The concept is using 32.768kHz crystal as a clock for the PIC. Therefor, the internal instruction clock is 32768/4 = 8192 Hz. By using the 16 bit Timer1 to count the instruction clock cycles, the interrupt will occur every 8 second. This period can be reduced by setting initial value of the Timer1 (TMR1H:TMR1L). I have to make Timer1 to count up to 8192 for generating overflow interrupt every 1 second. To make Timer1 count up to 8192, the initial value of TMR1 must be 65536-8192 = 57344 or 0xE000. This means TMR1H = 0xE0 and TMR1L = 0x00. In this case, I need to set only the TMR1H=0xE0 and let TMR1L runs continuously. By changing the initial value of Timer1, I can generate almost any frequencies.
An application for this project is a precise 1Hz blinking LED signal :) ha ha. I know that it's not useful but I think it's fun to look at (am I crazy?). Another application is a precise 1Hz time base for a clock.
The source code is written in MikroC.
The schematic is as the following image.