If you have read How Pendulum Clocks Work, you know that all clocks (regardless of technology) have a few required components:

• A source of power to run the clock
  In a pendulum clock, the weights or the springs handle this role.

• An accurate timebase that acts as the clock’s heartbeat
  In a pendulum clock, the pendulum and escapement handle this role.
• A way to gear down the timebase to extract different components of time (hours, minutes, seconds)
  In a pendulum clock, gearsserve this role.
• A way to display the time
  In a pendulum clock, the hands and face serve this role.

A digital clock is no different. It simply handles these functions electronically rather than mechanically. So in a digital clock, there is an electrical power supply (either a battery or 120-volt AC power from the wall). There is an electronic timebase that “ticks” at some known and accurate rate. There is an electronic “gearing mechanism” of some sort — generally a digital clock handles gearing with a component called a “counter.” And there is a display, usually either LEDs (light emitting diodes) or an LCD (liquid crystal display).

For more detail: How Digital Clocks Work