How do computers read code?

Found this pretty useful video, been looking to get into this recently. To understand compilers etc.
Never actually found a source that describes compiling this well.
So if anyone is interested, here you go:

Got another one for you. This is a super cool video that show how digital logic gates work...but the guy has built them using string and pulley (no electricity). Really show you what the gate is 'doing'

https://vimeo.com/93042377

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.