does every desktop computer have the big outside cpu?

Every computer has a central processing unit, yes.

You have to elaborate a bit more with this question, as it sounds like something a five year old might say. I understand English is unlikely your mother-tongue but please try pad the question a little more so we can understand what you are really asking and what you actually want to know further than "Has every computer got a cpu"...
 
I presume you are not technical. What you call the computer actually is the monitor and what you call the big CPU is in fact the PC. The CPU (processor) is installed on the motherboard and it's rather small. A visit to Wikipedia may help.