Step-by-step Solution:

\[ \textbf{For an } n\text{-bit signed representation:} \] \[ \begin{aligned} \text{1's complement range: } & \; -\big(2^{n-1}-1\big) \;\leq\; N \;\leq\; 2^{\,n-1}-1 \\[6pt] \text{2's complement range: } & \; -2^{\,n-1} \;\leq\; N \;\leq\; 2^{\,n-1}-1 \end{aligned} \] \[ \text{For } n = 9 \; \Big(2^{8} = 256\Big): \] \[ \begin{aligned} \text{(i) Smallest in 1's complement } &= -\big(2^{8}-1\big) = -255 \\[6pt] \text{(ii) Smallest in 2's complement } &= -2^{8} = -256 \end{aligned} \] \[ \boxed{\text{Smallest (1's complement) } = -255, \quad \text{Smallest (2's complement) } = -256} \]