Okay, we are tasked with adding 4100 and 5319. Let's begin!

Step 1: We'll start by adding the digits 0 & 9 in column 1 and get 9.

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

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

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

So, 4100 + 5319 = 9419.

