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I would reccommend my old CDP1802 microprocessor. It does not get any lower power than that, if you can live without power wasters like LEDs or displays. Still, it's now becoming hard to get after a long lifetime and you are probably better off with a modern microcontroller.
I think a PIC microcontroller might do it. They cost five bucks or even less and need prctically no additional parts if you pick the right one out of a vast sortiment. It should have a UART to communicate with the Pi, and perhaps A/D converters for the temperature sensor. Also, it should have a power-on reset built in (not all have that), an internal oscillator, and it should be a low power CMOS version. Hint: The operating power of CMOS devices is dependent on the clock frequency, so set the internal oscillator to the lowest value that still cuts the cake for you.
I have lived with several Zen masters - all of them were cats.
His last invention was an evil Lasagna. It didn't kill anyone, and it actually tasted pretty good.
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Good. I will look if I can find some component that goes from UART to Bluetooth or similar. Thanks!
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Did a quick search and found this: Bluetooth HC-06 Module Interfacing with PIC Microcontroller[^] You might use a similar module and the PIC's USART.
And this, what the temerature sensor is concerned, which is indeed hooked up to an analog input for the D/A converter: Temperature Sensor using PIC microcontroller[^]
If this PIC16F877A has a USART, you can hook it up as shown, forget about the display and hook up the the Bluetooth module to the USART. Done with the hardware, let the software part begin!
I have lived with several Zen masters - all of them were cats.
His last invention was an evil Lasagna. It didn't kill anyone, and it actually tasted pretty good.
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Man, you basically solved the problem! Thanks! 
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Microchip do a massive range of different micro controllers, all at different price points.
If your in the UK, I usually use these guys to supply my PIC's:
V&U Electronic components LTD
You can also use the Microchip search/match tool to find the perfect PIC you need for your project
Microchip MAPS
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This is definitely the way I would do it, but I'd go with a Bluetooth Low Energy version of the HC-06. There are variants, but HM-10 is a good starting search term for a lower power drop-in hardware replacement for an HC-06. Start with the HC-06, get familiar with the hardware/software, then switch to using the BLE version and figure out the differences in usage.
The bluetooth radio is going to be your biggest power draw, hands down, so you should definitely consider the BLE version.
PIC is a really good idea, you can get nA sleep currents out of them if you pick the right chip and know what you're doing (read the datasheets).
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Will do when I manage to fight this boss 
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Yea, that was going to be my suggestion too.
The current PIC18F series are all ultra low power, I have a couple of 18F4550's and some of the really new 18F24Jxx series too.
All of them have built in Analog to Digital, and I2C/USART/SPI serial connections.
On top of that, they all have wake on external interrupt line too, so you could code them to go to sleep, attach the ext int logic line to a WiFi unit that can pull the line high when it receives a wake up packet, the PIC would then sample the analog, send the result to the WiFi unit for broadcast, and go back into ultra low power sleep mode.
Take a look at this guys channel on YouTube:
Andreas Spiess
He does tons of stuff with really low power sensors and WiFi.
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I'm already thinking about how I can use these PICs when I rebuild my old computer. The old processor was CMOS and with it's now low clock speed it was low power at a time when nobody else wasted a thought on that. A PIC would be a perfect companion to feed it its clock, measure the temperature over a sensor and lower the clock frequency if it gets too warm. Automatic overclocking and temperature monitoring. Not bad for a computer design from 1976 
I have lived with several Zen masters - all of them were cats.
His last invention was an evil Lasagna. It didn't kill anyone, and it actually tasted pretty good.
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ha ha, you've obviously not seen my crazy experiments with a 6502 and a bunch of PIC's on a breadboard then
I basically got a tube (25) of PIC16F54's and then proceeded to program them as CMOS/Discrete logic.
Rather than use 4 or 5 different chips, you can easily just build the address decoding directly on the I/O lines or even just program the damn things to replicate a 74LS quad and/nand/or/nor/xor if need be.
Couple that with this that I found on eBAY:
Homebrew 6502 + 6809 + Z80 IC kit with SRAM, EPROM, TMS9918, 6847, 6845 VDPs etc
I've now got a working model of a BBC Model B micro running on a bread board, and executing the original OS and BBC Basic V2.
It get's a bit upset that some of the actual hardware is not there, chiefly the 1770 FDC controller, the serial Acia/ULA and the teletext hardware, but in general it works mostly, and can even play back audio.
On top of that, I built this:
GitHub - shawty/sn76489arduino: Project and Supporting files to turn an arduino into a BBC Micro music player.
A couple of years ago, and (as time permits) am currently replacing the PC side of things, with a PIC and an SDCard reader, so I can just put an SD with music on it in the device and have it play them.
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Peter Shaw wrote: I basically got a tube (25) of PIC16F54's and then proceeded to program them as CMOS/Discrete logic.
That's exactly the idea. These are the things I am sure to know how to pull them off:
- Processor clock and mode control, plus reading programs from a serial ROM and loading them into RAM by DMA. This eliminates the need for any ROM in the memory map, allows bootloading and also allows to stay compatible to the old designs which had a front panel with switches and LED displays to enter code by DMA.
- An interrupt controller. The 'official' interrupt controller takes up too much memory space or too many I/O ports with its numerous registers and awkward addressing if memory mapped.
- PS/2 keyboard aand mouse ports. I would not know where to get an oldschool parallel Keyboard these days.
- The front panel I mentioned before: Both hexadecimal keyboard encoders and hex seven segment drivers are long out of production. Both jobs can easily be done by PICs.
Here some stuff I don't have figured out yet:
- A standard IDE interface is basically just a fancy parallel port. I have a 82C55 here, which would do the trick, but a PIC could be faster. The only thing that I have not figured out yet is how to communicate with the main processor. Even a PIC with a PSP does not appear to be up to the job.
- A 'MMU' that allows me to extend the address bus to 24 bits and fetch any byte from up to 16Mb RAM quickly enough. Here the PSP is again too limited. I need three 'registers' for the address extension of three banks and of course I need to read and write bytes to memory, all over that PSP. Also, I doubt that a PIC can easily do the job within the main processor's bus cycles. At 20 MHz it could only execute one instruction per clock pulse of the main processor. It would only have four or perhaps five instructions to do its addressing. Not enough, unless I slow down the main processor.
I have lived with several Zen masters - all of them were cats.
His last invention was an evil Lasagna. It didn't kill anyone, and it actually tasted pretty good.
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Nice... a bit costly and over my needs though.
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Damn!
If only CDP1802 were still around!
I'd love to hear his take on this!
I wanna be a eunuchs developer! Pass me a bread knife!
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Woah, thanks a lot!
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Will take a look anyway, I read documentation in Russian (I can't read nor speak Russian) and made it work... maybe I will manage again!
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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I'll be happy to beta test the setup when you get it done.
Life is killing me
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It *will* take a while, I'm quite busy  don't hold your breath on it, but I will do it. The smartest thermostat I ever saw is no longer in production...
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Thank you. In new Orleans we have both hot and cold weather that is partially unpredictable.
Life is killing me...……..
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This brings back memories of the systems I used to configure and install back in the 1980s. RTDs for temperature sensors, unshielded twisted pair back to the cabinet, and wired into a multipoint analog input card that measured the resistance to which I applied a non-linear formula to get temperature.
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Look at Texas Instruments, they have a number of small inexpensive ($25) dev boards. They're called Launchpads. I used one on a project at work to start developing code before we had are own hardware. Also, you get the development environment for free, it's called Code Composer Studio (based on Eclipse).
If you use one of their 'Tiva' processors (ARM based) they've got lots of example projects and provide you with code that accesses all of their built in peripherals. The samples and such are include in what they call 'Tivaware'.
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