Okay, we are tasked with adding 3031 and 1582. Let's begin!

Step 1: We'll start by adding the digits 1 & 2 in column 1 and get 3.

Step 2: We'll start by adding the digits 3 & 8 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 5 in column 3 and get 6.

Step 4: We'll start by adding the digits 3 & 1 in column 4 and get 4.

So, 3031 + 1582 = 4613.

