How Difficult is it to Add 1? A Pedagogical Example of How Theory of Computing May be Useful

We show that while adding two generic b-bit integers requires = b bit operations, adding 1 to an integer requires, on average, only 2 bit operations. This fact explains why the operation of adding 1 is often separately hardware supported, and why this operation is often separately described in high-level programming languages like C++. This result shows that theoretical analysis can help in deciding which operations must be hardware supported, and thus, hopefully, will help in designing faster computers.