213A hexadecimal to binary

Here we will show you how to convert the hexadecimal number 213A 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 213A from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 213A by 16⁰, multiply the second to last digit in 213A by 16¹, multiply the third to last digit in 213A by 16², multiply the fourth to last digit in 213A by 16³, and so on, until all the digits are used.

A × 16⁰ = 10
3 × 16¹ = 48
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:

10 + 48 + 256 + 8192 = 8506

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.

8506 ÷ 2 = 4253 with 0 remainder
4253 ÷ 2 = 2126 with 1 remainder
2126 ÷ 2 = 1063 with 0 remainder
1063 ÷ 2 = 531 with 1 remainder
531 ÷ 2 = 265 with 1 remainder
265 ÷ 2 = 132 with 1 remainder
132 ÷ 2 = 66 with 0 remainder
66 ÷ 2 = 33 with 0 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 213A hexadecimal to binary:

213A hexadecimal = 10000100111010 binary

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213B hexadecimal to binary
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