Alright, let's solve this problem step by step. We have 477 and 9532 and we're adding them together.

Step 1: We'll start by adding the digits 7 & 2 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 3 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

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

Step 4: We'll start by adding the digits 0 & 9 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 477 + 9532 = 10009.

