One's Complement Method

Deciding on whether you need to add or subtract numbers is nasty, cumbersome, and error-prone (if you do it by hand.) Hence, a method called one's complement (or $\boldsymbol 1$'s complement) was devised as works as follows:

• If your number is positive, its representation is the same as with the sign & magnitude method.
• Otherwise, if your number is negative, do the following:
  1. Find the sign & magnitude representation of its absolute value, and then
  2. Flip all the bits: change $0$s to $1$s, and $1$s to $0$s.

The action of flipping the bits is called 'applying $1$'s complement' because $1$'s complement is $0$ (and vice versa.)

Example: The absolute value of $-5_{10}$ is $5$, so its sign & magnitude ("normal") representation in an 8-bit format is $00000101_2$. The $1$'s complement format simply asks to flip the bits: $11111010_2$. That's it!