258A hexadecimal to binary

Here we will show you how to convert the hexadecimal number 258A 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 258A from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 258A by 16⁰, multiply the second to last digit in 258A by 16¹, multiply the third to last digit in 258A by 16², multiply the fourth to last digit in 258A by 16³, and so on, until all the digits are used.

A × 16⁰ = 10
8 × 16¹ = 128
5 × 16² = 1280
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 + 128 + 1280 + 8192 = 9610

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.

9610 ÷ 2 = 4805 with 0 remainder
4805 ÷ 2 = 2402 with 1 remainder
2402 ÷ 2 = 1201 with 0 remainder
1201 ÷ 2 = 600 with 1 remainder
600 ÷ 2 = 300 with 0 remainder
300 ÷ 2 = 150 with 0 remainder
150 ÷ 2 = 75 with 0 remainder
75 ÷ 2 = 37 with 1 remainder
37 ÷ 2 = 18 with 1 remainder
18 ÷ 2 = 9 with 0 remainder
9 ÷ 2 = 4 with 1 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 258A hexadecimal to binary:

258A hexadecimal = 10010110001010 binary

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258B hexadecimal to binary
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