Well there's no such degree like 'computer engineering'. You mean to say computer science.
You couldnt have been more WRONG, there is a 'computer engineering' degree, it's offered at many universities, for example: http://ece.uwaterloo.ca/Undergrad/Q/
Computer Science on the other-hand, deals with programming, algorithmic and computational theory - on a software level.
CPUs deal with integrated circuits, so I recommend either Electric Engineering or Computer Engineering.