Let's solve this addition problem. We have 1001 and 4677, and we need to add them together.

Step 1: We'll start by adding the digits 1 & 7 in column 1 and get 8.

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

Step 3: We'll start by adding the digits 0 & 6 in column 3 and get 6.

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

So, 1001 + 4677 = 5678.

