Explanation:

The correct option is (C) motherboard. The motherboard is the primary circuit board that serves as the central hub for all communications within a computer system. It provides the physical connections and pathways (buses) that allow the CPU, memory, storage devices, expansion cards, and peripheral devices to exchange data and signals. Without the motherboard, the various components of a computer cannot communicate with each other. Option (A) the arithmetic-logic unit (ALU) is a part of the CPU responsible for performing arithmetic and logical operations, not overall system communication. Option (B) a semiconductor is a material with electrical conductivity between a conductor and an insulator, not a system component controlling communication. Option (D) a coprocessor is a specialized processor that assists the main CPU with specific tasks, but it does not control overall system communication.