See How Computers Add Numbers In One Lesson
Take a look inside your computer to see how transistors work together in a microprocessor to add numbers using logic gates.
Get the book CODE that inspired the video http://amzn.to/pR9MwK
This is a great book by Charles Petzold that really breaks down a computer conceptually so that non-technical readers can understand how it works.
EDIT: At 00:12, the chip that is circled is not actually the CPU on this motherboard. This is an older motherboard where the CPU was first inserted into a small board and that board was then inserted into a slot on the motherboard. The chip that is circled is called the "northbridge" and helps the CPU communicate with memory. The northbridge also uses transistors and logic gates just like the CPU.