FA16 hexadecimal to binary

Here we will show you how to convert the hexadecimal number FA16 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 FA16 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in FA16 by 16⁰, multiply the second to last digit in FA16 by 16¹, multiply the third to last digit in FA16 by 16², multiply the fourth to last digit in FA16 by 16³, and so on, until all the digits are used.

6 × 16⁰ = 6
1 × 16¹ = 16
A × 16² = 2560
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:

6 + 16 + 2560 + 61440 = 64022

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.

64022 ÷ 2 = 32011 with 0 remainder
32011 ÷ 2 = 16005 with 1 remainder
16005 ÷ 2 = 8002 with 1 remainder
8002 ÷ 2 = 4001 with 0 remainder
4001 ÷ 2 = 2000 with 1 remainder
2000 ÷ 2 = 1000 with 0 remainder
1000 ÷ 2 = 500 with 0 remainder
500 ÷ 2 = 250 with 0 remainder
250 ÷ 2 = 125 with 0 remainder
125 ÷ 2 = 62 with 1 remainder
62 ÷ 2 = 31 with 0 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 FA16 hexadecimal to binary:

FA16 hexadecimal = 1111101000010110 binary

Hexadecimal to Binary Converter
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FA17 hexadecimal to binary
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