DF15 hexadecimal to binary

Here we will show you how to convert the hexadecimal number DF15 to a binary number. First note that the hexadecimal number system has sixteen different digits (0 1 2 3 4 5 6 7 8 9 A B C D E F) and the binary number system has only two different digits (0 and 1).

The four steps used to convert DF15 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in DF15 by 16⁰, multiply the second to last digit in DF15 by 16¹, multiply the third to last digit in DF15 by 16², multiply the fourth to last digit in DF15 by 16³, and so on, until all the digits are used.

5 × 16⁰ = 5
1 × 16¹ = 16
F × 16² = 3840
D × 16³ = 53248

Remember that the hexadecimal number system has sixteen different digits, so when doing the above calculation, we use the following values if applicable: A=10, B=11, C=12, D=13, E=14, and F=15.

Step 2)
Next, we add up all the products we got from Step 1, like this:

5 + 16 + 3840 + 53248 = 57109

Step 3)
Now we divide the sum from Step 2 by 2. Put the remainder aside. Then divide the whole part by 2 again, and put the remainder aside again. Keep doing this until the whole part is 0.

57109 ÷ 2 = 28554 with 1 remainder
28554 ÷ 2 = 14277 with 0 remainder
14277 ÷ 2 = 7138 with 1 remainder
7138 ÷ 2 = 3569 with 0 remainder
3569 ÷ 2 = 1784 with 1 remainder
1784 ÷ 2 = 892 with 0 remainder
892 ÷ 2 = 446 with 0 remainder
446 ÷ 2 = 223 with 0 remainder
223 ÷ 2 = 111 with 1 remainder
111 ÷ 2 = 55 with 1 remainder
55 ÷ 2 = 27 with 1 remainder
27 ÷ 2 = 13 with 1 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 remainder
3 ÷ 2 = 1 with 1 remainder
1 ÷ 2 = 0 with 1 remainder

Step 4)
In the final step, we take the remainders from Step 3 and put them together in reverse order to get our answer to DF15 hexadecimal to binary:

DF15 hexadecimal = 1101111100010101 binary

Hexadecimal to Binary Converter
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