Alright, let's solve this problem step by step. We have 9100 and 5581 and we're adding them together.

Step 1: We'll start by adding the digits 0 & 1 in column 1 and get 1.

Step 2: We'll start by adding the digits 0 & 8 in column 2 and get 8.

Step 3: We'll start by adding the digits 1 & 5 in column 3 and get 6.

Step 4: We'll start by adding the digits 9 & 5 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 9100 + 5581 = 14681.

