Why is the "sign bit" included in the calculation of negative numbers?

Question

I'm new to Swift and is trying to learn the concept of "shifting behavior for signed integers". I saw this example from "the swift programming language 2.1".

My question is: Why is the sign bit included in the calculation as well?

I experienced with several number combinations and they all works, but I don't seem to get reasons behind including sign bit in the calculation.

To add -1 to -4, simply by performing a standard binary addition of all eight bits (including the sign bit), and discarding anything that doesn't fit in the eight bits once you are done:

Answer 1

This is not unique to Swift. Nevertheless, historically, computers didn't subtract, they just added. To calculate A-B, do a two's-complement of B and add it to A. The two's-complement (negate all the bits and add 1) means that the highest order bit will be 0 for positive numbers (and zero), or 1 for negative numbers.

Answer 2

This is called 2's compliment math and allows both addition and subtraction to be done with simple operations. This is the way many hardware platforms implement arithmetic. You should look more into 2's compliment arithmetic of you want a deeper understanding.