A21E hexadecimal to binary

Here we will show you how to convert the hexadecimal number A21E 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 A21E from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A21E by 16⁰, multiply the second to last digit in A21E by 16¹, multiply the third to last digit in A21E by 16², multiply the fourth to last digit in A21E by 16³, and so on, until all the digits are used.

E × 16⁰ = 14
1 × 16¹ = 16
2 × 16² = 512
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:

14 + 16 + 512 + 40960 = 41502

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.

41502 ÷ 2 = 20751 with 0 remainder
20751 ÷ 2 = 10375 with 1 remainder
10375 ÷ 2 = 5187 with 1 remainder
5187 ÷ 2 = 2593 with 1 remainder
2593 ÷ 2 = 1296 with 1 remainder
1296 ÷ 2 = 648 with 0 remainder
648 ÷ 2 = 324 with 0 remainder
324 ÷ 2 = 162 with 0 remainder
162 ÷ 2 = 81 with 0 remainder
81 ÷ 2 = 40 with 1 remainder
40 ÷ 2 = 20 with 0 remainder
20 ÷ 2 = 10 with 0 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 A21E hexadecimal to binary:

A21E hexadecimal = 1010001000011110 binary

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A21F hexadecimal to binary
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