I've run into a bit of an issue during my multiplication of these two binary values: $11001000\ (0.11001000 \times 2^2)$ and $10011010\ (0.10011010 \times 2^0)$. The answer I get when I did the calculations is $111110000101$, which I assumed would be $0.111110000101$. However, on the answer sheet, the answer is listed as $0.0111110000101$. Is there a reason why there is an added zero to the left?
I've attached a photo of the actual problem from my book here, if that helps.
Note that $$ 0.11001000 \times 2^2 = (11001000 \times 2^{-8}) \times 2^2 = 11001000 \times 2^{-6} $$ and $$ 0.10011010 \times 2^0 = (10011010 \times 2^{-8}) \times 2^0 = 10011010 \times 2^{-8}. $$
Therefore, $$ (0.11001000 \times 2^2) \times (0.10011010 \times 2^0) = (11001000 \times 2^{-6}) \times (10011010 \times 2^{-8}) \\ = (11001000 \times 10011010) \times (2^{-6} \times 2^{-8}) = 111110000101 \times 2^{-14} \\ = 0.00111110000101 = 0.111110000101 \times 2^{-2}. $$