Explanation:

All logic and mathematical calculations within a computer are performed by the Central Processing Unit (CPU). The CPU contains the Arithmetic Logic Unit (ALU), which is specifically designed for these operations. The system board (a) and mother board (d) are the main circuit boards that house the CPU and other components, but they don't perform the calculations themselves. The central control unit (b) is a part of the CPU, responsible for controlling operations, but the calculations are done by the ALU within the CPU. Memory (e) stores data and instructions but does not perform calculations. Therefore, the Central Processing Unit (CPU) is the correct answer.