A21B hexadecimal to binary

Here we will show you how to convert the hexadecimal number A21B 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 A21B from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in A21B by 16⁰, multiply the second to last digit in A21B by 16¹, multiply the third to last digit in A21B by 16², multiply the fourth to last digit in A21B by 16³, and so on, until all the digits are used.

B × 16⁰ = 11
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:

11 + 16 + 512 + 40960 = 41499

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.

41499 ÷ 2 = 20749 with 1 remainder
20749 ÷ 2 = 10374 with 1 remainder
10374 ÷ 2 = 5187 with 0 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 A21B hexadecimal to binary:

A21B hexadecimal = 1010001000011011 binary

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