In a computer, all of the main logic operations and mathematical calculations are performed in which component?

Introduction / Context:
This question covers one of the most fundamental ideas in computer architecture. The part of the computer responsible for performing arithmetic and logic operations is central to how any program runs. Understanding that this function belongs to the central processing unit is essential and is frequently tested in basic computer knowledge exams.

Given Data / Assumptions:

• The question asks where logic and mathematical calculations happen.
• Options include system board, central control unit, central processing unit, motherboard and power supply unit.
• We assume a standard computer where the CPU is mounted on the motherboard.

Concept / Approach:
The central processing unit CPU is often called the brain of the computer. It contains components such as the arithmetic logic unit and control unit, which together execute instructions, perform calculations and make decisions. The motherboard or system board is the main circuit board that holds the CPU and connects other components but does not itself perform calculations. A power supply unit delivers electrical power. The term central control unit is not a standard component name at this level.

Step-by-Step Solution:
Step 1: Recall that programs are executed as sequences of instructions that must be processed by some core component. Step 2: The component that fetches instructions, decodes them and performs arithmetic or logic operations is the central processing unit. Step 3: Inside the CPU, the arithmetic logic unit performs mathematical calculations and logical comparisons. Step 4: Therefore, when the question mentions all logic and mathematical calculations, it is referring to work done by the CPU. Step 5: Option c, central processing unit, is precisely the name of this component. Step 6: The system board or motherboard is the physical board that holds the CPU, memory and other chips. It provides connections but does not itself carry out computations. Step 7: Power supply units convert electrical power into the correct voltages needed by the system but do not process data. Step 8: Central control unit is not a widely used formal term; the control unit is part of the CPU, not a separate box.

Verification / Alternative check:
In any diagram of computer organisation, data flows from memory and input devices into the CPU, where the arithmetic logic unit and control unit reside. The CPU then sends results to memory or output devices. Study material consistently labels the CPU as the place where calculations occur. The motherboard is drawn as a board on which the CPU is mounted, reinforcing that the board is a host rather than the active processor.

Why Other Options Are Wrong:
System board and motherboard are alternative names for the main circuit board inside a computer case. Although they host the CPU, they do not themselves form the calculating unit. Power supply units simply provide electricity. The phrase central control unit is vague and not a standard label; even if one thinks of a control unit, it is part of the CPU and does not negate the fact that CPU is the correct high level answer.

Common Pitfalls:
Some students mistakenly think the motherboard is the brain of the computer because it connects everything. While the motherboard is very important, the actual processing of instructions happens inside the CPU chip. To avoid this confusion, remember that the CPU is the active worker that does calculations and decisions, while the motherboard is more like the office building that hosts all the workers.

Final Answer:
All main logic and mathematical operations are performed in the central processing unit or CPU.