The question asks for the result of adding the binary numbers $1010_2$ and $1101_2$. Step 1: Perform binary addition column by column, starting from the rightmost digit. $$ \begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline \end{array} $$ Step 2: Add the rightmost column ($0 + 1$). $0 + 1 = 1$. $$ \begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline & & & & 1 \\ \end{array} $$ Step 3: Add the second column from the right ($1 + 0$). $1 + 0 = 1$. $$ \begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline & & & 1 & 1 \\ \end{array} $$ Step 4: Add the third column from the right ($0 + 1$). $0 + 1 = 1$. $$ \begin{array}{c c c c c} & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline & & 1 & 1 & 1 \\ \end{array} $$ Step 5: Add the leftmost column ($1 + 1$). $1 + 1 = 10_2$. Write down $0$ and carry over $1$ to the next position. $$ \begin{array}{c c c c c} \text{carry} & 1 & & & \\ & 1 & 0 & 1 & 0_2 \\ + & 1 & 1 & 0 & 1_2 \\ \hline 1 & 0 & 1 & 1 & 1_2 \\ \end{array} $$ The sum is $10111_2$. Comparing this result with the given options: A. $10111_2$ B. $10011_2$ C. $11111_2$ D. $11000_2$ The calculated sum matches option A. The final answer is $\boxed{\text{A}}$.