1111 base 2 + 1010 base 2 my answers are either 20 or 30

You can solve this the same way you solve regular base 10 addition. In base 10, if you add two numbers and the result is greater than 10, you carry a 1 to the next column to the left. So 6+3=9 (no carry), but 6+5=11 (we carried a 1 to the next column).

In base 2, there are only 2 digits to use (0 and 1) and we carry when the result is greater than 2. So in base 2, 1+0=1 (no carry), but 1+1=10 (carry to the next column).

So to do your addition:

In the 1's column, 1+0=1, no carry
In the 2's column, 1+1=0, carry 1 left
In the 4's column, 1+0+1(the carry from before)=0, carry 1 left
and so on.

It's easier than base 10, with only two digits to deal with.

Neither of your guesses are correct.

1111 = ((1*2+1)*2+1)*2+1
1010 = ((1*2+0)*2+1)*2+0

Since the sum of the "low-order" bits (one '1' plus one '0') is an "odd" number, neither "20" ("even" number) nor "30" (another "even" number) could be the correct answer.