There are several microcontrollers that have very low current usage. Texas Instruments MSP430 series, some Atmel AVRs, and Microchip PICs, etc.
7 segment led displays are great users of current, so an LCD would be my preference.
The AVR Butterfly is a cheap (~$30) development tool that has on-board an ATMega169 microcontroller,
4Mbit dataflash, 32KHz crystal, speaker, 100 segment lcd, light and temperature sensors and a battery, all on one credit card sized board. I think Soanar handle it.
Dontronics has a MSP430F2131 (8K program flash, 256 bytes data and 256 bytes data flash) header board for about $20. Just add a cheap off-the-shelf 16x2 LCD and some buttons. Those should be banging around in any engineer's or technician's box-o-bits. Code examples for the MSP430 series are freely available on the 'net, and it's supported by the Yahoo MSP430 group.
For such a simple application, tools such as the Butterfly or the 'F2131 might be considered an overkill, but when you have all (or nearly all) the hardware on one small cheap board, it makes it difficult to ignore them, especially if there won't be many units in the field.
One thing you didn't mention, is how many pulses per 24 hour period you are expecting.
Pulses, well the way I was originally thinking was to use the pulse to trigger the LED display - so that would be 1 pulse per 24 hours time frame.
Basically I need a timer that will count and displays days that have past. My original post was not all that clear - teached me to avoid posting when not feeling so great.
The display has to be visiable from 10' away which is why I was thinking LED's (not above using an external power supply if have to, I know solar cells are not enough to drive a LED display). Exploring all options right now.
May I ask what application this is for and what you want to spend? How accurate does the 24 hours have to be? We have literally $50 units that have
2.5 inch 7 segments displays running ATMEL Cpus with realtime clocks. They would raw a few microamp in sleep mode. You would have to toggle a switch to turn on the LED display, otherwise you would pulse it and its brightness would be really low (unless you get a giant battery of course).
Perhaps you could just have 1 low duty cycle blinking LED for each day that has elapsed. This would only work if the number of days was less than 20 or so or else the unit would be impractically large.
There's heaps of micros that could do the function and you could power it from 2 Alkaline cells if you kept the power use low.
Information purposes of the number of days past since an certain event. They almost need to be displaying info almost constantly (external power supply may have to be used). It needs to count to probably 999 days.
How big are the units (mostly interested in depth) and can an external source be applied? It will also need to be modifiable (ie: key switch installed for the reset - so as it can only be reset via 'authorized person') :)
You could use mechanical flip over segment type displays, this way power would only be needed for a brief period once a day to change the digits, and when the unit was reset.
Is solar power an option, with some small cells and a rechargable battery (or supercap) to keep it running at night?
Otherwise, Large LCD units are available from selected sources.
Dallas makes a 32KHz temp compensated oscillator module the DS32KHz which gives 4 minutes a year accuracy over a pretty good temperature range. This could be fed into any microcontroller you like to run the clock accurately without a lot of messing about with calibration.