The CPU doesn't receive the instruction as a mnemonic, but rather as a binary string. It is then up to the CPU architecture, as in the physical composition of the thousands of switches, to decide what to do with the code.
The CPU receives the data, it takes the first byte (8 bits) which represents the instruction and decodes this in order to take appropriate action, next are values which may or may not be needed depending on the instruction, they represent memory addresses. The last order of bits is a specified value. It may be a value to store or a value to process (add, subtract, send to another process.) The timer inside the CPU assures that instructions are processed properly. E.G you don't want an instruction to access the wrong data.
In answer to your question, If you take 7 and put it in the AX register, the CPU will receive a 32bit binary sequence (or 64 or whatever your processor does) and it will process this. The way the switches are logically designed,the CPU will know to take the value 7 and store it in the AX register. The same goes for storing 2 in the BX register. Lastly, the CPU will receive the instruction to add value to AX in the 8-bit word. The next bits tell it to add the value currently in BX and the next bit sequence will tell it to store it in CX.
SHORT ANSWER: Yes, the CPU does the calculation. That, when you break through all of the mess of instruction codes and such, is the basic function of the CPU. To apply take binary input, perform some arithmetic on it and output the result. In diagrams of CPUs, you'll see there are whole sections dedicated to performing specific mathematical tasks.
I hope this helps. Basically, the logic of the switches determines how the CPU will act depending on whether each switch receives a '1' or a '0' at any one time. It's hard to explain and takes a whole text-book to learn, really. I would recommend studying binary arithmetic and boolean logic, then moving onto applying this to logic gates and switches. This should help explain the physical aspect of the CPU.
Are you doing a course in computer engineering? If not I would recommend it. It gets rather complex but it's to do with clocks and switches and a whole lot of boolean arithmetic.
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