Okay, we are tasked with adding 683 and 1781. Let's begin!

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

Step 2: We'll start by adding the digits 8 & 8 in column 2 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 6 & 7 in column 3 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 0 & 1 in column 4 and get 2.

So, 683 + 1781 = 2464.

