Alright, let's solve this problem step by step. We have 2603 and 7583 and we're adding them together.

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

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 6 & 5 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 2 & 7 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 2603 + 7583 = 10186.

