Binary Arithmetic and Two's Complement

Two's complement: to negate a number, invert all bits and add 1.

 5  = 0000 0101
−5  = 1111 1011

An $n$-bit signed integer ranges from $-2^{n-1}$ to $2^{n-1} - 1$ (8-bit: −128 to 127). Addition works the same for signed and unsigned numbers — that's why every CPU uses two's complement.

Overflow happens when the result doesn't fit: in 8-bit signed arithmetic, 100 + 100 = −56.