First, we convert the binary numbers to decimal:

For $(1001011)_{2}$:
$$ \begin{aligned} (1001011)_{2} &= 1 \cdot 2^6 + 0 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \\ &= 64 + 0 + 0 + 8 + 0 + 2 + 1 \\ &= 75_{10} \end{aligned} $$
For $(1011)_{2}$:
$$ \begin{aligned} (1011)_{2} &= 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \\ &= 8 + 0 + 2 + 1 \\ &= 11_{10} \end{aligned} $$
Now, multiply the decimal values:
$$ 75 \times 11 = 825 $$
Finally, convert the binary product $(1100111001)_{2}$ to decimal to verify:
$$ \begin{aligned} (1100111001)_{2} &= 1 \cdot 2^9 + 1 \cdot 2^8 + 0 \cdot 2^7 + 0 \cdot 2^6 + 1 \cdot 2^5 + 1 \cdot 2^4 + 1 \cdot 2^3 + 0 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0 \\ &= 512 + 256 + 0 + 0 + 32 + 16 + 8 + 0 + 0 + 1 \\ &= 825_{10} \end{aligned} $$
Since both results are $825_{10}$, the binary multiplication is verified as correct.