FFFF hexadecimal to binary

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

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

F × 16⁰ = 15
F × 16¹ = 240
F × 16² = 3840
F × 16³ = 61440

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:

15 + 240 + 3840 + 61440 = 65535

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.

65535 ÷ 2 = 32767 with 1 remainder
32767 ÷ 2 = 16383 with 1 remainder
16383 ÷ 2 = 8191 with 1 remainder
8191 ÷ 2 = 4095 with 1 remainder
4095 ÷ 2 = 2047 with 1 remainder
2047 ÷ 2 = 1023 with 1 remainder
1023 ÷ 2 = 511 with 1 remainder
511 ÷ 2 = 255 with 1 remainder
255 ÷ 2 = 127 with 1 remainder
127 ÷ 2 = 63 with 1 remainder
63 ÷ 2 = 31 with 1 remainder
31 ÷ 2 = 15 with 1 remainder
15 ÷ 2 = 7 with 1 remainder
7 ÷ 2 = 3 with 1 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 FFFF hexadecimal to binary:

FFFF hexadecimal = 1111111111111111 binary

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