The canonical work to read here is "Computer Organization and Design" by Hennessy / Patterson. Basically the first 4-6 bits of the machine code is called the opcode which tells the ALU on the processor which operation to perform (addition, subtraction, multiplication, division), and the remaining bits are the 2 operands to perform the addition on and where to store the result. The actual arthmetic is done by the ALU which is composed bu mux, decoder, fulladder and primitives. If you look at how an ALU (arhithmetic-logic unit) is working, you will know the important part of the processor. A modern processor also has cache memory, pipelining, data forwarding and branch prediction but that is not central for the question you ask. To intrepret machine code, the processor uses the opcode to decide the operation and the rest of the bit sequence is the two registers that are the operands and which register to store the result in. The rest is specific circuits that you can find in the book "Computer Organization and Design"