The component of a personal computer that is often referred to as the "brain" and controls the operation of the computer is the microprocessor.

Explanation:
The microprocessor is a small chip located on the motherboard of a personal computer. It is often considered the "brain" of the computer because it performs all the major processing tasks and controls the overall operation of the computer system. Here is a detailed explanation of why the microprocessor is considered the brain of the computer:

1. Processing Power:
The microprocessor is responsible for executing all instructions and calculations in a computer system. It performs tasks such as arithmetic and logical operations, data manipulation, and control flow. It has the ability to process large amounts of data at incredible speeds, making it the most critical component for the computer's performance.

2. Control Unit:
The microprocessor consists of various components, including the control unit. The control unit coordinates and controls the flow of data and instructions within the computer system. It fetches instructions from the computer's memory, decodes them, and executes them in the appropriate sequence. This control unit ensures that all the components of the computer work together in a synchronized manner.

3. Clock Speed:
The microprocessor operates at a specific clock speed, measured in megahertz (MHz) or gigahertz (GHz). The clock speed determines the number of instructions the microprocessor can execute per second. A higher clock speed means faster processing and better performance.

4. Multiple Cores:
Modern microprocessors often have multiple cores, which are individual processing units within a single chip. Each core can handle separate tasks simultaneously, providing increased processing power and multitasking capabilities. This allows the microprocessor to handle multiple applications and processes at the same time.

5. Compatibility and Compatibility:
The microprocessor is designed to be compatible with various software and hardware components. It follows specific instruction sets and architectures, such as x86 or ARM, which enable it to run different operating systems and software applications. This compatibility makes it a versatile component that can be used in various computer systems.

In conclusion, the microprocessor is considered the "brain" of a personal computer because it performs all the major processing tasks, controls the flow of data and instructions, and determines the overall performance of the computer system. Its ability to handle complex calculations, multitask, and provide compatibility makes it an essential component for the functioning of a computer.

The microprocessor, also known as the CPU, is often referred to as the "brain" of the computer. It controls the operation of the computer and executes commands and instructions.