FFAE hexadecimal to binary

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

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

E × 16⁰ = 14
A × 16¹ = 160
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:

14 + 160 + 3840 + 61440 = 65454

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.

65454 ÷ 2 = 32727 with 0 remainder
32727 ÷ 2 = 16363 with 1 remainder
16363 ÷ 2 = 8181 with 1 remainder
8181 ÷ 2 = 4090 with 1 remainder
4090 ÷ 2 = 2045 with 0 remainder
2045 ÷ 2 = 1022 with 1 remainder
1022 ÷ 2 = 511 with 0 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 FFAE hexadecimal to binary:

FFAE hexadecimal = 1111111110101110 binary

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FFAF hexadecimal to binary
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