Creating a low power device which runs on a battery. It only needs to count up. Resettable would be nice but not required. Something in the range of 10-12 bits should be fine. Though for margin, closer to 11 or 12 bit would be preferred. There are a couple external devices which periodically and asynchronously trigger INTs (~100Hz range). The problem, in order to save power I need the uC to sleep a fair bit. Obviously if its counting INTs its not sleeping. I know there are IC counters and I've hears some offer SPI/TWI interfaces. Would it be possible to have a counter count the INT from the two external devices and simply periodically wake, pole, and reset the counts via TWI or SPI? This way the uC only needs to wake at perhaps 1-10Hz. The exactly uC poll rate has not been determined yet.
Obviously the first question is, is it likely to be worth the effort and save power? Does such an IC exist? How much does it approximately cost? Does this sound like a reasonable approach? Obviously if there are better approaches, lay it on me.
Note: I may not be referring to the proper type of IC. I'm not talking about a visual counter LCD. I'm talking about something which counts pulses. So please correct me if I'm referring to the wrong type of component.
Edit: Note made.