Okay, we are tasked with adding 1980 and 5743. Let's begin!

Step 1: We'll start by adding the digits 0 & 3 in column 1 and get 3.

Step 2: We'll start by adding the digits 8 & 4 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 9 & 7 in column 3 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 1 & 5 in column 4 and get 7.

So, 1980 + 5743 = 7723.

