25A8 hexadecimal to binary

Here we will show you how to convert the hexadecimal number 25A8 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 25A8 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 25A8 by 16⁰, multiply the second to last digit in 25A8 by 16¹, multiply the third to last digit in 25A8 by 16², multiply the fourth to last digit in 25A8 by 16³, and so on, until all the digits are used.

8 × 16⁰ = 8
A × 16¹ = 160
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:

8 + 160 + 1280 + 8192 = 9640

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.

9640 ÷ 2 = 4820 with 0 remainder
4820 ÷ 2 = 2410 with 0 remainder
2410 ÷ 2 = 1205 with 0 remainder
1205 ÷ 2 = 602 with 1 remainder
602 ÷ 2 = 301 with 0 remainder
301 ÷ 2 = 150 with 1 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 25A8 hexadecimal to binary:

25A8 hexadecimal = 10010110101000 binary

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25A9 hexadecimal to binary
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