for carry - so 8+2 = 10 which is the mantissa size in the HP15c. However, for more than 26 registers the carry digits are 3 - and we need now to plan for 7 digits + 3 carry = 10 mantissa digits per register. So step 11 needs to be changed from 8 to 7. Now we could only fit 26*7 = 182 decimals in the original machine - but now we have additional memory.

With this new program we can get up to 42*2 + 10 + 3 = 97 registers used, with 42*7 = 294 digits of e !!

The speed is still very good: less than 48 seconds to calculate all of 294 digits !

Another example of the power of the new HP15c Collector's edition !!

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## Selling the HP15c CE to non-fanatics

We created this website because we are calculator fanatics - much like you. And we see the beauty of the HP15c. In some cases we've been longing for the calculator for a long time. In any case, no one needs to give us a reason to get one.

However, it is difficult to "sell" the HP15c to non-fanatics. As example, to my children. Both are technically-minded: one has just finished sophomore year in engineering, and the other is in international baccalaureat and intending to get into engineering too. Both are users of the HP Prime, and swear by it. It gives them an edge compared with their peers that use Casios or Texas.

However, it is difficult for me to convince them to get a HP15c - when it becomes available within a year.

The first obstacle comes with RPN. No matter how I insist, they prefer the text entry method of the prime - with a clear view of the equation being introduced. They have never enabled the RPN mode in their Primes.

The second obstacle is the small screen. You need to know what you are doing at every time, You need to know what you have in the four stack levels. Also you have no alphanumerics, and you can't get any graphics. What is the point, also, to edit a matrix in such a cumbersome interface? Can't touch the HP Prime when editing matrices, programs, etc.

Calculating with the HP15c has become second nature for most of us - and that gives us incredible speed when using these machines - well above in many cases than when using the HP Prime or the HP50g - simply because we know the machine better and RPN helps us. But this speed does not apply to our children.

So, I have not been able to convince them yet. At this point, they cannot see any instance where they could not have a Prime with them. I can tell them that in my professional life I have seen people with their 48 on their tables - but for any of them I have seen 4 or 5 with HP17bII or HP12c (gold or platinum) and 40 people using 4-bangers. There is just some times when you cannot take a Prime with you - but there will always have a place in your jacket for a Voyager.

Me? I like the landscape format of the Voyagers, and I am now having a good time using the HP15c for really everything now. They will come onboard sooner or later.

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## Solving a 8x8 equation system in the new HP15C Collector's Edition

We have tested the matrix capabilities of the new HP15C Collector's Edition, by trying a 8x8 equation system. This was completely impossible to do with any of the previous releases: they maxed memory allocable to matrices at 64 - so you could only invert a 8x8 matrix - but not solving a system since you needed the independent values' vector.

We started creating the two matrices, and filling them with random data, in the hope they would not be singular. To do that, we wrote a short program using the USER feature so that it fills cell by cell of both matrices.

Here is the result:

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## Just in...

Here is what we have received this morning - aHP15c CE test unit.

Let's do a proper unboxing tonigh, shall we?

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## Difference between standard case and leather case for the HP15c calculator

We have received many questions on the leather vs PU cases for the new HP15c calculator.

The first comment that comes to mind is that it is not "either/or". When you select the Leather version, you get the leather case plus the case the HP15c comes with. So if and when one of the two breaks down, you still have the other.

The second: here is how the HP15c CE PU case looks like:

The leather case is a true Ubrique cowhide leather: (the one sold with the HP15c is the black model). However, it can be available in 3 colors: Burgundy, black and brown. The one that looks ok with the HP15c is the black one!

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## HP15c Collector's Edition speed tests

I mentioned in yesterday's blog that I intended to do some speed comparisons between the HP15c Collector's Edition and othe HP15c models - however, I am missing a HP15c LE since the one I have is bricked from a previous attempt at reprogramming it with a firmware with more memory. Also my Mac cannot handle a RS232 interface properly (at least I have not managed to do it - I did with older verisons of Mac OS) which is required for the LE to be reprogrammed.

However, Gene Wright has managed to do it with all three models - you can see his findings here:

(I have to say that I replicated perfectly the measures for both the original machine and the HP15c Collector's Edition prototype I have. You can find the original programs in HPmuseum)

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## The HP15c Collector's Edition

You may already know the news: there is a new reissue of the HP15c: the Collector's Edition. Today the HP licensee Moravia has announced this new product, of which only 10.000 units will be produced. The calculator will be sold in a package that can also be used for display - same as the HP15c Limited Edition of 2011, or the HP12c 30th Anniversary.

The units are expected to arrive to Europe early July, with a part being flown in and the rest shipped in a container with the rest of the production of new HP calculators.

What are the differences between this unit and the previous two versions?

• 100x faster than the original model - similar speed as the limited Edition.
• More memory: 98 registers instead of 65 - 672 programming steps instead of 442. There could have been more registers, but the team chose a safer memory configuration instead of more memory but that can give problems on display and in extreme situations (more than 1000 programming steps, big matrices, etc.)
• All known LE bugs have been fixed.
• Far longer battery life than the Limited Edition: aside from the original model (whose batteries lasted many years ), the Limited Edition was not known for long battery life: typically two months of normal use. In addition, the low battery indicator would not lit, not giving the user the chance to change batteries in time to avoid memory loss. This new version has longer life: my prototype has been running with the same charge since August 2022. Apart from having a lower consumption processor, there have been some strategies to reduce consumption: not all keys run at the same speed. Those that run programs, matrix calculations, solve or integrate run at 4x the speed of the rest of the keys.
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## Are the new Voyagers firmware re-programmable?

Well, yes and no.

Yes, it can be done. We have reprogrammed HP12c into HP15c and HP16c - with the proviso that you need to place an overlay in front of the keyboard since the key assignment is completely different!

However, to do so you need a suitable file (there are several available in the web), but, most importantly, you need to get a programming cable - and that's the difficult thing, since it is a non-standard cable. For a while HP produced some 1000 cables for the HP15c Limited Edition. Now, this cable fits in the hole for the new Voyagers - but uses a different pin scheme and protocol - the latter being USB protocol, while the old HP15c LE has a different protocol. So even if you have the cable, you need to modify it so that it can be used! There are instructions available if you have managed to secure one of the original cables.

Once you have that, you need an Atmel-provided program to download the firmware. That is an easy part, once you have the above. In fact, it is an easier process than the old calculators: you just need to press and hold erase in the cable, then press reset, then release erase - and you're set to go! I have not managed to brick a single unit - while I bricked several of the old HP15C LE units.

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