How do computers read code?

This is how I understand it. I assume that people understand, how high level languages are compiled to machine code - its pretty much taking high level instructions and unwrapping them to highly verbose machine commands. After that, CPU has a place where numbers(0 and 1) are stored - registers, and a place to accept the commands(instructions). The CPU is hardwired for each instruction to do some specific task to the numbers. Like add, subtract, move to another register and so on. Every time the cpu sees a command, it completes a particular electric circuit. When that circuit is applied to a particular register value, it produces a result, like addition or subtraction.