Okay, we are tasked with adding 477 and 4114. Let's begin!

Step 1: We'll start by adding the digits 7 & 4 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

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

Step 3: We'll start by adding the digits 4 & 1 in column 3 and get 5.

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

So, 477 + 4114 = 4591.

