101110111+1101110

To add the binary numbers \( 101110111 \) and \( 1101110 \), we align them as follows:

      101110111
    +  01101110
    ___________

Now, we add them column by column, starting from the rightmost side:

1. \( 1 + 0 = 1 \)
2. \( 1 + 1 = 10 \) (write down 0 and carry over 1)
3. \( 1 + 1 + 1 (carry) = 11 \) (write down 1 and carry over 1)
4. \( 1 + 1 + 1 (carry) = 11 \) (write down 1 and carry over 1)
5. \( 1 + 0 + 1 (carry) = 10 \) (write down 0 and carry over 1)
6. \( 0 + 1 + 1 (carry) = 10 \) (write down 0 and carry over 1)
7. \( 1 + 1 + 1 (carry) = 11 \) (write down 1 and carry over 1)
8. \( 0 + 0 + 1 (carry) = 1 \)
9. \( 1 + 0 = 1 \)

Now, let's put it all together:

      101110111
    +  01101110
    ___________
   1001101101

So, \( 101110111 + 1101110 = 1001101101_2 \).

In decimal, the original numbers are:

• \( 101110111_2 = _dash\_ (binary) = 379 (decimal) \)
• \( 1101110_2 = 110 (decimal) \)

And indeed, \( 379 + 110 = 489 \), which is \( 1001101101_2 \).

Therefore, the final answer is:

\( 101110111 + 1101110 = 1001101101_2 \).