To add the binary numbers $1101_2$ and $1001_2$:

1. Align the numbers:

       1101
   +   1001
   

2. Add each column from right to left, carrying over as needed:

   • Rightmost column: $1 + 1 = 10_2$ (write down 0, carry over 1)
   • Next column: $0 + 0 + 1 = 1$
   • Next column: $1 + 0 = 1$
   • Leftmost column: $1 + 1 = 10_2$ (write down 0, carry over 1)

3. The result after adding the carry over:

      10110
   

Thus, $1101_2 + 1001_2 = 10110_2$.

Would you like further details on binary addition, or have any questions?

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Here are some related questions to deepen your understanding:

1. How do you add binary numbers with more than four digits?
2. What is the difference between binary and decimal addition?
3. How do you perform subtraction in binary?
4. Can you explain how binary addition works with negative numbers?
5. What are practical applications of binary arithmetic?

Tip: When adding in binary, remember that $1 + 1 = 10_2$, which is why there's a carry to the next column.