825C hexadecimal to binary

Here we will show you how to convert the hexadecimal number 825C 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 825C from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 825C by 16⁰, multiply the second to last digit in 825C by 16¹, multiply the third to last digit in 825C by 16², multiply the fourth to last digit in 825C by 16³, and so on, until all the digits are used.

C × 16⁰ = 12
5 × 16¹ = 80
2 × 16² = 512
8 × 16³ = 32768

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:

12 + 80 + 512 + 32768 = 33372

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.

33372 ÷ 2 = 16686 with 0 remainder
16686 ÷ 2 = 8343 with 0 remainder
8343 ÷ 2 = 4171 with 1 remainder
4171 ÷ 2 = 2085 with 1 remainder
2085 ÷ 2 = 1042 with 1 remainder
1042 ÷ 2 = 521 with 0 remainder
521 ÷ 2 = 260 with 1 remainder
260 ÷ 2 = 130 with 0 remainder
130 ÷ 2 = 65 with 0 remainder
65 ÷ 2 = 32 with 1 remainder
32 ÷ 2 = 16 with 0 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 825C hexadecimal to binary:

825C hexadecimal = 1000001001011100 binary

Hexadecimal to Binary Converter
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