DFFE hexadecimal to binary

Here we will show you how to convert the hexadecimal number DFFE 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 DFFE from hexadecimal to binary are explained below.

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

E × 16⁰ = 14
F × 16¹ = 240
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:

14 + 240 + 3840 + 53248 = 57342

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.

57342 ÷ 2 = 28671 with 0 remainder
28671 ÷ 2 = 14335 with 1 remainder
14335 ÷ 2 = 7167 with 1 remainder
7167 ÷ 2 = 3583 with 1 remainder
3583 ÷ 2 = 1791 with 1 remainder
1791 ÷ 2 = 895 with 1 remainder
895 ÷ 2 = 447 with 1 remainder
447 ÷ 2 = 223 with 1 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 DFFE hexadecimal to binary:

DFFE hexadecimal = 1101111111111110 binary

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DFFF hexadecimal to binary
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