Okay, we are tasked with adding 580 and 453. Let's begin!

Step 1: We'll start by adding the digits 0 & 3 in column 1 and get 3.

Step 2: We'll start by adding the digits 8 & 5 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 4 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 580 + 453 = 1033.

