DF40 hexadecimal to binary

Here we will show you how to convert the hexadecimal number DF40 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 DF40 from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in DF40 by 16⁰, multiply the second to last digit in DF40 by 16¹, multiply the third to last digit in DF40 by 16², multiply the fourth to last digit in DF40 by 16³, and so on, until all the digits are used.

0 × 16⁰ = 0
4 × 16¹ = 64
F × 16² = 3840
D × 16³ = 53248

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:

0 + 64 + 3840 + 53248 = 57152

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.

57152 ÷ 2 = 28576 with 0 remainder
28576 ÷ 2 = 14288 with 0 remainder
14288 ÷ 2 = 7144 with 0 remainder
7144 ÷ 2 = 3572 with 0 remainder
3572 ÷ 2 = 1786 with 0 remainder
1786 ÷ 2 = 893 with 0 remainder
893 ÷ 2 = 446 with 1 remainder
446 ÷ 2 = 223 with 0 remainder
223 ÷ 2 = 111 with 1 remainder
111 ÷ 2 = 55 with 1 remainder
55 ÷ 2 = 27 with 1 remainder
27 ÷ 2 = 13 with 1 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 remainder
3 ÷ 2 = 1 with 1 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 DF40 hexadecimal to binary:

DF40 hexadecimal = 1101111101000000 binary

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DF41 hexadecimal to binary
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