807D hexadecimal to binary

Here we will show you how to convert the hexadecimal number 807D 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 807D from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 807D by 16⁰, multiply the second to last digit in 807D by 16¹, multiply the third to last digit in 807D by 16², multiply the fourth to last digit in 807D by 16³, and so on, until all the digits are used.

D × 16⁰ = 13
7 × 16¹ = 112
0 × 16² = 0
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:

13 + 112 + 0 + 32768 = 32893

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.

32893 ÷ 2 = 16446 with 1 remainder
16446 ÷ 2 = 8223 with 0 remainder
8223 ÷ 2 = 4111 with 1 remainder
4111 ÷ 2 = 2055 with 1 remainder
2055 ÷ 2 = 1027 with 1 remainder
1027 ÷ 2 = 513 with 1 remainder
513 ÷ 2 = 256 with 1 remainder
256 ÷ 2 = 128 with 0 remainder
128 ÷ 2 = 64 with 0 remainder
64 ÷ 2 = 32 with 0 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 807D hexadecimal to binary:

807D hexadecimal = 1000000001111101 binary

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807E hexadecimal to binary
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