What are fan-in and fan-out in logic gates?

Fan-in is the number of inputs a logic gate can accept. High fan-in increases gate delay due to series transistors (NMOS in NAND, PMOS in NOR) and internal capacitance. Fan-out is the number of gates a single output can drive. High fan-out increases load capacitance, slowing down the driving gate. Fan-out is limited by the drive strength of the output buffer. Design must balance fan-in (typically 4 or less) and fan-out (inserting buffers when needed) for optimal timing.