21F hexadecimal to binary

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

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

F × 16⁰ = 15
1 × 16¹ = 16
2 × 16² = 512

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 + 16 + 512 = 543

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.

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 21F hexadecimal to binary:

21F hexadecimal = 1000011111 binary

Hexadecimal to Binary Converter
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