Okay, we are tasked with adding 1034 and 3775. Let's begin!

Step 1: We'll start by adding the digits 4 & 5 in column 1 and get 9.

Step 2: We'll start by adding the digits 3 & 7 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 0 & 7 in column 3 and get 8.

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

So, 1034 + 3775 = 4809.

