2203 ÷ 2 = 1101 R1
Alright, let's work through the division of 2203 by 2 step by step.

Step 1:
2 goes into 2 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 2 from 2 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 2

Step 2:
2 goes into 2 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 2 from 2 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 2

Step 3:
2 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 110
Subtract 0 from 0 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 2

Step 4:
2 goes into 3 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1101
Subtract 2 from 3 to get 1.

The final result is 1101 with a remainder of 1.