In order to expand the display to displaying DDD MM HH, you need five more I/O lines for the DDD and SS. The PIC16F84A microntroller shown in the linked circuit has only 13 I/O lines and there are all used. (If you don't need the buzzer and relay outputs then potentially you have two spare outputs, but as I mentioned above, you need five.)
So If you want to stay with the PIC16F series of microcontrollers in your linked circuit, I would expand it to meet your needs using a PIC16F883 which has 24 I/O pins. (They make PIC16F microcontrollers with 18 and 20 I/O pins, but only in SMD packages, and I assume you want through-hole). Just add five more outputs going to additional transistors like T1-T4 driving the five new seven segment displays, and the a-g inputs of the displays to the parallel bus coming out of resistor pack R5-R11.
For a crystal, you need to choose one that has a tight tolerance as possible to keep the drift to a minimum. Timer1 of the PIC16F883 can run off of a 32KHz 30 ppm watch crystal.
Software wise, set up Timer1 to interrupt once a second. Use the Set and Select buttons as in the previous application to set up the initial DDD:HH:MM:SS values. On each interrupt, update the display -- decrement seconds, when they roll over from 00 to 59, decrement minutes etc.
TTL
"? The PIC is a microcontroller, whereas TTL i.e. Transistor-Transistor-Logic, is a set of logic signaling standards used by various electronic components, including some microcontrollers. On the question itself, please edit the question to describe, with relevant links, your findings so far, to enable other members to understand how far you are along the path to your goal, and what level of answer would help you best. \$\endgroup\$