To tell time a Reed switch is activated with a magnet (black cylinder in which strong magnets are placed) and first the number of hours are counted by the up/down pulses of the "bob" that lights up each time current flows through the electromagnet residing below it and inside the large cylindrical case. After a brief pause the number of 5 minute intervals after the hour are counted- the amplitude of the pulse is smaller for minutes.

Pulsar's mechanism of action is explained by Faraday's and Lenz's Laws*. A current is generated in a non-magnetic metal, e.g., copper cylinder, when it's exposed to a changing magnetic field created by an AC current powered electromagnet that is placed below it. This current creates a magnetic field in the copper cylinder that is opposite to the one in the electromagnet. As a result the copper cylinder moves upward, along the steel shaft, until it's magnetic field is balanced by the downward force of gravity and the upward force of the electromagnet. For Pulsar this balance point is approximately 1" above the top of the clock case.
 

*Faraday’s Law

Any change in the magnetic environment of a conductor will cause a voltage (emf) to be "induced" in the conductor. No matter how the change is produced, a voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the conductor, moving the conductor into or out of the magnetic field, rotating the conductor relative to the magnet, etc.

*Lenz’s Law

When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field always acts to keep the magnetic flux constant. If the magnetic field is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to try to keep it constant.