What are two advantages of using binary numbers rather than decimal numbers in a computer system?

Your question is actually flawed...binary system is not used in digital systems... Rather, systems using binary numbers only are called digital systems...

It is common knowledge that, digital electronics employs just 2 states (or rather numbers, as mathematicians put it...) the two numbers being '0' and '1'.

Obviously, it is easier to design electronic systems dealing with just 2 states...It's majorly this ease, that led to such exponential development in the field of digital electronics. It iOS also cheaper to make or produce such systems...