The logical unit of a computer that makes logical decisions is the Central Processing Unit (CPU) or the processor. The CPU is a primary component of the computer that performs most of the processing inside the computer. It's an electronic circuit that carries out instructions of a computer program by performing basic arithmetical, logical, and input/output (I/O) operations.
If we take the process step-by-step:
1. Firstly, the CPU fetches the instruction from the computer's memory.
2. Then, the CPU decodes the instruction to determine what task needs to be performed.
3. After that, if the operation involves data, the CPU will fetch those data from the memory.
4. Then, it will perform the operation on the appropriate data.
5. Finally, the result is stored back in the memory.
So, the CPU or the processor of any computer is responsible for making logical decisions by running all basic and essential operations, which makes it the heart of a computer system.