This is more for my curiosity than anything else as I understand how to find the two's complement of a binary number via the standard approach which is to convert all 0s to 1s and 1s to 0s and then add $1_2$, but this "quick method" truly puzzles me. I see that the author of the book I am going through suggests that this method be skipped but I am wondering whether anyone understands what is going on here because I am truly lost.
This is all the description that is given. I don't understand why the first six bits are left alone while the last eight bits are changed. I would be much obliged if someone could provide some background to this methodology.