Step-by-step Solution:

Let's walk through the correct process:

Conversion of \( (-100)_{10} \) to binary using 2's complement:

1. Convert \( 100_{10} \) to binary: \[ 100_{10} = 1100100_2 \]

2. Pad the binary representation to 8 bits: \[ 100_{10} = 01100100_2 \quad \text{(8 bits)} \]

3. Find the 1's complement of \( 01100100_2 \): \[ 10011011_2 \quad \text{(invert all bits)} \]

4. Find the 2's complement by adding 1 to the 1's complement: \[ 10011011_2 + 1 = 10011100_2 \]

Thus, the 2's complement representation of \( (-100)_{10} \) in an 8-bit system is 10011100. ### Correct Answer: \[ \textbf{D. 10011100} \]