To perform the addition of $101110_2 + 110001_2$ in base 2, we proceed with binary addition.

Step-by-step calculation:

   101110
+  110001
-----------

1. Start from the rightmost column (least significant bit):

   • $0 + 1 = 1$ (write 1).

2. Second column:

   • $1 + 0 = 1$ (write 1).

3. Third column:

   • $1 + 0 = 1$ (write 1).

4. Fourth column:

   • $1 + 0 = 1$ (write 1).

5. Fifth column:

   • $0 + 1 = 1$ (write 1).

6. Sixth column:

   • $1 + 1 = 10$ (write 0, carry 1).

7. Finally, we have a carry of 1, which we write on the leftmost side.

Thus, the sum is:

  101110
+ 110001
-----------
  1011111

Final result in base 2:

The sum of $101110_2 + 110001_2$ is $1011111_2$.

Let me know if you'd like further details or clarification! Here are some follow-up questions for you:

1. How would you convert the binary result $1011111_2$ to decimal?
2. Can you explain the concept of carrying in binary addition?
3. What is the result of the binary addition $111 + 1011$?
4. How does binary subtraction differ from binary addition?
5. How do you handle addition in other bases, like base 8 or base 16?

Tip: Always remember that in binary, the sum of $1 + 1$ results in a carry of 1, just like in decimal when adding 9 + 9.