Step-by-step Solution:

To simplify, let us first convert the given binary numbers to their decimal equivalents: \[ (1100)_2 = (1 \times 8) + (1 \times 4) + (0 \times 2) + (0 \times 1) = 12_{10} \] \[ (1011)_2 = (1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1) = 11_{10} \] Now, multiply their decimal values: \[ 12 \times 11 = 132 \] Finally, convert the decimal product back into binary notation: \[ 132 = 128 + 4 = 2^7 + 2^2 \] Placing 1s in the \( 2^7 \) and \( 2^2 \) positions, we get: \[ (10000100)_2 \]