Electronic – replace watch quartz with DS3231 32 kHz output

The only RTC I know of which worked with hundredths of a second was the long obsolete Intersil ICM7170. The datasheet isn't clear how the 100Hz was achieved. The crystal frequencies which it was designed for are perfect powers of 2: 32.768kHz (i.e \$2^{15}\$), \$2^{20}\$Hz, \$2^{21}\$Hz, \$2^{22}\$Hz, yet the datasheet says it derives a 4000Hz clock from them, from which the 100Hz is derived. 32768Hz is not a multiple of 4000Hz, so this can't be done with a normal divider. They probably used a fractional divider, like supercat describes.

Anyway, the ICM7170 is obsolete, so we need something different. While there might not be 32kHz RTCs, there are 32.000kHz crystals, and with a 74HC4060 you get an oscillator + divider.

The 32kHz crystal probably needs the same load capacitor as a 32.768kHz crystal. The 330k\$\Omega\$ resistor limits the drive power to the crystal. This is significantly higher than the 2.2k\$\Omega\$ recommended by NXP; a 32kHz crystal typically has a drive level of less than 1\$\mu\$W. If the oscillator doesn't start decrease the resistor's value somewhat.
Use the :32 output Q5 (pin 5) to get a 1kHz clock which you can feed to your microcontroller interrupt pin.

You can then use the 1kHz heartbeat interrupt to derive a 10ms software timer.

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Alternatively a microcontroller can be used. This will be slightly more expensive than the 74HC4060, however, and might also consume a bit more power. I've used TI's MSP430F1101 at 32kHz and 3.3V which needed only 4\$\mu\$A though. Run it off the 32kHz crystal and use a timer to output the 100Hz signal. You can even output different frequencies simultaneously, for instance 1000Hz, 100Hz and 1Hz, or select the frequency on a specific output by setting a pair of I/O pins. Or you can select the frequency via the UART.

Usually 32768Hz quartz crystals are used in the clock applications. This standard is very widespread and these crystals are cheap and highly easy to find.

In order to switch the clock to work twice as fast, you will need 65536Hz crystal, that is not standard, not so common and probably not so easy to be purchased. For example my local distributor has 32768Hz crystals on $0.1 each and the next frequency available is 1.8432MHz

Another possible issue is the work of the internal oscillator with the changed crystal. It will probably work, but some capacitors might need to be replaced with other values.

And at the end, the last possible problem is the stepper motor of the clock. Is it capable of stepping twice as fast as usual?