How do you negate a number in two's complement?

Flip every bit, then add 1: −x = ~x + 1.

Example: Negate 5 (0101):

Original:    0101  (+5)
Complement:  1010
Add 1:       1011  (-5) ✓

Example: Negate -5 (1011):

Original:    1011  (-5)
Complement:  0100
Add 1:       0101  (+5) ✓

Special case: Negating TMin gives TMin (overflow)

TMin:        1000...0
~TMin:       0111...1
+1:          1000...0  (back to TMin!)

Tip: "Flip and add 1" - the universal two's complement negation formula.

Go deeper:

• Two's complement (Wikipedia) — see the "Working from LSB" and negation sections for why flip-and-add-1 works.