7FED hexadecimal to binary

Here we will show you how to convert the hexadecimal number 7FED 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 7FED from hexadecimal to binary are explained below.

Step 1)
Multiply the last digit in 7FED by 16⁰, multiply the second to last digit in 7FED by 16¹, multiply the third to last digit in 7FED by 16², multiply the fourth to last digit in 7FED by 16³, and so on, until all the digits are used.

D × 16⁰ = 13
E × 16¹ = 224
F × 16² = 3840
7 × 16³ = 28672

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 + 224 + 3840 + 28672 = 32749

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.

32749 ÷ 2 = 16374 with 1 remainder
16374 ÷ 2 = 8187 with 0 remainder
8187 ÷ 2 = 4093 with 1 remainder
4093 ÷ 2 = 2046 with 1 remainder
2046 ÷ 2 = 1023 with 0 remainder
1023 ÷ 2 = 511 with 1 remainder
511 ÷ 2 = 255 with 1 remainder
255 ÷ 2 = 127 with 1 remainder
127 ÷ 2 = 63 with 1 remainder
63 ÷ 2 = 31 with 1 remainder
31 ÷ 2 = 15 with 1 remainder
15 ÷ 2 = 7 with 1 remainder
7 ÷ 2 = 3 with 1 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 7FED hexadecimal to binary:

7FED hexadecimal = 111111111101101 binary

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7FEE hexadecimal to binary
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