To add the binary numbers $1010_2$ and $1101_2$, we perform column-wise addition, carrying over any $1+1$ sums. Step 1: Align the binary numbers. ` 1010 + 1101 ------ ` Step 2: Add the rightmost column (least significant bit). $0 + 1 = 1$. Write down 1. Carry 0. ` 1010 + 1101 ------ 1 ` Step 3: Add the second column from the right. $1 + 0 + \text{carry (0)} = 1$. Write down 1. Carry 0. ` 1010 + 1101 ------ 11 ` Step 4: Add the third column from the right. $0 + 1 + \text{carry (0)} = 1$. Write down 1. Carry 0. ` 1010 + 1101 ------ 111 ` Step 5: Add the leftmost column (most significant bit). $1 + 1 + \text{carry (0)} = 10_2$. Write down 0. Carry 1 to the next position. ` 1010 + 1101 ------ 0111 ` (with a carry of 1 to the left) Step 6: Bring down the final carry. The carry of 1 from the previous step becomes the new leftmost bit. ` 1010 + 1101 ------ 10111 ` The result of adding the binary numbers $1010_2$ and $1101_2$ is $10111_2$. $$ 1010_2 + 1101_2 = 10111_2 $$ The final answer is $\boxed{10111_2}$.