They require power even in a static state. CMOS circuits draw only leakage current when static. Look at the difference in power requirements between the bipolar 74xx series logic as compared the 74Cxx CMOS logic as an example.
I have been reading a book by Hans Camenzind ( the designer of the 555 Timer) which is called "Designing Analog Chips".
It has been a great reading so far and it is gentle to beginners (which I am). It explains things that are skipped through most electronics courses in college (The most basic things, like for example why the Collector current is Beta times higher than the Base current. What "is" that "Beta", etc)..