Narrow-Bandwidth Television Association

A mathematical conundrum, there are many others too..one could say totally useless, but a novelty at the same time...

https://en.wikipedia.org/wiki/Collatz_conjecture

Just like Andrew mentioned here many years ago, why not have a device that continually displays the calculated number of pi to greater and greater precision? It's an apparently irrational number and potentially never ends. We don't know. Perhaps another almost futile exercise, but it's just a bit of fun.

So how far could a small PIC micro would get before it simply runs out of memory space? A novelty, yes. A waste of time, perhaps. It's been done before to far greater numbers than I could ever imagine, very true. So why bother?

"I don't know." would be my honest answer, "Why not?" my defense.

Steve A.

There are 3 types of people.
Those that are good at maths and those that aunt.
.........and some cannot spell either.

Which reminds me of the signoff of a member on another forum to which I belong that goes something like:
"There are 10 types of people - those who understand binary and those who don't."

There are 3 types of medical doctors:

1: Surgeons, they don't know what happend, but they will repair it,
2: Internists: they can tell you precise what is wrong, but they can't do anything against it
3: Psychiatrists: they don't know what went wrong and they cannot repair it.

Unhappily I am at the moment in treatment of a cathegory 2 medical doctor.....

Dave Moll wrote:Which reminds me of the signoff of a member on another forum to which I belong that goes something like:
"There are 10 types of people - those who understand binary and those who don't."

I only have one opinion about binary but on analogue it varies.

Does anyone know of a Terminal Emulator for Win 10 that has a baud rate above 921,600? I use RealTerm and that's its maximum speed. It's just the software that's needed, the hardware is sorted out already...he hopes...

Though the manual for RealTerm does say that it can go at any speed the PC is capable of generating - just enter the number in the 'Speed Box', overwriting the standard rates. I've not tried that yet.

Steve A.

To continue...

"I used to be indecisive, but now I'm not so sure."

Steve A.

Some people are good at spelling. Others aunt.
Others cannot spell SCHOOL. They incorrectly, put the first O after the second O.

OK, returning to the rather useless (it would appear) Collatz Conjecture...

Start with 1, that very quickly gets stuck in the terminal loop of 4,2,1,4,2,1...obviously 2 and 4 as well...3 also. Continue on in sequence testing all numbers incrementing the starting number by 1 each time. Try all up to 9 say, that gets 'stuck' too. Next 10 which being even is divided by 2, so 5. Now we've already tested 5 so halt and try 11 next. That gets 'stuck' also...

Next 12, becomes 6 - already tested. likewise 14, and it's true for all even numbers when working in this manner, so there is no point in testing even numbers. If there is an 'escape' from this conjecture it's gonna be an odd number. Tell me if I'm wrong here.

That's cut down the amount of time this takes by half, maybe(?)

So start at 1, when it gets 'stuck' increment the starting number by 2.

Also say when you reach 1001 the sequence runs 1001, 3004, 1502, 751, so if the sequence becomes less than the number you started with, halt, as 751 has already been tested and will get 'stuck' as well. I've no idea how much time this might save but with larger numbers it could be significant.

r.e. above...1001 becomes 3004, but that's even, as before there is no point in testing even numbers. So stop right there!

Does this solve/prove/disprove the conjecture? Or have I missed something?

Steve A.

Now as this has been tested up to 2^68, so you may as well start from there (if you really must), 2^68 is

0x10 00 00 00 00 00 00 00 00h Hex. (Nine bytes). Or..

295,147,905,179,352,825,856d Decimal.

Steve A.

Now, 2^68, let's get there first, irrespective of others who may already have done it already.

There's probably not enough time for this poor micro to get anywhere near it, but when I expire I can say I gave it a shot...

Note the battery arrangement even for the briefest of power outages...or up to several hours, even here they're very rare for more than a few seconds...not so 20 years ago...

Stupid and worthless idea? Yep, you bet!

A question a few may ask is why use a 28-pin device when there's so many pins free? The future implementations might/would be one response, but smaller (physically) devices mostly cannot reach these speeds...the white LED, "Record Set" is just whimsical hopefulness.

I wanted to reduce the +5V current consumption when power does fail. So the micro continues on with no real LED drain on the battery supply. If it's been running two years I don't want it to have to start over...therefore I need a way to replace the batteries without compromising that ethos...

Steve A

I've made a few minor changes to the previous, mainly in the power supply, plus one or two others in the device proper. They're all quite minor so there's no point in updating the circuit diagram at this point. Also considering Andrew's suggestion for a 'Pi' version. More on that later...I've still got a few Nixies spare, maybe another use for them?

This is all being done in spare time outside of 'real work' and other NBTV/SSTV stuff...

Steve A.

A few other changes...I've changed to processor to a PIC18F25K20 and dropped the logic supply to +3.3V which may help on power failure. So now only 4x1.5v AA cells needed during a power outage. Very little other changes required, the micro pin-out is virtually identical. 'Pi' version in the works...speeds still the same.

Steve A.

Reviewing the Duracell site, if the power consumption is 16mA, probably less, a set of four 'Coppertop' AA batteries should last around a week. Good enough. Though I'd prefer something better than relying on spring contacts...especially at these lower currents and voltages...

Steve A.

Contact problems are a point at low voltages, say less than 1 volt. Low currents may contribute. But 6 volts is not a low voltage and 16 mA is not a low current. I regularly have contact problems with the reed contact in the sensor of my bike computer. There the voltage is low, may be 1.5 volts, and the current is low, much lower than 1mA.