AF21 hexadecimal to binary

Here we will show you how to convert the hexadecimal number AF21 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 AF21 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in AF21 by 16⁰, multiply the second to last digit in AF21 by 16¹, multiply the third to last digit in AF21 by 16², multiply the fourth to last digit in AF21 by 16³, and so on, until all the digits are used.

1 × 16⁰ = 1
2 × 16¹ = 32
F × 16² = 3840
A × 16³ = 40960

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:

1 + 32 + 3840 + 40960 = 44833

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.

44833 ÷ 2 = 22416 with 1 remainder
22416 ÷ 2 = 11208 with 0 remainder
11208 ÷ 2 = 5604 with 0 remainder
5604 ÷ 2 = 2802 with 0 remainder
2802 ÷ 2 = 1401 with 0 remainder
1401 ÷ 2 = 700 with 1 remainder
700 ÷ 2 = 350 with 0 remainder
350 ÷ 2 = 175 with 0 remainder
175 ÷ 2 = 87 with 1 remainder
87 ÷ 2 = 43 with 1 remainder
43 ÷ 2 = 21 with 1 remainder
21 ÷ 2 = 10 with 1 remainder
10 ÷ 2 = 5 with 0 remainder
5 ÷ 2 = 2 with 1 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 AF21 hexadecimal to binary:

AF21 hexadecimal = 1010111100100001 binary

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AF22 hexadecimal to binary
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