Fan-in and Fan-out are the characteristics of digital ICs. Digital ICs are complete functioning logic circuits. Typically, a digital IC requires only a power supply, input and output.

Fan-in:

It is defined as the maximum number of inputs that a logic gate can accept. If the number of inputs exceeds, the output will be undefined or incorrect. It is specified by manufaturer and is provided in the data sheet.

Fan-out:

It is defined as the maximum number of inputs that can be connected to the output of a gate without exceeding its worst case loading specifiation.

The fan-out depends not only on the characteristics of the output but also on the inputs it is driving.