Consider the number 1110. The steps below show how to convert this number to binary using repeated division. The 'R' stands for the remainder of the division.



  1. First, we divide 11 by 2 to find the least significant digit (the rightmost digit). Since 1 is our remainder, the least significant digit in our answer is 1.
11 / 2 = 5 R 1
Answer:
? ? ? 1
  1. Next, we take the result of the previous division (5) and divide by 2 again. Since 5 divided by 2 leaves a remainder of 1, the next digit of our answer is 1.
5 / 2 = 2 R 1
Answer:
? ? 1 1
  1. Again we take the result of the previous division (2) and divide by 2. This time our division does not have a remainder, so we write a 0 as the next digit of our answer.
2 / 2 = 1 R 0
Answer:
? 0 1 1
  1. One more division by 2 gives us the most significant digit (the leftmost digit) of our answer. Since 2 will not divide 1, our result is 0 with a remainder of 1. We know we are done when we get 0 as the result of our division.
1 / 2 = 0 R 1
Answer:
1 0 1 1


A good way to organize this conversion is to list the divisions in table form as below.

 11 / 2 = 5  R of 1  (rightmost digit)
  5 / 2 = 2  R of 1
  2 / 2 = 1  R of 0
  1 / 2 = 0  R of 1  (leftmost digit)

Reading from bottom to top, the final answer is 10112. Remember that the first division gives us the least significant digit of our answer, and the final division gives us the most significant digit of our answer. Also, the result of the final division is always 0.

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