Question

In class we discussed decimal to binary conversion. What is the result of the following conversion? (You can't use a calculator)

17 (decimal) = _______ (binary)

Don't leave spaces between digits in your answer.

Answer 1

To convert the decimal number 17 to binary, you can use the method of dividing the number by 2 and recording the remainders.

1. Divide 17 by 2:
- 17 ÷ 2 = 8 with a remainder of 1

2. Divide 8 by 2:
- 8 ÷ 2 = 4 with a remainder of 0

3. Divide 4 by 2:
- 4 ÷ 2 = 2 with a remainder of 0

4. Divide 2 by 2:
- 2 ÷ 2 = 1 with a remainder of 0

5. Divide 1 by 2:
- 1 ÷ 2 = 0 with a remainder of 1

Now, collect the remainders from bottom to top:
1 (from 1)
0 (from 2)
0 (from 4)
0 (from 8)
1 (from 17)

Reading from bottom to top gives us: 10001.

Therefore, 17 in decimal is equal to 10001 in binary.

So, the final answer is:
10001