Reading Two's Complement

To read a two's complement number, check the leftmost bit. If 0, treat it as unsigned binary. If 1, it is negative: flip all bits, add 1, then negate the result.

Example: What is $11111011$ in 8-bit two's complement? Leftmost bit is 1, so it is negative. Flip: $00000100$. Add 1: $00000101$ (which is 5). Negate: $-5$. Result: $11111011 = -5$.

Shortcut: the leftmost 1 in a negative number is worth $-2^{n-1}$, and the rest are positive powers. For $11111011$: $-128 + 64 + 32 + 16 + 8 + 2 + 1 = -5$. With practice, you can read two's complement as fast as unsigned.