21FE hexadecimal to binary

Here we will show you how to convert the hexadecimal number 21FE 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 21FE from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 21FE by 16⁰, multiply the second to last digit in 21FE by 16¹, multiply the third to last digit in 21FE by 16², multiply the fourth to last digit in 21FE by 16³, and so on, until all the digits are used.

E × 16⁰ = 14
F × 16¹ = 240
1 × 16² = 256
2 × 16³ = 8192

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 + 256 + 8192 = 8702

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.

8702 ÷ 2 = 4351 with 0 remainder
4351 ÷ 2 = 2175 with 1 remainder
2175 ÷ 2 = 1087 with 1 remainder
1087 ÷ 2 = 543 with 1 remainder
543 ÷ 2 = 271 with 1 remainder
271 ÷ 2 = 135 with 1 remainder
135 ÷ 2 = 67 with 1 remainder
67 ÷ 2 = 33 with 1 remainder
33 ÷ 2 = 16 with 1 remainder
16 ÷ 2 = 8 with 0 remainder
8 ÷ 2 = 4 with 0 remainder
4 ÷ 2 = 2 with 0 remainder
2 ÷ 2 = 1 with 0 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 21FE hexadecimal to binary:

21FE hexadecimal = 10000111111110 binary

Hexadecimal to Binary Converter
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21FF hexadecimal to binary
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